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  • Quantum Matter
    12:00 am-1:30 pm
    12/01/2024-03/19/2021
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-9-2018 Math Physics Seminar

    12:00 am
    12/01/2024
  • Program
    All day
    12/01/2024-03/29/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Arithmetic Quantum Field Theory Program

    To receive email updates and program announcements, visit this link to sign up for the CMSA Arithmetic Quantum Field Theory Program mailing list.

    Dates: Feb. 5–Mar. 29, 2024

    Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138

    Directions to CMSA

    Organizers:

    This program will feature a weekly seminar series, workshops, and a conference.

    The object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions.

    On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions.

    The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions. Conversely, we will explore potential geometric and physical consequences of arithmetic ideas, for example, the Langlands correspondence theory of L-functions for 3-manifolds.


    Schedule

    The first week of the program will feature several lecture series aimed at a broad local community of mathematicians and physicists, aiming to introduce the main ideas underlying our program and help establish a common reference point.

    The program will host a weekly seminar series on Fridays.

    The speakers will be selected with the aim of covering a wide panorama of the subjects over the course of the program.

    The program will conclude with a week-long Conference on Arithmetic Quantum Field Theory March 25–29, 2024.


    AQFT Youtube Playlist

    Lecture series

    All lectures take place in Room G10, Harvard CMSA, 20 Garden Street Cambridge.

    Week 1: Feb. 5–9, 2024

    Abstract: In this lecture series we will introduce some of the themes underlying the CMSA program on Arithmetic Quantum Field Theory taking place this winter and the upcoming conference March 25-29, 2024.

    Some of the themes we plan to discuss include:

    Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.

    The setup of arithmetic topology as a bridge between the background of QFT to that of arithmetic (both “global” and “local”), including the “middle realm” of positive characteristic function fields.

    Questions and structures in arithmetic that have been / might be amenable to inspiration from QFT, in particular the theory of L-functions and the Langlands program.

    Schedule

     

    Monday, Feb. 5, 2024  
    11:00 am – 12:00 pm Minhyong KimArithmetic topology and field theory (Slides part 1 pdf)
    1:30 – 2:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
    2:30 – 3:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    Wednesday, Feb. 7, 2024  
    11:00 am – 12:00 pmMinhyong KimArithmetic topology and field theory (Slides part 2 pdf)
    2:30 – 3:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
    Thursday, Feb.8, 2024  
    2:30 – 3:30 pmMinhyong KimArithmetic topology and field theory (Slides part 3 pdf)
    4:00 – 5:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    Friday, Feb. 9, 2024  
    1:00 – 2:00 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
    2:00 – 3:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    3:30 – 4:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    Monday, Feb. 26, 2024
    1:00 – 2:00 pmOmer Offen (Brandeis)Period integrals of automorphic forms and the residue method
    Tuesday, Feb. 27, 2024
    2:00 – 3:00 pmWei Zhang (MIT)Shtuka special cycles and their generating series
    Friday, March 1, 2024
    11:00 am – 12:00 pmChen Wan (Rutgers Newark)Some examples of the relative Langlands duality
    2:00 – 3:00 pmPeng Shan (Tsinghua)Skein algebras and quantized Coulomb branches
    Thursday, March 7, 2024
    1:30 – 2:30 pmAn Huang (Brandeis)Tate’s thesis and p-adic strings
    3:00 – 4:00 pmJohn Francis (Northwestern)Integrating braided categories over 3-manifolds
    Friday, March 8, 2024
    1:00 – 2:00 pmDihua Jiang (U Minnesota)Shalika Periods: Functoriality and Arithmetic
    Friday, March 15, 2024
    11:45 – 1:00 pmBaiying Liu (Purdue)Recent progress on certain problems related to local Arthur packets of classical groups
    2:15 – 3:30 pmTasho Kaletha (Michigan)Covers of reductive groups and functoriality
    Monday, March 18, 2024
    1:00 – 3:00 pmXinwen Zhu (Stanford)The tame categorical local Langlands correspondence (Slides)
    4:30 – 5:30 pmNatalie Paquette (U  Washington)Koszul duality & twisted holography for asymptotically flat spacetimes (CMSA)
    Wednesday, March 20, 2024
    11:00 – 12:15 pmStephen D. Miller (Rutgers)What 4-graviton scattering amplitudes had to say about the unitary dual
    Friday, March 22, 2024
    1:45 – 3:00 pmJayce Getz (Duke)The Poisson summation conjecture and the fiber bundle method
    3:30 – 4:30 pmTBATBA

     


    Program Visitors

    • Mina Aganagic, University of California, Berkeley
    • Anne-Marie Aubert, Institut de Mathématiques de Jussieu-Paris Rive Gauche, March 15-29
    • Clark Barwick, University of Edinburgh, February 19-March 15
    • Alexander Braverman, Perimeter Institute
    • Alejandra Castro, Cambridge University, March 25-29
    • YoungJu Choie, Pohang University of Science and Technology, February 12-16; March 22-28
    • John Francis, Northwestern University, March 1-14
    • David Gaiotto, Perimeter Institute, March 25-29
    • Jayce Getz, Duke University, March 18-22
    • Ezra Getzler, Northwestern University, March 11-22
    • Sam Gunningham, Montana State University, February 9-12
    • Sarah Harrison, Northeastern University
    • Dihua Jiang, University of Minnesota, February 29-March 9
    • Tasho Kaletha, University of Michigan, March 12-20
    • Minhyong Kim, University of Edinburgh, February 1-29
    • Axel Kleinschmidt, Max Planck Institute for Gravitational Physics, Potsdam, March 18-28
    • Kim Klinger-Logan, Kansas State University, March 25-29
    • Kobi Kremnitzer, Oxford University, March 25-29
    • Baiying Liu, Purdue University, March 13-16
    • Steven Miller, Rutgers University
    • Greg Moore, Rutgers University, February 5-9
    • David Nadler, University of California, Berkeley, March 17-30
    • Bảo Châu Ngô, University of Chicago, March 25-29
    • George Pappas, Michigan State University, March 25-29
    • Daniel Persson, Chalmers Institute of Technology, March 25-29
    • Sam Raskin, Yale University, March 26-29
    • Yiannis Sakellaridis, Johns Hopkins University, March 18-22
    • Peng Shan, Tsinghua University, February 12-April 14
    • Akshay Venkatesh, Institute for Advanced Study
    • Roberto Volpato, University of Padova, February 4-10
    • Chen Wan, Rutgers University, February 29-March 9
    • Fei Yan, Brookhaven National Laboratory, March 18-29
    • Xinwen Zhu, Stanford University

     

  • CMSA EVENT: Big Data Conference 2021
    All day
    12/01/2024

    On August 24, 2021, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The 2021 Big Data Conference took place virtually on Zoom.

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Time (ET; Boston time)SpeakerTitle/Abstract
    9:00AMConference OrganizersIntroduction and Welcome
    9:10AM – 9:55AMAndrew Blumberg, University of Texas at AustinTitle: Robustness and stability for multidimensional persistent homology

    Abstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However, for many data sets, it is very natural to consider multiple filtrations, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.

    10:00AM – 10:45AMKatrina Ligett, The Hebrew University of JerusalemTitle: Privacy as Stability, for Generalization

    Abstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity, via a connection to the notion of differential privacy. In this talk, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open.

    Joint work with: Christopher Jung (UPenn), Seth Neel (Harvard), Aaron Roth (UPenn), Saeed Sharifi-Malvajerdi (UPenn), and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020

    10:50AM – 11:35AMHima Lakkaraju, Harvard UniversityTitle: Towards Reliable and Robust Model Explanations

    Abstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP, and also introduce novel methods to address some of these vulnerabilities. More specifically, I will first demonstrate that these methods are brittle, unstable, and are vulnerable to a variety of adversarial attacks. Then, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.

    11:40AM – 12:25PMMoran Koren, Harvard CMSATitle: A Gatekeeper’s Conundrum

    Abstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e., ignore her private information with some probability).

    12:25PMConference OrganizersClosing Remarks
  • CMSA EVENT: Mathematics in Science: Perspectives and Prospects
    All day
    12/01/2024-10/28/2023
    1 Oxford Street, Cambridge MA 02138

    Mathematics in Science: Perspectives and Prospects

    A showcase of mathematics in interaction with physics, computer science, biology, and beyond.

    October 27–28, 2023

    Location: Harvard University Science Center Hall D & via Zoom.

    Directions and Recommended Lodging

    Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

    Youtube Playlist

     

    Speakers

    Organizers

    • Michael R. Douglas (Harvard CMSA)
    • Dan Freed (Harvard Math & CMSA)
    • Mike Hopkins (Harvard Math)
    • Cumrun Vafa (Harvard Physics)
    • Horng-Tzer Yau (Harvard Math)

    Schedule

    Friday, October 27, 2023

    2:00–3:15 pmGreg Moore (Rutgers)

    Title: Remarks on Physical Mathematics

    Abstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting, I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet, so I don’t know how it will end any more than you do.

    Slides (PDF)

    3:15–3:45 pmBreak
    3:45–5:00 pmBernd Sturmfels (MPI Leipzig)

    Title: Algebraic Varieties in Quantum Chemistry

    Abstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.

    Slides (PDF)

     

    Saturday, October 28, 2023

    9:00 amBreakfast
    9:30–10:45 amMike Freedman (Harvard CMSA)

    Title: ML, QML, and Dynamics: What mathematics can help us understand and advance machine learning?

    Abstract: Vannila deep neural nets DNN repeatedly stretch and fold. They are reminiscent of the logistic map and the Smale horseshoe.  What kind of dynamics is responsible for their expressivity and trainability. Is chaos playing a role? Is the Kolmogorov Arnold representation theorem relevant? Large language models are full of linear maps. Might we look for emergent tensor structures in these highly trained maps in analogy with emergent tensor structures at local minima of certain loss functions in high-energy physics.

    Slides (PDF)

    10:45–11:15 amBreak
    11:15 am–12:30 pm
    via Zoom
    Nima Arkani-Hamed (IAS)

    Title: All-Loop Scattering as A Counting Problem

    Abstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model, the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

    12:30–2:00 pmLunch break
    2:00–3:15 pmConstantinos Daskalakis (MIT)

    Title: How to train deep neural nets to think strategically

    Abstract: Many outstanding challenges in Deep Learning lie at its interface with Game Theory: from playing difficult games like Go to robustifying classifiers against adversarial attacks, training deep generative models, and training DNN-based models to interact with each other and with humans. In these applications, the utilities that the agents aim to optimize are non-concave in the parameters of the underlying DNNs; as a result, Nash equilibria fail to exist, and standard equilibrium analysis is inapplicable. So how can one train DNNs to be strategic? What is even the goal of the training? We shed light on these challenges through a combination of learning-theoretic, complexity-theoretic, game-theoretic and topological techniques, presenting obstacles and opportunities for Deep Learning and Game Theory going forward.

    Slides (PDF)

    3:15–3:45 pmBreak
    3:45–5:00 pmAlison Etheridge (Oxford)

    Title: Modelling hybrid zones

    Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection, spatial structure, and, if time permits, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection.

    Slides (PDF)

     


    Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to mathsci2023@cmsa.fas.harvard.edu no later than October 9, 2023.

    Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV.

     

  • Holiday
    All day
    12/01/2024

    Holiday: Friday after Thanksgiving

    The CMSA will be closed on Friday, November 25, 2022.

  • Seminars

    Seminars Colloquia & Seminar
    1/27/2020 Math Physics Seminar

    12:00 am-1:00 pm
    12/01/2024
  • CMSA EVENT: Quantum Matter Workshop
    All day
    12/01/2024
    Layer-2-600x338

    Please note: this workshop has been postponed to a later date. Details will be posted to this page when they are available.

    Throughout the summer, scheduled speakers for the Quantum Matter Workshop will give talks on Zoom for the Quantum Matter/Condensed Matter seminar.

    The CMSA will be hosting our second workshop on Quantum Matter. Both of these workshops are part of our program on Quantum Matter in Mathematics and Physics. The first workshop took place in December 2019, and was extremely successful, attracting participants worldwide. Learn more about the first workshop here.

     

    Organizers: Du Pei, Ryan Thorngren, Juven Wang, Yifan Wang, and Shing-Tung Yau.

    Speakers:

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-16-2018 Mathematical Physics Seminar

    12:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/7/2018 Hodge Seminar

    1:30 am-3:00 pm
    12/01/2024
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Some remarks on contact Calabi-Yau 7-manifolds

    3:00 am-4:00 am
    12/01/2024

    Abstract: In geometry and physics it has proved useful to relate G2 and Calabi-Yau geometry via circle bundles. Contact Calabi-Yau 7-manifolds are, in the simplest cases, such circle bundles over Calabi-Yau 3-orbifolds. These 7-manifolds provide testing grounds for the study of geometric flows which seek to find torsion-free G2-structures (and thus Ricci flat metrics with exceptional holonomy). They also give useful backgrounds to examine the heterotic G2 system (also known as the G2-Hull-Strominger system), which is a coupled set of PDEs arising from physics that involves the G2-structure and gauge theory on the 7-manifold. I will report on recent progress on both of these directions in the study of contact Calabi-Yau 7-manifolds, which is joint work with H. Sá Earp and J. Saavedra.

  • Colloquium
    5:00 am
    12/01/2024

    No additional detail for this event.

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Arthur Jaffe (Harvard University)

    Title: Is relativity compatible with quantum theory?

    Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.”  Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed.

    Talk chair: Zhengwei Liu

    Video

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Edward Witten (IAS)

    Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions

    Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification.

    Talk chair: Cliff Taubes

    Video

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Nigel Hitchin (University of Oxford)

    Title: Michael Atiyah: Geometry and Physics

    Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists.

    Talk chair: Peter Kronheimer

    Video

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Alain Connes (Collège de France)

    Title: Noncommutative Geometry, the Spectral Aspect

    Abstract: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function.

    Talk chair: Peter Kronheimer

    Video 

  • CMSA EVENT: Workshop on Quantum Information
    8:00 am-6:07 pm
    12/01/2024-04/24/2017
    banner-image-1

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 23-24, 2018. In the days leading up to the conference, the American Mathematical Society will also be hosting a sectional meeting on quantum information on April 21-22. You can find more information here.

    Register for the event here.

    The following speakers are confirmed:

  • Math Science Literature Lecture Series
    8:00 am-9:00 am
    12/01/2024
    Lecture-Series-Don-pdf

    Donald Rubin (Harvard)

    Title: Why do some universities have separate departments of statistics? And are they all anachronisms, destined to follow the path of other dinosaurs?

    Video | Slides

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Yuri Manin (Max Planck Institute for Mathematics)

    Title: Homotopy spectra and Diophantine equations

    Abstract: For a long stretch of time in the history of mathematics, Number Theory and Topology formed vast, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC)  that contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory, named after Diophantus of Alexandria (about 250 BC). Topology was born much later, but arguably, its cousin — modern measure theory, — goes back to Archimedes, author of Psammites (“Sand Reckoner”), who was approximately a contemporary of Diophantus. In modern language, Archimedes measures the volume of observable universe by counting the number of small grains of sand necessary to fill this volume. Of course, many qualitative geometric models and quantitative estimates of the relevant distances precede his calculations. Moreover, since the estimated numbers of grains of sand are quite large (about $10^{64}$), Archimedes had to invent and describe a system of notation for large numbers going far outside the possibilities of any of the standard ancient systems. The construction of the first bridge between number theory and topology was accomplished only about fifty years ago: it is the theory of spectra in stable homotopy theory. In particular, it connects $Z$, the initial object in the theory of commutative rings, with the sphere spectrum $S$. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this talk based upon the authors’ (Yu. Manin and M. Marcolli) joint research project, I suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.

    Talk chair: Michael Hopkins

    Slides | Video

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrations

    8:00 am-9:30 am
    12/01/2024

    Caucher Birkar (University of Cambridge)

    Title: Log Calabi-Yau fibrations

    Abstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry, differential geometry, arithmetic geometry, mathematical physics, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties, their fibrations, as well as their local birational counterparts such as flips and singularities. Such fibrations can be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations, to remind some known results, and to state some open problems.

    Video

     

  • Special Seminar
    8:00 am-9:00 am
    12/01/2024
    Gromov-Witten

    During the Spring 2021 Semester Artan Sheshmani (CMSA/ I.M. A.U.) will be teaching a CMSA special lecture series on Gromov-Witten/Donaldson Thomas theory and Birational/Symplectic invariants for algebraic surfaces.

    In order to attend this series, please fill out this form.

    The lectures will be held Mondays from 8:00 – 9:30 AM ET and Wednesdays from 8:00 – 9:00 AM ET beginning January 25 on Zoom.

    You can watch Prof. Sheshmani describe the series here. 

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Andrei Okounkov (Columbia University)

    Title: Classical and quantum integrable systems in enumerative geometry

    Abstract: For more than a quarter of a century, thanks to the ideas and questions originating in modern high-energy physics, there has been a very fruitful interplay between enumerative geometry and integrable system, both classical and quantum. While it is impossible to summarize even the most important aspects of this interplay in one talk, I will try to highlight a few logical points with the goal to explain the place and the role of certain more recent developments.

    Talk chair: Cumrun Vafa

    Video

  • Quantum Matter
    8:00 am-9:30 am
    12/01/2024
  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Yujiro Kawamata (University of Tokyo)

    Title: Kunihiko Kodaira and complex manifolds

    Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions.  After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces.  Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts.

    Talk chair: Baohua Fu

    Video 

  • CMSA EVENT: Geometric Analysis Approach to AI Workshop
    8:30 am-5:30 pm
    12/01/2024-01/21/2019
    Geo-Analysis-Poster-final-e1547584167900

    Geo-Analysis-1-e1543848888343

    Due to inclement weather on Sunday, the second half of the workshop has been moved forward one day. Sunday and Monday’s talks will now take place on Monday and Tuesday.

    On January 18-21, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI.

    This workshop will focus on the theoretic foundations of AI, especially various methods in Deep Learning. The topics will cover the relationship between deep learning and optimal transportation theory, DL and information geometry, DL Learning and information bottle neck and renormalization theory, DL and manifold embedding and so on. Furthermore, the recent advancements, novel methods, and real world applications of Deep Learning will also be reported and discussed.

    The workshop will take place from January 18th to January 23rd, 2019. In the first four days, from January 18th to January 21, the speakers will give short courses; On the 22nd and 23rd, the speakers will give conference representations. This workshop is organized by Xianfeng Gu and Shing-Tung Yau.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please register here

    Speakers: 

  • CMSA EVENT: Big Data Conference 2018
    8:30 am-2:50 pm
    12/01/2024-08/24/2018
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2018-1

     

    shutterstock_547250785-e1527881194717

    On August 23-24, 2018 the CMSA will be hosting our fourth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The talks will take place in Science Center Hall B, 1 Oxford Street.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

    Please register here. 

    Confirmed Speakers: 

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
    • Jun Liu, Professor of Statistics, Harvard University
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
  • CMSA EVENT: 2019 Big Data Conference
    8:30 am-4:40 pm
    12/01/2024-08/20/2019
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2019-Poster-5-2

    shutterstock_547250785-e1527881194717

    On August 19-20, 2019 the CMSA will be hosting our fifth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The talks will take place in Science Center Hall D, 1 Oxford Street.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

    Videos can be found in this Youtube playlist or in the schedule below.

  • CMSA EVENT: Workshop on Aspects of General Relativity
    8:30 am-3:30 pm
    12/01/2024-05/26/2017

    The Center of Mathematical Sciences and Applications will be hosting a workshop on General Relativity from May 23 – 24, 2016. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138The workshop will start on Monday, May 23 at 9am and end on Tuesday, May 24 at 4pm.

    Speakers:

    1. Po-Ning Chen, Columbia University
    2. Piotr T. Chruściel, University of Vienna
    3. Justin Corvino, Lafayette College
    4. Greg Galloway, University of Miami
    5. James Guillochon, Harvard University
    6. Lan-Hsuan Huang, University of Connecticut
    7. Dan Kapec, Harvard University
    8. Dan Lee, CUNY
    9. Alex Lupsasca, Harvard University
    10. Pengzi Miao, University of Miami
    11. Prahar Mitra, Harvard University
    12. Lorenzo Sironi, Harvard University
    13. Jared Speck, MIT
    14. Mu-Tao Wang, Columbia University

    Please click Workshop Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Please click here for registration – Registration is capped at 70 participants.

    Schedule:

    May 23 – Day 1
    8:30amBreakfast
    8:55amOpening remarks
    9:00am – 9:45amGreg Galloway, “Some remarks on photon spheres and their uniqueness
    9:45am – 10:30amPrahar Mitra, “BMS supertranslations and Weinberg’s soft graviton theorem
    10:30am – 11:00amBreak
    11:00am – 11:45amDan Kapec, “Area, Entanglement Entropy and Supertranslations at Null Infinity
    11:45am – 12:30pmPiotr T. Chruściel, “The cosmological constant and the energy of gravitational radiation”
    12:30pm – 2:00pmLunch
    2:00pm – 2:45pmJames Guillochon, “Tidal disruptions of stars by supermassive black holes: dynamics, light, and relics”
    2:45pm – 3:30pmMu-Tao Wang, “Quasi local conserved quantities in general relativity
    3:30pm – 4:00pmBreak
    4:00pm – 4:45pmPo-Ning Chen, “Quasi local energy in presence of gravitational radiations
    4:45pm – 5:30pmPengzi Miao, “Total mean curvature, scalar curvature, and a variational analog of Brown York mass
    May 24 – Day 2
    8:45amBreakfast
    9:00am – 9:45amJustin Corvino, “Scalar curvature deformation and the Bartnik mass
    9:45am – 10:30amLan-Hsuan Huang, “Constraint Manifolds with the Dominant Energy Condition
    10:30am – 11:00amBreak
    11:00am – 11:45amDan Lee, “Lower semicontinuity of Huisken’s isoperimetric mass
    11:45am – 12:30pmJared Speck, “Shock Formation in Solutions to the Compressible Euler Equations
    12:30pm – 2:00pmLunch
    2:00pm – 2:45pmLorenzo Sironi, “Electron Heating and Acceleration in the Vicinity of Supermassive Black Holes
    2:45pm – 3:30pmAlex Lupsasca, “Near Horizon Extreme Kerr Magnetospheres
    * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Workshop on Aspects on General Relativity“.
    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    Organizers: Piotr T. Chruściel and Shing-Tung Yau

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Angular momentum in general relativity

    8:30 am-9:30 am
    12/01/2024

    Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

  • CMSA EVENT: F-Theory Conference
    8:30 am-3:00 pm
    12/01/2024-09/30/2018

    The CMSA will be hosting an F-Theory workshop September 29-30, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. 

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Click here for videos of the talks. 

    Organizers:

    Speakers:

  • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
    8:30 am-2:00 pm
    12/01/2024-10/24/2018

    In Fall 2018, the CMSA will host a Program on Mathematical Biology, which aims to describe recent mathematical advances in using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.

    The plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale, the   shapes seen in a garden at the scale of a pollen grain, a seed, a sapling, a root, a flower or leaf are so numerous that “it is enough to drive the sanest man mad,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively?

    In biology, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists, to understand how polymeric assemblies grow and shrink (in the cytoskeleton), and how cells divide, change size and shape, and move to organize tissues, change their topology and geometry, and link multiple scales and connect biochemical to mechanical aspects of these problems, all in a self-regulated setting.

    To understand these questions, we need to describe shape (biomathematics), predict shape (biophysics), and design shape (bioengineering).

    For example, in mathematics there are some beautiful links to Nash’s embedding theorem,  connections to quasi-conformal geometry, Ricci flows and geometric PDE, to Gromov’s h principle, to geometrical singularities and singular geometries, discrete and computational differential geometry, to stochastic geometry and shape characterization (a la Grenander, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor, Adler) to look for similarities and differences across species during development, and across evolution.

    In physics, there are questions of generalizing classical theories to include activity, break the usual Galilean invariance, as well as isotropy, frame indifference, homogeneity, and create both agent (cell)-based and continuum theories for ordered, active machines, linking statistical to continuum mechanics, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals, polar materials, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied.

    The CMSA will be hosting a Workshop on Morphometrics, Morphogenesis and Mathematics from October 22-24 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Videos of the talks

    Confirmed Speakers:

  • CMSA EVENT: Workshop on Foundations of Computational Science
    8:30 am-2:45 pm
    12/01/2024-08/31/2019
    AI-Poster-3

    On August 29-31, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on Foundations of Computational Science. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA This workshop is organized by David Xianfeng Gu.

    Please register here. 

    Speakers:

    Videos of the talks are contained in the Youtube playlist below. They can also be found through links in the schedule.

  • Quantum Matter
    8:30 am-10:00 am
    12/01/2024
  • CMSA EVENT: Morphogenesis: Geometry and Physics
    8:30 am-2:30 pm
    12/01/2024-12/05/2018

    Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book – a literary masterpiece – is a visionary synthesis of the geometric biology of form. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. So, how far are we from realizing the century-old vision that “Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed” ?

    To address this requires an appreciation of the enormous ‘morphospace’ in terms of the potential shapes and sizes that living forms take, using the language of mathematics. In parallel, we need to consider the biological processes that determine form in mathematical terms is based on understanding how instabilities and patterns in physical systems might be harnessed by evolution.

    In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.
    The first workshop will focus on the interface between Morphometrics and Mathematics, while the second will focus on the interface between Morphogenesis and Physics.The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

    As part of the program on Mathematical Biology a workshop on Morphogenesis: Geometry and Physics will take place on December 3-5, 2018.  The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Videos

    Please Register Here

    PDF of the Schedule

    Speakers:

  • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
    8:30 am-5:20 pm
    12/01/2024-08/20/2018
    Mumford-3

    David_Mumford-1

    On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center, Hall B.

     Saturday, August 18th:  A day of talks on Vision, AI and brain sciences
    Monday, August 20th: a day of talks on Math

    Speakers:

    Organizers:

     

    Publication:

    Pure and Applied Mathematics Quarterly

    Special Issue: In Honor of David Mumford

    Guest Editors: Ching-Li Chai, Amnon Neeman

     

  • Member Seminar
    8:45 am-10:15 am
    12/01/2024

    Speaker: Jörn Boehnke

    Title: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning

    Abstract:  In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.

  • CMSA EVENT: 2015 Conference on Big Data
    8:45 am-4:00 pm
    12/01/2024-10/26/2015
    1 Oxford Street, Cambridge MA 02138

    The Center of Mathematical Sciences and Applications will be having a conference on Big Data August 24-26, 2015, in Science Center Hall B at Harvard University.  This conference will feature many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    For more info, please contact Sarah LaBauve at slabauve@math.harvard.edu.

     

    Registration for the conference is now closed.

    Please click here for a downloadable version of this schedule.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found here.

    Monday, August 24

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amSendhil MullainathanPrediction Problems in Social Science: Applications of Machine Learning to Policy and Behavioral Economics
    9:45amMike LucaDesigning Disclosure for the Digital Age
    10:30Break
    10:45Jianqing FanBig Data Big Assumption: Spurious discoveries and endogeneity
    11:30amDaniel GoroffPrivacy and Reproducibility in Data Science
    12:15pmBreak for Lunch
    2:00pmRyan AdamsExact Markov Chain Monte Carlo with Large Data
    2:45pmDavid DunsonScalable Bayes: Simple algorithms with guarantees
    3:30pmBreak
    3:45pmMichael JordanComputational thinking, inferential thinking and Big Data
    4:30pmJoel TroppApplied Random Matrix Theory
    5:15pmDavid WoodruffInput Sparsity and Hardness for Robust Subspace Approximation

    Tuesday, August 25

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amGunnar CarlssonPersistent homology for qualitative analysis and feature generation
    9:45amAndrea MontanariSemidefinite Programming Relaxations for Graph and Matrix Estimation: Algorithms and Phase Transitions
    10:30amBreak
    10:45amSusan AtheyMachine Learning and Causal Inference for Policy Evaluation
    11:30amDenis NekipelovRobust Empirical Evaluation of Large Competitive Markets
    12:15pmBreak for Lunch
    2:00pmLucy ColwellUsing evolutionary sequence variation to make inferences about protein structure and function: Modeling with Random Matrix Theory
    2:45pmSimona CoccoInverse Statistical Physics approaches for the modeling of protein families
    3:30pmBreak
    3:45pmRemi MonassonInference of top components of correlation matrices with prior informations
    4:30pmSayan MukherjeeRandom walks on simplicial complexes and higher order notions of spectral clustering

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    A Banquet from 7:00 – 8:30pm will follow Tuesday’s talks. This event is by invitation only.

     Wednesday, August 26 

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amAnkur MoitraBeyond Matrix Completion
    9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
    10:30amBreak
    10:45amPiotr IndykFast Algorithms for Structured Sparsity
    11:30amGuido ImbensExact p-values for network inference
    12:15pmBreak for lunch
    2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
    2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
    3:30pmBreak
    3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
    4:30pmJelani NelsonDimensionality reductions via sparse matrices
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024
    Lecture_Fukaya-pdf

    Kenji Fukaya (Simons Center for Geometry and Physics)

    Title: Homological (homotopical) algebra and moduli spaces in Topological Field theories

    Abstract: Moduli spaces of various gauge theory equations and of various versions of (pseudo) holomorphic curve equations have played important role in geometry in these 40 years. Started with Floer’s work people start to obtain more sophisticated object such as groups, rings, or categories from (system of) moduli spaces. I would like to survey some of those works and the methods to study family of moduli spaces systematically.

    Talk chair: Peter Kronheimer

    Slides | Video

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Don Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics)

    Title: Quantum topology and new types of modularity

    Abstract: The talk concerns two fundamental themes of modern 3-dimensional topology and their unexpected connection with a theme coming from number theory. A deep insight of William Thurston in the mid-1970s is that the vast majority of complements of knots in the 3-sphere, or more generally of 3-manifolds, have a unique metric structure as hyperbolic manifolds of constant curvature -1, so that 3-dimensional topology is in some sense not really a branch of topology at all, but of differential geometry. In a different direction, the work of Vaughan Jones and Ed Witten in the late 1980s gave rise to the field of Quantum Topology, in which new types of invariants of knot complements and 3-manifolds are introduced that have their origins in ideas coming from quantum field theory. These two themes then became linked by Kashaev’s famous Volume Conjecture, now some 25 years old, which says that the Kashaev invariant _N of a hyperbolic knot K (this is a quantum invariant defined for each positive integer N and whose values are algebraic numbers) grows exponentially as N tends to infinity with an exponent proportional to the hyperbolic volume of the knot complement. About 10 years ago, I was led by numerical experiments to the discovery that Kashaev’s invariant could be upgraded to an invariant having rational numbers as its argument (with the original invariant being the value at 1/N) and that the Volume Conjecture then became part of a bigger story saying that the new invariant has some sort of strange transformation property under the action x -> (ax+b)/(cx+d) of the modular group SL(2,Z) on the argument. This turned out to be only the beginning of a fascinating and multi-faceted story relating quantum invariants, q-series, modularity, and many other topics. In the talk, which is intended for a general mathematical audience, I would like to recount some parts of this story, which is joint work with Stavros Garoufalidis (and of course involving contributions from many other authors). The “new types of modularity” in the title refer to a specific byproduct of these investigations, namely that there is a generalization of the classical notion of holomorphic modular form – which plays an absolutely central role in modern number theory – to a new class of holomorphic functions in the upper half-plane that no longer satisfy a transformation law under the action of the modular group, but a weaker extendability property instead. This new class, called “holomorphic quantum modular forms”, turns out to contain many other functions of a more number-theoretical nature as well as the original examples coming from quantum invariants.

    Talk chair: Mark Kisin

    Video

  • Combinatorics Physics and Probability
    9:00 am-10:00 am
    12/01/2024

    Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Liang Kong (Sustech)

    Title: Topological Wick Rotation and Holographic duality

    Abstract: I will explain a new type of holographic dualities between
    n+1D topological orders with a chosen boundary condition and nD
    (potentially gapless) quantum liquids. It is based on the idea of
    topological Wick rotation, a notion which was first used in
    arXiv:1705.01087 and was named, emphasized and generalized later in
    arXiv:1905.04924. Examples of these holographic dualities include the
    duality between 2+1D toric code model and 1+1D Ising chain and its
    finite-group generalizations (independently discovered by many
    others); those between 2+1D topological orders and 1+1D rational
    conformal field theories; and those between n+1D finite gauge theories
    with a gapped boundary and nD gapped quantum liquids. I will also
    briefly discuss some generalizations of this holographic duality and
    its relation to AdS/CFT duality.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: João Caetano (CERN)

    Title: Unorientable Quantum Field Theories: From crosscaps to holography

    Abstract: In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state.

    In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4-manifold. I will show how to do this in the example of N=4 Supersymmetric Yang-Mills, discuss its holographic description and present a new solvable setup of AdS/CFT.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Michele Del Zotto (Uppsala University)

    Title: On the six-dimensional origin of non-invertible symmetries

    Abstract: I will present a review about recent progress in charting non-invertible symmetries for four-dimensional quantum field theories that have a six-dimensional origin. These include in particular N=4 supersymmetric Yang-Mills theories, and also a large class of N=2 supersymmetric theories which are conformal and do not have a conventional Lagrangian description (the so-called theories of “class S”). Among the main results, I will explain criteria for identifying examples of systems with intrinsic and non-intrinsic non-invertible symmetries, as well as explore their higher dimensional origin. This seminar is based on joint works with Vladimir Bashmakov, Azeem Hasan, and Justin Kaidi.

     

    https://www.youtube.com/watch?v=0Tscbn9RhF8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=31

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 11.2.22

    Topological Quantum Matter Seminar

    Speaker: Junyeong Ahn (Harvard)

    Title: Optical axion electrodynamics

    Abstract: Electromagnetic fields in a magneto-electric medium behave in close analogy to photons coupled to the hypothetical elementary particle, the axion. This emergent axion electrodynamics is expected to provide novel ways to detect and control material properties with electromagnetic fields. Despite having been studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Formulating axion electrodynamics at general optical frequencies requires resolving the difficulty of calculating optical magneto-electric coupling in periodic systems and demands a proper generalization of the axion field. In this talk, I will introduce a theory of optical axion electrodynamics that allows for a simple quantitative analysis. Then, I will move on to discuss the issue of the Kerr effect in axion antiferromagnets, refuting the conventional wisdom that the Kerr effect is a measure of the net magnetic moment. Finally, I will apply our theory to a topological antiferromagnet MnBi2Te4.

    References:
    [1] Theory of Optical Axion Electrodynamics, J. Ahn, S.Y. Xu, A.Vishwanath, arXiv:2205.06843

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Ethan Lake (MIT)

    Title: Insulating BECs and other surprises in dipole-conserving systems

    Abstract: I will discuss recent work on bosonic models whose dynamics conserves both total charge and total dipole moment, a situation which can be engineered in strongly tilted optical lattices. Related models have received significant attention recently for their interesting out-of-equilibrium dynamics, but analytic and numeric studies reveal that they also possess rather unusual ground states. I will focus in particular on a dipole-conserving variant of the Bose-Hubbard model, which realizes an unusual phase of matter that possesses a Bose-Einstein condensate, but which is nevertheless insulating, and has zero superfluid weight. Time permitting, I will also describe the physics of a regime in which these models spontaneously fracture into an exotic type of glassy state.

     

    https://www.youtube.com/watch?v=Nad45apS8TE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=29

  • Quantum Matter
    9:00 am-4:00 pm
    12/01/2024
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Daniel A. Spielman

    Dan Spielman (Yale University)

    Title: Discrepancy Theory and Randomized Controlled Trials

    Abstract: Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other.  By “surprisingly similar” we mean much more similar than a random partition. I will begin by surveying fundamental results in discrepancy theory, including Spencer’s famous existence proofs and Bansal’s recent algorithmic realizations of them. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar.  When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we know information about the experimental subjects, called covariates, we can combine the strengths of randomization with the promises of discrepancy theory. This should allow us to obtain more accurate estimates of the effectiveness of treatments, or to conduct trials with fewer experimental subjects. I will introduce the Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, which produces random solutions to discrepancy problems. I will then explain how Chris Harshaw, Fredrik Sävje, Peng Zhang, and I use this algorithm to improve the design of randomized controlled trials. Our Gram-Schmidt Walk Designs have increased accuracy when the experimental outcomes are correlated with linear functions of the covariates, and are comparable to uniform random assignments in the worst case.

    Talk chair: Salil Vadhan

    Video

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 10.26.22

    Topological Quantum Matter Seminar

    Speaker: Bruno Mera, Tohoku University
    Title: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
    Abstract: The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect, certain geometric constraints, associated with the holomorphic character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.
    References:
    [1] Tomoki Ozawa and Bruno Mera. Relations between topology and the quantum metric for Chern insulators. Phys. Rev. B, 104:045103, Jul 2021.
    [2] Bruno Mera and Tomoki Ozawa. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Phys. Rev. B, 104:045104, Jul 2021.
    [3] Bruno Mera and Tomoki Ozawa. Engineering geometrically flat Chern bands with Fubini-Study  Kähler structure. Phys. Rev. B, 104:115160, Sep 2021.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Francisco Machado  (Berkeley/Harvard)

    Title: Kardar-Parisi-Zhang dynamics in integrable quantum magnets

    Abstract: Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.

    In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.

    Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.

    [1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
    B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
    (PRL in press) – arXiv:2205.02853

    [2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
    D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
    Science (2022) — arXiv:2107.00038

     

    https://www.youtube.com/watch?v=65DjgbX30FU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=27

  • Math Science Literature Lecture Series
    9:00 am-12:13 pm
    12/01/2024

    Harry Shum (Tsinghua University)

    Title: From Deep Learning to Deep Understanding

    Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model,  and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike GPT or similar language models learnt from data, it is a multi-turn decision making system which takes user input, updates the belief state, retrieved from the database via symbolic reasoning, and decides how to complete the task with grounded response.

    Talk chair: Shing-Tung Yau

    Video

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    10/12/2021 Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    Title: On counting algebraically defined graphs

    Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

  • Program
    9:00 am-5:00 pm
    12/01/2024-05/13/2022

    Please visit the Swampland Initiative for current events.

    The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.

     


    During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”

    The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology,  which has led to a great deal of activity in the field in the last few years.

    The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.

    This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.

    Seminars

    Swampland Seminar Series & Group Meetings

    Program Visitors

    • Pieter Bomans, Princeton, 10/30/21 – 11/02/21
    • Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
    • Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
    • Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
    • Timo Weigand, 03/21/22 – 03/28/22
    • Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
    • Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
    • Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
    • Sergio Cecotti, 05/08/22 – 05/21/22
    • Tom Rudelius, 05/09/22 – 05/13/22

    https://sites.harvard.edu/swampland-initiative/

  • Math Science Literature Lecture Series
    9:00 am-9:06 am
    12/01/2024

    Claire Voisin (Collège de France)

    Title: Hodge structures and the topology of algebraic varieties

    Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results  we will discuss  rely on Hodge theory, which  has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization,  is missing in the general Kaehler context. We will also discuss some results and problems related to algebraic cycles and motives.

    Talk chair: Joe Harris

    Video | Slides | Article

  • Conference
    9:00 am-5:30 pm
    12/01/2024-03/01/2023
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Poster_GeometryStatistics_8.5x11.final

    On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

    Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

    This conference will be held in person. Directions and Recommended Lodging

    Registration is required.

    Register here to attend in-person.

    Organizing Committee:
    Stephan Huckemann (Georg-August-Universität Göttingen)
    Ezra Miller (Duke University)
    Zhigang Yao (Harvard CMSA and Committee Chair)

    Scientific Advisors:
    Horng-Tzer Yau (Harvard CMSA)
    Shing-Tung Yau (Harvard CMSA)

    Speakers:

    • Tamara Broderick (MIT)
    • David Donoho (Stanford)
    • Ian Dryden (Florida International University in Miami)
    • David Dunson (Duke)
    • Charles Fefferman (Princeton)
    • Stefanie Jegelka (MIT)
    • Sebastian Kurtek (OSU)
    • Lizhen Lin (Notre Dame)
    • Steve Marron (U North Carolina)
    • Ezra Miller (Duke)
    • Hans-Georg Mueller (UC Davis)
    • Nicolai Reshetikhin (UC Berkeley)
    • Wolfgang Polonik (UC Davis)
    • Amit Singer (Princeton)
    • Zhigang Yao (Harvard CMSA)
    • Bin Yu (Berkeley)

    Moderator: Michael Simkin (Harvard CMSA)

     

    SCHEDULE

    Monday, Feb. 27, 2023 (Eastern Time)

    8:30 amBreakfast
    8:45–8:55 amZhigang YaoWelcome Remarks
    8:55–9:00 amShing-Tung Yau*Remarks
    Morning Session Chair: Zhigang Yao
    9:00–10:00 amDavid DonohoTitle: ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise

    Abstract: Truncation of the singular value decomposition is a true scientific workhorse. But where to Truncate?

    For 55 years the answer, for many scientists, has been to eyeball the scree plot, an approach which still generates hundreds of papers per year.

    I will describe ScreeNOT, a mathematically solid alternative deriving from the many advances in Random Matrix Theory over those 55 years. Assuming a model of low-rank signal plus possibly correlated noise, and adopting an asymptotic viewpoint with number of rows proportional to the number of columns, we show that ScreeNOT has a surprising oracle property.

    It typically achieves exactly, in large finite samples, the lowest possible MSE for matrix recovery, on each given problem instance – i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure.

    The talk is based on joint work with Matan Gavish and Elad Romanov, Hebrew University.

    10:00–10:10 amBreak
    10:10–11:10 amSteve MarronTitle: Modes of Variation in Non-Euclidean Spaces

    Abstract: Modes of Variation provide an intuitive means of understanding variation in populations, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts, including shapes as data objects, vectors of directional data, amplitude and phase variation and compositional data.

    11:10–11:20 amBreak
    11:20 am–12:20 pmZhigang YaoTitle: Manifold fitting: an invitation to statistics

    Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference:https://arxiv.org/abs/1909.10228

     12:20–1:50 pm12:20 pm Group Photo

    followed by Lunch

    Afternoon Session Chair: Stephan Huckemann
    1:50–2:50 pmBin Yu*Title: Interpreting Deep Neural Networks towards Trustworthiness

    Abstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.

    2:50–3:00 pmBreak
    3:00-4:00 pmHans-Georg MuellerTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression

    Abstract: Random objects, i.e., random variables that take values in a separable metric space, pose many challenges for statistical analysis, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions, covariance matrices or surfaces, graph Laplacians to represent networks, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics, an emerging collection of statistical tools to characterize, infer and relate samples of random objects. Recent developments include depth profiles, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey, Y. Chen 2022).

    These distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.

    4:00-4:10 pmBreak
    4:10-5:10 pmStefanie JegelkaTitle: Some benefits of machine learning with invariances

    Abstract: In many applications, especially in the sciences, data and tasks have known invariances. Encoding such invariances directly into a machine learning model can improve learning outcomes, while it also poses challenges on efficient model design. In the first part of the talk, we will focus on the invariances relevant to eigenvectors and eigenspaces being inputs to a neural network. Such inputs are important, for instance, for graph representation learning. We will discuss targeted architectures that can universally express functions with the relevant invariances – sign flips and changes of basis – and their theoretical and empirical benefits.

    Second, we will take a broader, theoretical perspective. Empirically, it is known that encoding invariances into the machine learning model can reduce sample complexity. For the simplified setting of kernel ridge regression or random features, we will discuss new bounds that illustrate two ways in which invariances can reduce sample complexity. Our results hold for learning on manifolds and for invariances to (almost) any group action, and use tools from differential geometry.

    This is joint work with Derek Lim, Joshua Robinson, Behrooz Tahmasebi, Lingxiao Zhao, Tess Smidt, Suvrit Sra, and Haggai Maron.

     

     

     

    Tuesday, Feb. 28, 2023 (Eastern Time)

    8:30-9:00 amBreakfast
    Morning Session Chair: Zhigang Yao
    9:00-10:00 amCharles Fefferman*Title: Lipschitz Selection on Metric Spaces

    Abstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.

    10:00-10:10 amBreak
    10:10-11:10 amDavid DunsonTitle: Inferring manifolds from noisy data using Gaussian processes

    Abstract: In analyzing complex datasets, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm, we provide simulated and real data examples to illustrate the performance. Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478

    11:10-11:20 amBreak
    11:20 am-12:20 pmWolfgang PolonikTitle: Inference in topological data analysis

    Abstract: Topological data analysis has seen a huge increase in popularity finding applications in numerous scientific fields. This motivates the importance of developing a deeper understanding of benefits and limitations of such methods. Using this angle, we will present and discuss some recent results on large sample inference in topological data analysis, including bootstrap for Betti numbers and the Euler characteristics process.

    12:20–1:50 pmLunch
    Afternoon Session Chair: Stephan Huckemann
    1:50-2:50 pmEzra MillerTitle: Geometric central limit theorems on non-smooth spaces

    Abstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data, such as angles or phylogenetic trees, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures, correct analogues of Gaussian random variables, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers, starting with a review of the usual linear CLT and its generalization to smooth manifolds, viewed through a lens that casts the singular CLT as a natural outgrowth, and concluding with how this investigation opens gateways to further advances in geometric probability, topology, and statistics. Joint work with Jonathan Mattingly and Do Tran.

    2:50-3:00 pmBreak
    3:00-4:00 pmLizhen LinTitle: Statistical foundations of deep generative models

    Abstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in empirical performance, theoretical understanding of such models is largely lacking. We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates, and ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session

     

     

     

    Wednesday, March 1, 2023 (Eastern Time)

    8:30-9:00 amBreakfast
    Morning Session Chair: Ezra Miller
    9:00-10:00 amAmit Singer*Title: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning

    Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.

    10:00-10:10 amBreak
    10:10-11:10 amIan DrydenTitle: Statistical shape analysis of molecule data

    Abstract: Molecular shape data arise in many applications, for example high dimension low sample size cryo-electron microscopy (cryo-EM) data and large temporal sequences of peptides from molecular dynamics simulations. In both applications it is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D sub-shape spaces and provide some practical fitting algorithms. The methodology is applied to cryo-EM data of a large sliding clamp multi-protein complex and to cluster analysis of peptides, where different states of the molecules can be identified. Further molecular modeling tasks include resolution matching, where coarse resolution models are back-mapped into high resolution (atomistic) structures. This is joint work with Kwang-Rae Kim, Charles Laughton and Huiling Le.

    11:10-11:20 amBreak
    11:20 am-12:20 pmTamara BroderickTitle: An Automatic Finite-Sample Robustness Metric: Can Dropping a Little Data Change Conclusions?

    Abstract: One hopes that data analyses will be used to make beneficial decisions regarding people’s health, finances, and well-being. But the data fed to an analysis may systematically differ from the data where these decisions are ultimately applied. For instance, suppose we analyze data in one country and conclude that microcredit is effective at alleviating poverty; based on this analysis, we decide to distribute microcredit in other locations and in future years. We might then ask: can we trust our conclusion to apply under new conditions? If we found that a very small percentage of the original data was instrumental in determining the original conclusion, we might not be confident in the stability of the conclusion under new conditions. So we propose a method to assess the sensitivity of data analyses to the removal of a very small fraction of the data set. Analyzing all possible data subsets of a certain size is computationally prohibitive, so we provide an approximation. We call our resulting method the Approximate Maximum Influence Perturbation. Our approximation is automatically computable, theoretically supported, and works for common estimators. We show that any non-robustness our method finds is conclusive. Empirics demonstrate that while some applications are robust, in others the sign of a treatment effect can be changed by dropping less than 0.1% of the data — even in simple models and even when standard errors are small.

     12:20-1:50 pmLunch
    Afternoon Session Chair: Ezra Miller
    1:50-2:50 pmNicolai Reshetikhin*Title: Random surfaces in exactly solvable models in statistical mechanics.

    Abstract: In the first part of the talk I will be an overview of a few models in statistical mechanics where a random variable is a geometric object such as a random surface or a random curve. The second part will be focused on the behavior of such random surfaces in the thermodynamic limit and on the formation of the so-called “limit shapes”.

    2:50-3:00 pmBreak
    3:00-4:00 pmSebastian KurtekTitle: Robust Persistent Homology Using Elastic Functional Data Analysis

    Abstract: Persistence landscapes are functional summaries of persistence diagrams designed to enable analysis of the diagrams using tools from functional data analysis. They comprise a collection of scalar functions such that birth and death times of topological features in persistence diagrams map to extrema of functions and intervals where they are non-zero. As a consequence, variation in persistence diagrams is encoded in both amplitude and phase components of persistence landscapes. Through functional data analysis of persistence landscapes, under an elastic Riemannian metric, we show how meaningful statistical summaries of persistence landscapes (e.g., mean, dominant directions of variation) can be obtained by decoupling their amplitude and phase variations. This decoupling is achieved via optimal alignment, with respect to the elastic metric, of the persistence landscapes. The estimated phase functions are tied to the resolution parameter that determines the filtration of simplicial complexes used to construct persistence diagrams. For a dataset obtained under geometric, scale and sampling variabilities, the phase function prescribes an optimal rate of increase of the resolution parameter for enhancing the topological signal in a persistence diagram. The proposed approach adds to the statistical analysis of data objects with rich structure compared to past studies. In particular, we focus on two sets of data that have been analyzed in the past, brain artery trees and images of prostate cancer cells, and show that separation of amplitude and phase of persistence landscapes is beneficial in both settings. This is joint work with Dr. James Matuk (Duke University) and Dr. Karthik Bharath (University of Nottingham).

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session
    5:10-5:20 pmStephan Huckemann, Ezra Miller, Zhigang YaoClosing Remarks

    * Virtual Presentation


     

  • Algebraic Geometry in String Theory Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 02.24.2023

    Algebraic Geometry in String Theory Seminar

    Speaker: Chao-Ming Lin (University of California, Irvine)

    Title: On the convexity of general inverse $\sigma_k$ equations and some applications

    Abstract: In this talk, I will show my recent work on general inverse $\sigma_k$ equations and the deformed Hermitian-Yang-Mills equation (hereinafter the dHYM equation). First, I will show my recent results. This result states that if a level set of a general inverse $\sigma_k$ equation (after translation if needed) is contained in the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the Monge-Ampère equation, the J-equation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special class of univariate polynomials and give a Positivstellensatz type result. These give a numerical criterion to verify whether the level set will be contained in the positive orthant. Last, as an application, I will prove one of the conjectures by Collins-Jacob-Yau when the dimension equals four. This conjecture states that under the supercritical phase assumption, if there exists a C-subsolution to the dHYM equation, then the dHYM equation is solvable.

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Geodesics and minimal surfaces

    9:00 am-10:00 am
    12/01/2024
    20220209_Andre-Neves_poster

    Abstract: There are several properties of closed geodesics which are proven using its Hamiltonian formulation, which has no analogue for minimal surfaces. I will talk about some recent progress in proving some of these properties for minimal surfaces.

  • Colloquium
    9:00 am-10:00 am
    12/01/2024
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Camillo De Lellis (IAS)

    Title: Area-minimizing integral currents and their regularity

    Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will also touch upon several fundamental open problems which still defy our understanding. 

    Talk Chair: William Minicozzi

    Video

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Rational Polypols

    9:00 am-10:00 am
    12/01/2024

    Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics, positive geometries are real semialgebraic sets together with a rational canonical form. We combine these two worlds by providing an explicit formula for the canonical form of a rational polypol in terms of defining equations of the adjoint curve and the facets of the polypol. For the special case of polygons, we show that the adjoint curve is hyperbolic and provide an explicit description of its nested ovals. Finally, we discuss the map that associates the adjoint curve to a given rational polypol, in particular the cases where this map is finite. For instance, using monodromy we find that a general quartic curve is the adjoint of 864 heptagons.

    This talk is based on joint work with R. Piene, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn,  M.-S. Sorea, and S. Telen.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Greedy maximal independent sets via local limits

    9:00 am-10:00 am
    12/01/2024

    Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge.

    In this talk, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs, such as paths and various random graphs, and by providing new results for other models such as random trees.

    If time allows, I will discuss a more delicate (and combinatorial) result, according to which, in expectation, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order.

    The talk is based on joint work with Michael Krivelevich, Tamás Mészáros and Clara Shikhelman.

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Theorems of Torelli type

    9:00 am-10:30 am
    12/01/2024
    Lecture_Looijenga-pdf

    Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University)

    Title: Theorems of Torelli type

    Abstract: Given a closed manifold of even dimension 2n, then Hodge showed around 1950 that a  kählerian complex structure on that manifold determines a decomposition of its complex cohomology. This decomposition, which can potentially vary continuously with the complex structure, extracts from a non-linear given,  linear data. It can contain a lot of information. When there is essentially no loss of data in this process, we say that the Torelli theorem holds.  We review the underlying theory and then survey some cases where this is the case. This will include the classical case n=1, but the emphasis will be on K3 manifolds (n=2) and more generally, on hyperkählerian manifolds. These cases stand out, since one can then also tell which decompositions occur.

    Talk chair: Gerard van der Geer

    Video 

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Yang Qi (Fudan)

    Title: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon

    Abstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon, leading to a significant broadening of the single-particle spectral functions. Quantitatively, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.

    https://www.youtube.com/watch?v=p1q0ots1X5s&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=20

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 10.12.22

    Topological Quantum Matter Seminar

    Speaker: Jennifer Cano (Stony Brook and Flatiron Institute)

    Title: Engineering topological phases with a superlattice potential
    Abstract: We propose an externally imposed superlattice potential as a platform for manipulating topological phases, which has both advantages and disadvantages compared to a moire superlattice. In the first example, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long sought-after goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example, we show that a superlattice potential applied to Bernal-stacked bilayer graphene can generate flat Chern bands, similar to in twisted bilayer graphene, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry, making it a promising alternative to achieve designer flat bands without a moire heterostructure.
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    10/5/2021 Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    Title: Geodesic Geometry on Graphs

    Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

    We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

    Joint work with Nati Linial.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Federico Bonetti (Oxford)

    Title: Non-Invertible Symmetries from Holography and Branes

    Abstract:  The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects, and of their action on extended operators of the 4d QFT.

    https://www.youtube.com/watch?v=opvlpWdTXr4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=21

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Junkai Dong (Harvard University)

    Title: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

    Abstract: Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

     

    https://www.youtube.com/watch?v=RfUKlzKs70o&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=23

  • Workshop
    9:00 am-3:30 pm
    12/01/2024-12/01/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Videos are available on the CMSA Youtube Playlist.

    On November 28 – Dec 1, 2022, the CMSA hosted a Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.

    Organizers: An Huang (Brandeis University) | Siu-Cheong Lau (Boston University) | Tsung-Ju Lee (CMSA, Harvard) | Andrew Linshaw (University of Denver)

    Scientific Advisor: Shing-Tung Yau (Harvard, Tsinghua)

    Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

    Directions and Recommended Lodging

    The conference was held in hybrid format, both in-person and online.

    The workshop was partially supported by Simons and NSF Grant DMS-2227199.

     

    Speakers: 

    • Tomoyuki Arakawa (Kyoto)
    • Thomas Creutzig (Edmonton)
    • Jonathan Mboyo Esole (Northeastern)
    • Fei Han (National University of Singapore)
    • Shinobu Hosono (Gakushuin University)
    • Flor Orosz Hunziker (Colorado)
    • Cuipo Jiang (Shanghai)
    • Shashank Kanade (Denver)
    • Matt Kerr (Washington University in St. Louis)
    • Carl Lian (Humboldt-Universität zu Berlin)
    • Nai-Chung Conan Leung (CUHK)
    • Ivan Loseu (Yale)
    • Robert McRae (Tsinghua University)
    • Anne Moreau (Université Paris-Saclay, Orsay)
    • Tony Pantev (University of Pennsylvania)
    • Mauricio Romo (Tsinghua University)
    • Bailin Song (USTC)
    • Cumrun Vafa (Harvard University)
    • Chin-Lung Wang (National Taiwan University)
    • Weiqiang Wang (Virginia)
    • Yaping Yang (University of Melbourne)
    • Shing-Tung Yau (Tsinghua University)
    • Chenglong Yu (Tsinghua University)
    • Gufang Zhao (University of Melbourne)

     

    Schedule (Eastern Time)

    Schedule (pdf)

    11/28 (Monday)

    08:30am – 08:55amRefreshments
    08:55am – 09:00amOpening remarks by Horng-Tzer Yau
    09:00am – 09:45amShing-Tung Yau*Title: The Hull-Strominger system through conifold transitions

    Abstract: In this talk I discuss the geometry of C-Y manifolds outside of the Kähler regime and especially describe the Hull-Strominger system through the conifold transitions.

    10:00am – 10:45amChenglong Yu*Title: Commensurabilities among Lattices in PU(1,n)

    Abstract: In joint work with Zhiwei Zheng, we study commensurabilities among certain subgroups in PU(1,n). Those groups arise from the monodromy of hypergeometric functions. Their discreteness and arithmeticity are classified by Deligne and Mostow. Thurston also obtained similar results via flat conic metrics. However, the classification of the lattices among them up to conjugation and finite index (commensurability) is not completed. When n=1, it is the commensurabilities of hyperbolic triangles. The cases of n=2 are almost resolved by Deligne-Mostow and Sauter’s commensurability pairs, and commensurability invariants by Kappes-Möller and McMullen. Our approach relies on the study of some higher dimensional Calabi-Yau type varieties instead of complex reflection groups. We obtain some relations and commensurability indices for higher n and also give new proofs for existing pairs in n=2.

    11:00am – 11:45amThomas Creutzig*Title: Shifted equivariant W-algebras

    Abstract: The CDO of a compact Lie group is a family of VOAs whose top level is the space of functions on the Lie group. Similar structures appear at the intersections of boundary conditions in 4-dimensional gauge theories, I will call these new families of VOAs shifted equivariant W-algebras. I will introduce these algebras, construct them and explain how they can be used to quickly prove the GKO-coset realization of principal W-algebras.

    11:45am – 1:30 pmLunch
    01:30pm – 02:15pmCumrun VafaTitle: Reflections on Mirror Symmetry

    Abstract: In this talk I review some of the motivations leading to the search and discovery of mirror symmetry as well as some of the applications it has had.

    02:30pm – 03:15pmJonathan Mboyo EsoleTitle: Algebraic topology and matter representations in F-theory

    Abstract: Recently, it was observed that representations appearing in geometric engineering in F-theory all satisfy a unique property: they correspond to characteristic representations of embedding of Dynkin index one between Lie algebras. However, the reason why that is the case is still being understood. In this talk, I will present new insights, giving a geometric explanation for this fact using K-theory and the topology of Lie groups and their classifying spaces. In physics, this will be interpreted as conditions on the charge of instantons and the classifications of Wess-Zumino-Witten terms.

    03:15pm – 03:45 pmBreak
    03:45pm – 04:30pmWeiqiang WangTitle: A Drinfeld presentation of affine i-quantum groups

    Abstract: A quantum symmetric pair of affine type (U, U^i) consists of a Drinfeld-Jimbo affine quantum group (a quantum deformation of a loop algebra) U and its coideal subalgebra U^i (called i-quantum group). A loop presentation for U was formulated by Drinfeld and proved by Beck. In this talk, we explain how i-quantum groups can be viewed as a generalization of quantum groups, and then we give a Drinfeld type presentation for the affine quasi-split i-quantum group U^i. This is based on joint work with Ming Lu (Sichuan) and Weinan Zhang (Virginia).

    04:45pm – 05:30pmTony PantevTitle: Decomposition, anomalies, and quantum symmetries

    Abstract: Decomposition is a phenomenon in quantum physics which converts quantum field theories with non-effectively acting gauge symmetries into equivalent more tractable theories in which the fields live on a disconnected space. I will explain the mathematical content of decomposition which turns out to be a higher categorical version of Pontryagin duality. I will examine how this duality interacts with quantum anomalies and secondary quantum symmetries and will show how the anomalies can be canceled by homotopy coherent actions of diagrams of groups. I will discuss in detail the case of 2-groupoids which plays a central role in anomaly cancellation, and will describe a new duality operation that yields decomposition in the presence of anomalies. The talk is based on joint works with Robbins, Sharpe, and Vandermeulen.

     

    11/29 (Tuesday)

     

    Refreshments
    09:00am – 09:45amRobert MacRae*Title: Rationality for a large class of affine W-algebras

    Abstract: One of the most important results in vertex operator algebras is Huang’s theorem that the representation category of a “strongly rational” vertex operator algebra is a semisimple modular tensor category. Conversely, it has been conjectured that every (unitary) modular tensor category is the representation category of a strongly rational (unitary) vertex operator algebra. In this talk, I will describe my results on strong rationality for a large class of affine W-algebras at admissible levels. This yields a large family of modular tensor categories which generalize those associated to affine Lie algebras at positive integer levels, as well as those associated to the Virasoro algebra.

    10:00am – 10:45amBailin Song*Title: The global sections of chiral de Rham complexes on compact Calabi-Yau manifolds

    Abstract: Chiral de Rham complex is a sheaf of vertex algebras on a complex manifold. We will describe the space of global sections of the chiral de Rham complexes on compact Calabi-Yau manifolds.

    11:00am – 11:45amCarl Lian*Title: Curve-counting with fixed domain

    Abstract: The fixed-domain curve-counting problem asks for the number of pointed curves of fixed (general) complex structure in a target variety X subject to incidence conditions at the marked points. The question comes in two flavors: one can ask for a virtual count coming from Gromov-Witten theory, in which case the answer can be computed (in principle) from the quantum cohomology of X, or one can ask for the “honest” geometric count, which tends to be more subtle. The answers are conjectured to agree in the presence of sufficient positivity, but do not always. I will give an overview of some recent results and open directions. Some of this work is joint with Alessio Cela, Gavril Farkas, and Rahul Pandharipande.

    11:45am – 01:30pmLunch
    01:30pm – 02:15pmChin-Lung WangTitle: A blowup formula in quantum cohomology

    Abstract: We study analytic continuations of quantum cohomology $QH(Y)$ under a blowup $\phi: Y \to X$ of complex projective manifolds along the extremal ray variable $q^{\ell}$. Under $H(Y) = \phi^* H(X) plus K$ where $K = \ker \phi_*$, we show that (i) the restriction of quantum product along the $\phi^*H(X)$ direction, denoted by $QH(Y)_X$, is meromorphic in $x := 1/q^\ell$, (ii) $K$ deforms uniquely to a quantum ideal $\widetilde K$ in $QH(Y)_X$, (iii) the quotient ring $QH(Y)_X/\widetilde K$ is regular over $x$, and its restriction to $x = 0$ is isomorphic to $QH(X)$. This is a joint work (in progress) with Y.-P. Lee and H.-W. Lin.

    02:30pm – 03:15pmIvan LoseuTitle: Quantizations of nilpotent orbits and their Lagrangian subvarieties

    Abstract: I’ll report on some recent progress on classifying quantizations of the algebras of regular functions of nilpotent orbits (and their covers) in semisimple Lie algebras, as well as the classification of quantizations of certain Lagrangian subvarieties. An ultimate goal here is to understand the classification of unitary representations of real semisimple Lie groups.

    03:15pm – 03:45pmBreak
    03:45pm – 04:30pmMatt Kerr*Title: $K_2$ and quantum curves

    Abstract: The basic objects for this talk are motives consisting of a curve together with a $K_2$ class, and their mixed Hodge-theoretic invariants.

    My main objective will be to explain a connection (recently proved in joint work with C. Doran and S. Sinha Babu) between (i) Hodge-theoretically distinguished points in the moduli of such motives and (ii) eigenvalues of operators on L^2(R) obtained by quantizing the equations of the curves.

    By local mirror symmetry, this gives evidence for a conjecture in topological string theory (due to M. Marino, A. Grassi, and others) relating enumerative invariants of toric CY 3-folds to spectra of quantum curves.

    04:45pm – 05:30pmFlor Orosz HunzikerTitle: Tensor structures associated to the N=1 super Virasoro algebra

    Abstract:  We have recently shown that there is a natural category of representations associated to the N=1 super Virasoro vertex operator algebras that have braided tensor structure. We will describe this category and discuss the problem of establishing its rigidity at particular central charges. This talk is based on joint work in progress with Thomas Creutzig, Robert McRae and Jinwei Yang.

     

     

     

    11/30 (Wednesday)

    08:30am – 09:00amRefreshments
    09:00am – 09:45amTomoyuki ArakawaTitle: 4D/2D duality and representation theory

    Abstract: This talk is about the 4D/2D duality discovered by Beem et al. rather recently in physics. It associates a vertex operator algebra (VOA) to any 4-dimensional superconformal field theory, which is expected to be a complete invariant of thl theory. The VOAs appearing in this manner may be regarded as chiralization of various symplectic singularities and their representations are expected to be closely related with the Coulomb branch of the 4D theory. I will talk about this remarkable 4D/2D duality from a representation theoretic perspective.

    10:00am – 10:45amShashank KanadeTitle: Combinatorics of principal W-algebras of type A

    Abstract: The combinatorics of principal W_r(p,p’) algebras of type A is controlled by cylindric partitions. However, very little seems to be known in general about fermionic expressions for the corresponding characters. Welsh’s work explains the case of Virasoro minimal models W_2(p,p’). Andrews, Schilling and Warnaar invented and used an A_2 version of the usual (A_1) Bailey machinery to give fermionic characters (up to a factor of (q)_\infty) of some, but not all, W_3(3,p’) modules. In a recent joint work with Russell, we have given a complete set of conjectures encompassing all of the remaining modules for W_3(3,p’), and proved our conjectures for small values of p’. In another direction, characters of W_r(p,p’) algebras also arise as appropriate limits of certain sl_r coloured Jones invariants of torus knots T(p,p’), and we expect this to provide further insights on the underlying combinatorics.

    11:00am – 11:45amGufang ZhaoTitle: Quasimaps to quivers with potentials

    Abstract: This talk concerns non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of the potential. The construction borrows ideas from the theory of gauged linear sigma models as well as recent development in shifted symplectic geometry and Donaldson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual counts arising from quivers with potentials are discussed. This is based on work in progress, in collaboration with Yalong Cao.

    11:45am – 01:30pmGroup Photo, Lunch
    01:30pm – 02:15pmYaping YangTitle: Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

    Abstract: Let X be a smooth local toric Calabi-Yau 3-fold. On the cohomology of the moduli spaces of certain sheaves on X, there is an action of the cohomological Hall algebra (COHA) of Kontsevich and Soibelman via “raising operators”. I will discuss the “double” of the COHA that acts on the cohomology of the moduli space by adding the “lowering operators”. We associate a root system to X. The double COHA is expected to be the shifted Yangian of this root system. We also give a prediction for the shift in terms of an intersection pairing. We provide evidence of the aforementioned expectation in various examples. This is based on my joint work with M. Rapcak, Y. Soibelman, and G. Zhao

    02:30pm – 03:15pmFei HanTitle: Graded T-duality with H-flux for 2d sigma models

    Abstract: T-duality in string theory can be realised as a transformation acting on the worldsheet fields in the two-dimensional nonlinear sigma model. Bouwknegt-Evslin-Mathai established the T-duality in a background flux for the first time upon compactifying spacetime in one direction to a principal circle by constructing the T-dual maps transforming the twisted cohomology of the dual spacetimes. In this talk, we will describe our recent work on how to promote the T-duality maps of Bouwknegt-Evslin-Mathai in two aspects. More precisely, we will introduce (1) graded T-duality, concerning the graded T-duality maps of all levels of twistings; (2) the 2-dimensional sigma model picture, concerning the double loop space of spacetimes. This represents our joint work with Mathai.

    03:15pm – 3:45pmBreak
    03:45pm – 04:30pmMauricio RomoTitle: Networks and BPS Counting: A-branes view point

    Abstract: I will review the countings of BPS invariants via exponential/spectral networks and present an interpretation of this counting as a count of certain points in the moduli space of A-branes corresponding to degenerate Lagrangians.

    04:45pm – 05:30pmShinobu HosonoTitle: Mirror symmetry of abelian fibered Calabi-Yau manifolds with ρ = 2

    Abstract: I will describe mirror symmetry of Calabi-Yau manifolds fibered by (1,8)-polarized abelian surfaces, which have Picard number two. Finding a mirror family over a toric variety explicitly, I  observe that mirror symmetry of all related Calabi-Yau manifods arises from the corresponding boundary points, which are not necessarily toric boundary points.  Calculating Gromov-Witten invariants up to genus 2, I find that the generating functions are expressed elliptic (quasi-)modular forms, which reminds us the modular anomaly equation found for elliptic surfaces. This talk is based on a published work with Hiromichi Takaki (arXiv:2103.08150).

    06:00pmBanquet @ Royal East Restaurant, 782 Main St, Cambridge, MA 02139

     

    12/1 (Thursday)

    08:30am – 09:00amRefreshments
    09:00am – 09:45amConan Nai Chung Leung*Title: Quantization of Kahler manifolds

    Abstract: I will explain my recent work on relationships among geometric quantization, deformation quantization, Berezin-Toeplitz quantization and brane quantization.

    10:00am – 10:45amCuipo Jiang*Title: Cohomological varieties associated to vertex operator algebras

    Abstract: We define and examine the cohomological variety of a vertex algebra, a notion cohomologically dual to that of the associated variety, which measures the smoothness of the associated scheme at the vertex point.  We study its basic properties. As examples, we construct a closed subvariety of the cohomological variety for rational affine vertex operator algebras constructed from finite dimensional simple Lie algebras. We also determine the cohomological varieties of the simple Virasoro vertex operator algebras. These examples indicate that, although the associated variety for a rational $C_2$-cofinite vertex operator algebra is always a simple point, the cohomological variety can have as large a dimension as possible. This talk is based on joint work with Antoine Caradot and Zongzhu Lin.

    11:00am – 11:45amAnne Moreau*Title: Action of the automorphism group on the Jacobian of Klein’s quartic curve

    Abstract: In a joint work with Dimitri Markouchevitch, we prove that the quotient variety of the 3-dimensional Jacobian of the plane Klein quartic curve by its full automorphism group of order 336 is isomorphic to the 3-dimensional weighted projective space with weights 1,2,4,7.

    The latter isomorphism is a particular case of the general conjecture of Bernstein and Schwarzman suggesting that a quotient of the n-dimensional complex space by the action of an irreducible complex crystallographic group generated by reflections is a weighted projective space.

    In this talk, I will explain this conjecture and the proof of our result. An important ingredient is the computation of the Hilbert function of the algebra of invariant theta-functions on the Jacobian.

    11:45am – 11:50amClosing remarks
    11:50amFree discussions and departure

    * = Online speaker

    CMSA COVID-19 Policies

     

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 11.23.22

    Topological Quantum Matter Seminar

    Speaker: Jian Kang, School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

    Title: Continuum field theory of graphene bilayer system

    Abstract: The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the magic-angle twisted bilayer graphene (MATBG), and nowadays is a starting point for most theoretical works. In this talk, I will briefly review the BM model and then present a continuum field theory [1] for graphene bilayer system allowing any smooth lattice deformation including the small twist angle. With the gradient expansion to the second order, the continuum theory for MATBG [2] produces the spectrum that almost perfectly matches the spectrum of the microscopic model, suggesting the validity of this theory. In the presence of the lattice deformation, the inclusion of the pseudo-vector potential does not destroy but shift the flat band chiral limit to a smaller twist angle. Furthermore, the continuum theory contains another important interlayer tunneling term that was overlooked in all previous works. This term non-negligibly breaks the particle-hole symmetry of the narrow bands and may be related with the experimentally observed particle-hole asymmetry.

    1. O. Vafek and JK, arXiv: 2208.05933.
    2. JK and O. Vafek, arXiv: 2208.05953.

     

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Sungwoo Hong (U Chicago & KAIST)

    Title: Neutrino Masses from Generalized Symmetry Breaking

    Abstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

     

    https://www.youtube.com/watch?v=4eZa06kiPCs&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=22

  • Program
    9:00 am-5:00 pm
    12/01/2024-05/24/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Mathematical Aspects of Scattering Amplitudes Program

    To receive email updates and program announcements, visit this link to sign up for the CMSA Mathematical Aspects of Scattering Amplitudes Program mailing list.

    Dates: April 15 – May 24, 2024

    Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138

    Organizers:

    Participants:

    This program will feature a weekly seminar series.
    Further Details TBA.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Justin Kulp (Perimeter Institute)

    Title: Holomorphic Twists and Confinement in N=1 SYM

    Abstract: Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

  • Workshop
    9:00 am-5:00 pm
    12/01/2024-05/05/2022
    GR Workshop Poster

    General Relativity Workshop on scalar curvature, minimal surfaces, and initial data sets

    Dates: May 2–5, 2022

    Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138 and via Zoom webinar.
    Advanced registration for in-person components is required.

    Organizers: Dan Lee (CMSA/CUNY), Martin Lesourd (CMSA/BHI), and Lan-Hsuan Huang (University of Connecticut).

    Speakers:

    • Zhongshan An, University of Connecticut
    • Paula Burkhardt-Guim, NYU
    • Hyun Chul Jang, University of Miami
    • Chao Li, NYU
    • Christos Mantoulidis, Rice University
    • Robin Neumayer, Carnegie Mellon University
    • Andre Neves, University of Chicago
    • Tristan Ozuch, MIT
    • Annachiara Piubello, University of Miami
    • Antoine Song, UC Berkeley
    • Tin-Yau Tsang, UC Irvine
    • Ryan Unger, Princeton
    • Zhizhang Xie, Texas A & M
    • Xin Zhou, Cornell University
    • Jonathan Zhu, Princeton University

    Schedule

    Download PDF

    Monday, May 2, 2022

    9:30–10:30 amHyun Chul JangTitle: Mass rigidity for asymptotically locally hyperbolic manifolds with boundary

    Abstract: Asymptotically locally hyperbolic (ALH) manifolds are a class of manifolds whose sectional curvature converges to −1 at infinity. If a given ALH manifold is asymptotic to a static reference manifold, the Wang-Chruściel-Herzlich mass integrals are well-defined, which is a geometric invariant that essentially measure the difference from the reference manifold. In this talk, I will present the result that an ALH manifold which minimize the mass integrals admits a static potential. To show this, we proved the scalar curvature map is locally surjective when it is defined on (1) the space of ALH metrics that coincide exponentially toward the boundary or (2) the space of ALH metrics with arbitrarily prescribed nearby Bartnik boundary data. And then, we establish the rigidity of the known positive mass theorems by studying the static uniqueness. This talk is based on joint work with L.-H. Huang.

    10:40–11:40 amAnnachiara PiubelloTitle: Estimates on the Bartnik mass and their geometric implications.

    Abstract: In this talk, we will discuss some recent estimates on the Bartnik mass for data with non-negative Gauss curvature and positive mean curvature. In particular, if the metric is round the estimate reduces to an estimate found by Miao and if the total mean curvature approaches 0, the estimate tends to 1/2 the area radius, which is the bound found by Mantoulidis and Schoen in the blackhole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.

    LUNCH BREAK
    1:30–2:30 pmRyan UngerTitle: Density and positive mass theorems for black holes and incomplete manifolds

    Abstract: We generalize the density theorems for the Einstein constraint equations of Corvino-Schoen and Eichmair-Huang-Lee-Schoen to allow for marginally outer trapped boundaries (which correspond physically to apparent horizons). As an application, we resolve the spacetime positive mass theorem in the presence of MOTS boundary in the non-spin case. This also has a surprising application to the Riemannian setting, including a non-filling result for manifolds with negative mass. This is joint work with Martin Lesourd and Dan Lee.

    2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications I

    Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

    TEA BREAK
    4:10–5:10 pmAntoine Song (virtual)Title: The spherical Plateau problem

    Abstract: For any closed oriented manifold with fundamental group G, or more generally any group homology class for a group G, I will discuss an infinite codimension Plateau problem in a Hilbert classifying space for G. For instance, for a closed oriented 3-manifold M, the intrinsic geometry of any Plateau solution is given by the hyperbolic part of M.

    Tuesday, May 3, 2022

    9:30–10:30 amChao LiTitle: Stable minimal hypersurfaces in 4-manifolds

    Abstract: There have been a classical theory for complete minimal surfaces in 3-manifolds, including the stable Bernstein conjecture in R^3 and rigidity results in 3-manifolds with positive Ricci curvature. In this talk, I will discuss how one may extend these results in four dimensions. This leads to new comparison theorems for positively curved 4-manifolds.

    10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds I

    Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

    LUNCH BREAK
    1:30–2:30 pmZhongshan AnTitle: Local existence and uniqueness of static vacuum extensions of Bartnik boundary data

    Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data — the induced metric and mean curvature of the boundary — is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang.

    2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications II

    Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

    TEA BREAK
    4:10–5:10 pmTin-Yau TsangTitle: Dihedral rigidity, fill-in and spacetime positive mass theorem

    Abstract: For compact manifolds with boundary, to characterise the relation between scalar curvature and boundary geometry, Gromov proposed dihedral rigidity conjecture and fill-in conjecture. In this talk, we will see the role of spacetime positive mass theorem in answering the corresponding questions for initial data sets.

    Speakers Banquet

    Wednesday, May 4, 2022

    9:30–10:30 amTristan OzuchTitle: Weighted versions of scalar curvature, mass and spin geometry for Ricci flows

    Abstract: With A. Deruelle, we define a Perelman-like functional for ALE metrics which lets us study the (in)stability of Ricci-flat ALE metrics. With J. Baldauf, we extend some classical objects and formulas from the study of scalar curvature, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.

    10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds II

    Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

    LUNCH BREAK
    1:30–2:30 pmChristos MantoulidisTitle: Metrics with lambda_1(-Delta+kR) > 0 and applications to the Riemannian Penrose Inequality

    Abstract: On a closed n-dimensional manifold, consider the space of all Riemannian metrics for which -Delta+kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally, for different values of k, in the study of scalar curvature in dimension n + 1 via minimal surfaces, the Yamabe problem in dimension n, and Perelman’s surgery for Ricci flow in dimension n = 3. We study these spaces in unison and generalize, as appropriate, scalar curvature results that we eventually apply to k = 1/2, where the space above models apparent horizons in time-symmetric initial data sets to the Einstein equations and whose flexibility properties are intimately tied with the instability of the Riemannian Penrose Inequality. This is joint work with Chao Li.

    2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications III

    Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

    TEA BREAK
    4:10–5:10 pmXin Zhou
    (Virtual)
    Title: Min-max minimal hypersurfaces with higher multiplicity

    Abstract: It is well known that minimal hypersurfaces produced by the Almgren-Pitts min-max theory are counted with integer multiplicities. For bumpy metrics (which form a generic set), the multiplicities are one thanks to the resolution of the Marques-Neves Multiplicity One Conjecture. In this talk, we will exhibit a set of non-bumpy metrics on the standard (n+1)-sphere, in which the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere. Such non-bumpy metrics form the first set of examples where the min-max theory must produce higher multiplicity minimal hypersurfaces. The talk is based on a joint work with Zhichao Wang (UBC).

    May 5, 2022

    9:00–10:00 amAndre NevesTitle: Metrics on spheres where all the equators are minimal

    Abstract: I will talk about joint work with Lucas Ambrozio and Fernando Marques where we study the space of metrics where all the equators are minimal.

    10:10–11:10 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds III

    Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

    11:20–12:20 pmPaula Burkhardt-GuimTitle: Lower scalar curvature bounds for C^0 metrics: a Ricci flow approach

    Abstract: We describe some recent work that has been done to generalize the notion of lower scalar curvature bounds to C^0 metrics, including a localized Ricci flow approach. In particular, we show the following: that there is a Ricci flow definition which is stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C^0 initial data.

    LUNCH BREAK
    1:30–2:30 pmJonathan ZhuTitle: Widths, minimal submanifolds and symplectic embeddings

    Abstract: Width or waist inequalities measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels.

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.26.2022-1583x2048-1

    Abstract: In spatial population genetics, it is important to understand the probability of extinction in multi-species interactions such as growing bacterial colonies, cancer tumor evolution and human migration. This is because extinction probabilities are instrumental in determining the probability of coexistence and the genealogies of populations. A key challenge is the complication due to spatial effect and different sources of stochasticity. In this talk, I will discuss about methods to compute the probability of extinction and other long-time behaviors for stochastic reaction-diffusion equations on metric graphs that flexibly parametrizes the underlying space. Based on recent joint work with Adrian Gonzalez-Casanova and Yifan (Johnny) Yang.

  • Colloquium

    Colloquium Colloquia & Seminar
    Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a seminar on Combinatorics, Physics and Probability, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu).

    The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/25/2022
    *note special time 9:00–10:00 AM ET
    Jacob Bourjaily (Penn State University, Eberly College of ScienceTitle: Adventures in Perturbation Theory

    Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

    2/3/2022Ran Tessler
    (Weizmann Institute of Science)
    Title: The Amplituhedron BCFW Triangulation

    Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

    2/8/2022Anna Seigal (Harvard)Title: Invariant theory for maximum likelihood estimation

    Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

    2/15/2022Igor Balla, Hebrew University of JerusalemTitle: Equiangular lines and regular graphs

    Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

    Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
    the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/21/2021Nima Arkani-Hamed
    IAS (Institute for Advanced Study), School of Natural Sciences
    Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes
    9/28/2021Melissa Sherman-Bennett
    University of Michigan, Department of Mathematics
    Title: The hypersimplex and the m=2 amplituhedron

    Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

    10/5/2021Daniel Cizma, Hebrew UniversityTitle: Geodesic Geometry on Graphs

    Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

    We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

    Joint work with Nati Linial.

    10/12/2021Lisa Sauermann, MITTitle: On counting algebraically defined graphs

    Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

    10/19/2021Pavel Galashin
    UCLA, Department of Mathematics
    Title: Ising model, total positivity, and criticality

    Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
    The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
    I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model.

    10/26/2021Candida Bowtell, University of OxfordTitle: The n-queens problem

    Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

    In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

    This is joint work with Peter Keevash.

    11/9/2021Steven Karp
    Universite du Quebec a Montreal, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)
    Title: Gradient flows on totally nonnegative flag varieties

    Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.
    11/16/2021
    *note special time 12:30–1:30 ET*
    Yinon Spinka (University of British Columbia)Title: A tale of two balloons

    Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
    Joint work with Omer Angel and Gourab Ray.

    11/23/2021Lutz Warnke (UC San Diego)Title: Prague dimension of random graphs

    Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

    11/30/2021Karel Devriendt (University of Oxford)Title: Resistance curvature – a new discrete curvature on graphs

    Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
    In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
    Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
    This work was done in collaboration with Renaud Lambiotte.

    12/7/2021Matthew Jenssen (University of Birmingham)Title: The singularity probability of random symmetric matrices

    Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

    12/14/2021Stefan Glock (ETH Zurich)Title: The longest induced path in a sparse random graph

    Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

    12/21/2021
    01/25/2022Jacob Bourjaily
    Penn State University, Department of Physics
  • Program
    9:00 am-5:00 pm
    12/01/2024-06/12/2022
    CMSA-2-600x338

    The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

    Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

    In this course, we will start with an introduction to computer programming, algorithms, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, and differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

    The program hopes to provide several research mentors from various disciplines who will give some of the course lectures. Students will have the opportunity to work with one of the research mentors offered by the program.

    Prerequisites: Basic coding ability in some programming language (C/Python/Matlab or CS50 experience). Some background in calculus and linear algebra is needed too. If you wish to work with a research mentor on differential geometry, more background in geometry such as from Math 132 or 136 will be useful. If you wish to work with a research mentor on computer science, coding experience mentioned above will be very useful. If you wish to work with a medical scientist, some background in life science or basic organic chemistry is recommended.

    The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

    This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard-related perks (such as a place to live if you are in Boston over the summer.)

    However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third-year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

    If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited, so don’t wait too long to apply.

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.19.22-1583x2048-1

    Abstract: Conditional independence (CI) is an important tool instatistical modeling, as, for example, it gives a statistical interpretation to graphical models. In general, given a list of dependencies among random variables, it is difficult to say which constraints are implied by them. Moreover, it is important to know what constraints on the random variables are caused by hidden variables. On the other hand, such constraints are corresponding to some determinantal conditions on the tensor of joint probabilities of the observed random variables. Hence, the inference question in statistics relates to understanding the algebraic and geometric properties of determinantal varieties such as their irreducible decompositions or determining their defining equations. I will explain some recent progress that arises by uncovering the link to point configurations in matroid theory and incidence geometry. This connection, in particular, leads to effective computational approaches for (1) giving a decomposition for each CI variety; (2) identifying each component in the decomposition as a matroid variety; (3) determining whether the variety has a real point or equivalently there is a statistical model satisfying a given collection of dependencies. The talk is based on joint works with Oliver Clarke, Kevin Grace, and Harshit Motwani.

    The papers are available on arxiv: https://arxiv.org/pdf/2011.02450
    and https://arxiv.org/pdf/2103.16550.pdf

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/22/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Conference
    9:00 am-6:00 pm
    12/01/2024
    150 Western Ave, Allston, MA 02134
    SMaSH_2022-2

    SMaSH: Symposium for Mathematical Sciences at Harvard

    On Tuesday, May 17, 2022, from 9:00 am – 5:30 pm, the Harvard John A Paulson School of Engineering and Applied Sciences (SEAS) and the Harvard Center of Mathematical Sciences and Applications (CMSA) held a Symposium for Mathematical Sciences for the mathematical sciences community at Harvard.

    Organizing Committee

    • Michael Brenner, Applied Mathematics (SEAS)
    • Michael Desai, Organismic and Evolutionary Biology (FAS)
    • Sam Gershman, Psychology (FAS)
    • Michael Hopkins, Mathematics (FAS)
    • Gary King, Government (FAS)
    • Peter Koellner, Philosophy (FAS)
    • Scott Kominers, Economics (FAS) & Entrepreneurial Management (HBS)
    • Xihong Lin, Biostatistics (HSPH) & Statistics (FAS)
    • Yue Lu, Electrical Engineering (SEAS)
    • Susan Murphy, Statistics (FAS) & Computer Science (SEAS)
    • Lisa Randall, Physics (SEAS)
    • Eugene Shakhnovich, Chemistry (FAS)
    • Salil Vadhan, Computer Science (SEAS)
    • Horng-Tzer Yau, Mathematics (FAS)

    This event was held in-person at the Science and Engineering Complex (SEC) at 150 Western Ave, Allston, MA 02134, and streamed on Zoom.

    Harvard graduate students and postdocs presented Poster Sessions.


    Venue: Science and Engineering Complex (SEC)


    Speakers

    • Anurag Anshu, Computer Science (SEAS)
    • Morgane Austern, Statistics (FAS)
    • Demba Ba, Electrical Engineering & Bioengineering (SEAS)
    • Michael Brenner, Applied Mathematics (SEAS)
    • Rui Duan, Biostatistics (HSPH)
    • Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)
    • Kosuke Imai, Government & Statistics (FAS)
    • Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)
    • Seth Neel, Technology & Operations Management (HBS)
    • Melanie Matchett Wood, Mathematics (FAS)

    Schedule PDF

    Schedule

    9:00–9:30 amCoffee and Breakfast
    West Atrium (ground floor of the SEC)
    9:30–10:30 amFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumKosuke Imai, Government & Statistics (FAS): Use of Simulation Algorithms for Legislative Redistricting Analysis and EvaluationYannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS): The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization
    10:30–11:00 amCoffee Break
    West Atrium (ground floor of the SEC)
    11:00–12:00 pmFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumSeth Neel, Technology & Operations Management (HBS): “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy LawDemba Ba, Electrical Engineering & Bioengineering (SEAS): Geometry, AI, and the Brain
    12:00–1:00 pmLunch Break
    Engineering Yard Tent
    1:00–2:30 pmFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMelanie Matchett Wood, Mathematics (FAS): Understanding distributions of algebraic structures through their momentsMorgane Austern, Statistics (FAS): Limit theorems for structured random objectsAnurag Anshu, Computer Science (SEAS): Operator-valued polynomial approximations and their use.
    2:30–3:00 pmCoffee Break
    West Atrium (ground floor of the SEC)
    3:00–4:30 pmFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMichael Brenner, Applied Mathematics (SEAS): Towards living synthetic materialsRui Duan, Biostatistics (HSPH): Federated and transfer learning for healthcare data integrationSham M. Kakade, Computer Science (SEAS) & Statistics (FAS): What is the Statistical Complexity of Reinforcement Learning?
    4:30–5:30 pmReception with Jazz musicians
    & Poster Session
    Engineering Yard Tent

    Faculty Talks

    SpeakerTitle / Abstract / Bio
    Anurag Anshu, Computer Science (SEAS)Title: Operator-valued polynomial approximations and their use.

    Abstract: Approximation of complicated functions with low degree polynomials is an indispensable tool in mathematics. This becomes particularly relevant in computer science, where the complexity of interesting functions is often captured by the degree of the approximating polynomials. This talk concerns the approximation of operator-valued functions (such as the exponential of a hermitian matrix, or the intersection of two projectors) with low-degree operator-valued polynomials. We will highlight the challenges that arise in achieving similarly good approximations as real-valued functions, as well as recent methods to overcome them. We will discuss applications to the ground states in physics and quantum complexity theory: correlation lengths, area laws and concentration bounds.

    Bio: Anurag Anshu is an Assistant Professor of computer science at Harvard University. He spends a lot of time exploring the rich structure of quantum many-body systems from the viewpoint of quantum complexity theory, quantum learning theory and quantum information theory. He held postdoctoral positions at University of California, Berkeley and University of Waterloo and received his PhD from National University of Singapore, focusing on quantum communication complexity.

    Morgane Austern, Statistics (FAS)Title: Limit theorems for structured random objects

    Abstract: Statistical inference relies on numerous tools from probability theory to study the properties of estimators. Some of the most central ones are the central limit theorem and the free central limit theorem. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting. We consider distributionally “structured’ and dependent random object i.e random objects whose distribution is invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory.

    Bio: Morgane Austern is an assistant professor in the Statistics Department of Harvard University. Broadly, she is interested in developing probability tools for modern machine learning and in establishing the properties of learning algorithms in structured and dependent data contexts. She graduated with a PhD in statistics from Columbia University in 2019 where she worked in collaboration with Peter Orbanz and Arian Maleki on limit theorems for dependent and structured data. She was a postdoctoral researcher at Microsoft Research New England from 2019 to 2021.

    Demba Ba, Electrical Engineering & Bioengineering (SEAS)Title: Geometry, AI, and the Brain

    Abstract: A large body of experiments suggests that neural computations reflect, in some sense, the geometry of “the world”. How do artificial and neural systems learn representations of “the world” that reflect its geometry? How, for instance, do we, as humans, learn representations of objects, e.g. fruits, that reflect the geometry of object space? Developing artificial systems that can capture/understand the geometry of the data they process may enable them to learn representations useful in many different contexts and tasks. My talk will describe an artificial neural-network architecture that, starting from a simple union-of-manifold model of data comprising objects from different categories, mimics some aspects of how primates learn, organize, and retrieve concepts, in a manner that respects the geometry of object space.

    Bio: Demba Ba serves as an Associate Professor of electrical engineering and bioengineering in Harvard University’s School of Engineering and Applied Sciences, where he directs the CRISP group. Recently, he has taken a keen interest in the connection between artificial neural networks and sparse signal processing. His group leverages this connection to solve data-driven unsupervised learning problems in neuroscience, to understand the principles of hierarchical representations of sensory signals in the brain, and to develop explainable AI. In 2016, he received a Research Fellowship in Neuroscience from the Alfred P. Sloan Foundation. In 2021, Harvard’s Faculty of Arts and Sciences awarded him the Roslyn Abramson award for outstanding undergraduate teaching.

    Michael Brenner, Applied Mathematics (SEAS)Title: Towards living synthetic materials

    Abstract: Biological materials are much more complicated and functional than synthetic ones. Over the past several years we have been trying to figure out why. A sensible hypothesis is that biological materials are programmable. But we are very far from being able to program materials we create with this level of sophistication.  I will discuss our (largely unsuccessful) efforts to bridge this gap, though as of today I’m somewhat optimistic that we are arriving at a set of theoretical models that is rich enough to produce relevant emergent behavior.

    Bio: I’ve been at Harvard for a long time. My favorite part of Harvard is the students.

    Rui Duan, Biostatistics (HSPH)Title: Federated and transfer learning for healthcare data integration

    Abstract: The growth of availability and variety of healthcare data sources has provided unique opportunities for data integration and evidence synthesis, which can potentially accelerate knowledge discovery and improve clinical decision-making. However, many practical and technical challenges, such as data privacy, high dimensionality, and heterogeneity across different datasets, remain to be addressed. In this talk, I will introduce several methods for the effective and efficient integration of multiple healthcare datasets in order to train statistical or machine learning models with improved generalizability and transferability. Specifically, we develop communication-efficient federated learning algorithms for jointly analyzing multiple datasets without the need of sharing patient-level data, as well as transfer learning approaches that leverage shared knowledge learned across multiple datasets to improve the performance of statistical models in target populations of interest. We will discuss both the theoretical properties and examples of implementation of our methods in real-world research networks and data consortia.

    Bio: Rui Duan is an Assistant Professor of Biostatistics at the Harvard T.H. Chan School of Public Health. She received her Ph.D. in Biostatistics in May 2020 from the University of Pennsylvania. Her research interests focus on developing statistical, machine learning, and informatics tools for (1) efficient data integration in biomedical research, (2) understanding and accounting for the heterogeneity of biomedical data, and improving the generalizability and transferability of models across populations (3) advancing precision medicine research on rare diseases and underrepresented populations.

    Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)Title: The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization

    Abstract: We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε > 0, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples.

    Our fully nonparametric approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that are not necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art.

    Joint work with S. Matthew Weinberg

    Bio: Yannai A. Gonczarowski is an Assistant Professor of Economics and of Computer Science at Harvard University—the first faculty member at Harvard to have been appointed to both of these departments. Interested in both economic theory and theoretical computer science, Yannai explores computer-science-inspired economics: he harnesses approaches, aesthetics, and techniques traditionally originating in computer science to derive economically meaningful insights. Yannai received his PhD from the Departments of Math and CS, and the Center for the Study of Rationality, at the Hebrew University of Jerusalem, where he was advised by Sergiu Hart and Noam Nisan. Yannai is also a professionally-trained opera singer, having acquired a bachelor’s degree and a master’s degree in Classical Singing at the Jerusalem Academy of Music and Dance. Yannai’s doctoral dissertation was recognized with several awards, including the 2018 Michael B. Maschler Prize of the Israeli Chapter of the Game Theory Society, and the ACM SIGecom Doctoral Dissertation Award for 2018. For the design and implementation of the National Matching System for Gap-Year Programs in Israel, he was awarded the Best Paper Award at MATCH-UP’19 and the inaugural INFORMS AMD Michael H. Rothkopf Junior Researcher Paper Prize (first place) for 2020. Yannai is also the recipient of the inaugural ACM SIGecom Award for Best Presentation by a Student or Postdoctoral Researcher at EC’18. His first textbook, “Mathematical Logic through Python” (Gonczarowski and Nisan), which introduces a new approach to teaching the material of a basic Logic course to Computer Science students, tailored to the unique intuitions and strengths of this cohort of students, is forthcoming in Cambridge University Press.

    Kosuke Imai, Government & Statistics (FAS)Title: Use of Simulation Algorithms for Legislative Redistricting Analysis and Evaluation

    Abstract: After the 2020 Census, many states have been redrawing the boundaries of Congressional and state legislative districts. To evaluate the partisan and racial bias of redistricting plans, scholars have developed Monte Carlo simulation algorithms. The idea is to generate a representative sample of redistricting plans under a specified set of criteria and conduct a statistical hypothesis test by comparing a proposed plan with these simulated plans. I will give a brief overview of these redistricting simulation algorithms and discuss how they are used in real-world court cases.

    Bio: Kosuke Imai is Professor in the Department of Government and Department of Statistics at Harvard University. Before moving to Harvard in 2018, Imai taught at Princeton University for 15 years where he was the founding director of the Program in Statistics and Machine Learning. Imai specializes in the development of statistical methods and machine learning algorithms and their applications to social science research. His areas of expertise include causal inference, computational social science, program evaluation, and survey methodology.

    Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)Title: What is the Statistical Complexity of Reinforcement Learning?

    Abstract: This talk will highlight much of the recent progress on the following fundamental question in the theory of reinforcement learning: what (representational or structural) conditions govern our ability to generalize and avoid the curse of dimensionality?  With regards to supervised learning, these questions are reasonably well understood, both practically and theoretically: practically, we have overwhelming evidence on the value of representational learning (say through modern deep networks) as a means for sample efficient learning, and, theoretically, there are well-known complexity measures (e.g. the VC dimension and Rademacher complexity) that govern the statistical complexity of learning.  Providing an analogous theory for reinforcement learning is far more challenging, where even characterizing structural conditions which support sample efficient generalization has been far less well understood, until recently.

    This talk will survey recent advances towards characterizing when generalization is possible in RL, focusing on both necessary and sufficient conditions. In particular, we will introduce a new complexity measure, the Decision-Estimation Coefficient, that is proven to be necessary (and, essentially, sufficient) for sample-efficient interactive learning.

    Bio: Sham Kakade is a professor at Harvard University and a co-director of the Kempner Institute for the Study of Artificial and Natural Intelligence.  He works on the mathematical foundations of machine learning and AI. Sham’s thesis helped lay the statistical foundations of reinforcement learning. With his collaborators, his additional contributions include foundational results on: policy gradient methods in reinforcement learning; regret bounds for linear bandit and Gaussian process bandit models; the tensor and spectral methods for latent variable models; and a number of convergence analyses for convex and non-convex algorithms.  He is the recipient of the ICML Test of Time Award, the IBM Pat Goldberg best paper award, and INFORMS Revenue Management and Pricing Prize. He has been program chair for COLT 2011.

    Sham was an undergraduate at Caltech, where he studied physics and worked under the guidance of John Preskill in quantum computing. He completed his Ph.D. with Peter Dayan in computational neuroscience at the Gatsby Computational Neuroscience Unit. He was a postdoc with Michael Kearns at the University of Pennsylvania.

    Seth Neel, Technology & Operations Management (HBS)Title: “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy Law

    Abstract:  Businesses like Facebook and Google depend on training sophisticated models on user data. Increasingly—in part because of regulations like the European Union’s General Data Protection Act and the California Consumer Privacy Act—these organizations are receiving requests to delete the data of particular users. But what should that mean? It is straightforward to delete a customer’s data from a database and stop using it to train future models. But what about models that have already been trained using an individual’s data? These are not necessarily safe; it is known that individual training data can be exfiltrated from models trained in standard ways via model inversion attacks. In a series of papers we help formalize a rigorous notion of data-deletion and propose algorithms to efficiently delete user data from trained models with provable guarantees in both convex and non-convex settings.

    Bio: Seth Neel is a first-year Assistant Professor in the TOM Unit at Harvard Business School, and Co-PI of the SAFR ML Lab in the D3 Institute, which develops methodology to incorporate privacy and fairness guarantees into techniques for machine learning and data analysis, while balancing other critical considerations like accuracy, efficiency, and interpretability. He obtained his Ph.D. from the University of Pennsylvania in 2020 where he was an NSF graduate fellow. His work has focused primarily on differential privacy, notions of fairness in a variety of machine learning settings, and adaptive data analysis.

    Melanie Matchett Wood, Mathematics (FAS)Title: Understanding distributions of algebraic structures through their moments

    Abstract: A classical tool of probability and analysis is to use the moments (mean, variance, etc.) of a distribution to recognize an unknown distribution of real numbers.  In recent work, we are interested in distributions of algebraic structures that can’t be captured in a single number.  We will explain one example, the fundamental group, that captures something about the shapes of possibly complicated or high dimensional spaces.  We are developing a new theory of the moment problem for random algebraic structures which helps to to identify distributions of such, such as fundamental groups of random three dimensional spaces.  This talk is based partly on joint work with Will Sawin.

    Bio: Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study.  Her work spans number theory, algebraic geometry, algebraic topology, additive combinatorics, and probability. Wood has been awarded a CAREER grant, a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, and the AWM-Microsoft Research Prize in Algebra and Number Theory, and she is a Fellow of the American Mathematical Society. In 2021, Wood received the National Science Foundation’s Alan T. Waterman Award, the nation’s highest honor for early-career scientists and engineers.


  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Frances Kirwan (University of Oxford)

    TitleMoment maps and the Yang-Mills functional

    Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led.

    This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

    Talk chair: Peter Kronheimer

    Video

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/29/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Conference in Memory of Professor Masatake Kuranishi
    9:00 am-12:30 pm
    12/01/2024-05/12/2022
    150 Western Ave, Allston, MA 02134
    Kuranishi_Harvard_10x12-2

    On May 9–12, 2022, the CMSA hosted the conference Deformations of structures and moduli in geometry and analysis: A Memorial in honor of Professor Masatake Kuranishi.

    Organizers:  Tristan Collins (MIT) and Shing-Tung Yau (Harvard and Tsinghua)

    Videos are available on the conference playlist.

     

    Speakers:

    Charles Fefferman (Princeton University)

    Teng Fei (Rutgers University)

    Robert Friedman (Columbia University)

    Kenji Fukaya (Simons Center, Stony Brook)

    Akito Futaki (Tsinghua University)

    Victor Guillemin (Massachusetts Institute of Technology)

    Nigel Hitchin (Oxford University)

    Blaine Lawson (Stony Brook University)

    Yu-Shen Lin (Boston University)

    Melissa C.C. Liu (Columbia University)

    Takeo Ohsawa (Nagoya University)

    Duong H. Phong (Columbia University)

    Sebastien Picard (University of British Columbia)

    Paul Seidel (Massachusetts Institute of Technology)

    Gabor Szekelyhidi (University of Notre Dame)

    Claire Voisin (Institut de Mathematiques, Jussieu, France)

    Shing-Tung Yau (Harvard University)

     

    Schedule (download pdf)


    Monday, May 9, 2022

    8:15 amLight breakfast & coffee/tea
    8:45–9:00 amOpening Remarks
    9:00–10:00 amKenji FukayaTitle: Gromov Hausdorff convergence of filtered A infinity category

    Abstract: In mirror symmetry a mirror to a symplectic manifold is actually believed to be a family of complex manifold parametrized by a disk (of radius 0). The coordinate ring of the parameter space is a kind of formal power series ring the Novikov ring. Novikov ring is a coefficient ring of Floer homology. Most of the works on homological Mirror symmetry so far studies A infinity category over Novikov field, which corresponds to the study of generic fiber. The study of A infinity category over Novikov ring is related to several interesting phenomenon of Hamiltonian dynamics. In this talk I will explain a notion which I believe is useful to study mirror symmetry.

    Video

    10:15–11:15 amNigel Hitchin (Zoom)Title: Deformations: A personal perspective

    Abstract: The talk, largely historical, will focus on different deformation complexes I have encountered in my work, starting with instantons on 4-manifolds, but also monopoles, Higgs bundles and generalized complex structures. I will also discuss some speculative ideas related to surfaces of negative curvature.

    Video

    11:30–12:30 pmH. Blaine LawsonTitle: Projective Hulls, Projective Linking, and Boundaries of Varieties

    Abstract: In 1958 John Wermer proved that the polynomial hull of a compact real analytic curve γ ⊂ Cn was a 1-dim’l complex subvariety of Cn − γ. This result engendered much subsequent activity, and was related to Gelfand’s spectrum of a Banach algebra. In the early 2000’s Reese Harvey and I found a projective analogue of these concepts and wondered whether Wermer’s Theorem could be generalized to the projective setting. This question turned out to be more subtle and quite intriguing, with unexpected consequences. We now know a great deal, a highpoint of which s a result with Harvey and Wermer. It led to conjectures (for Cω-curves in P2C) which imply several results. One says, roughly, that a (2p − 1)-cycle Γ in Pn bounds a positive holomorphic p-chain of mass ≤ Λ ⇐⇒ its normalized linking number with all positive (n − p)-cycles in Pn − |Γ| is ≥ −Λ. Another says that a class τ ∈ H2p(Pn,|Γ|;Z) with ∂τ = Γ contains a positive holomorphic p-chain ⇐⇒ τ•[Z]≥0 for all positive holomorphic (n−p)-cycles Z in Pn−|Γ|

    Video

    12:30–2:30 pmLunch Break
    2:30–3:30 pmGabor SzekelyhidiTitle: Singularities along the Lagrangian mean curvature flow.

    Abstract: We study singularity formation along the Lagrangian mean curvature flow of surfaces. On the one hand we show that if a tangent flow at a singularity is the special Lagrangian union of two transverse planes, then the flow undergoes a “neck pinch”, and can be continued past the flow. This can be related to the Thomas-Yau conjecture on stability conditions along the Lagrangian mean curvature flow. In a different direction we show that ancient solutions of the flow, whose blow-down is given by two planes meeting along a line, must be translators. These are joint works with Jason Lotay and Felix Schulze.

    Video

    3:30–4:00 pmCoffee Break 
    4:00–5:00 pmTakeo OhsawaTitle: Glimpses of embeddings and deformations of CR manifolds

    Abstract: Basic results on the embeddings and the deformations of CR manifolds will be reviewed with emphasis on the reminiscences of impressive moments with Kuranishi since his visit to Kyoto in 1975.

    Video

     

     

     

    Tuesday, May 10, 2022

     

    8:15 amLight breakfast & coffee/tea
    9:00–10:00 amCharles Fefferman (Zoom)Title: Interpolation of Data by Smooth Functions

    Abstract: Let X be your favorite Banach space of continuous functions on R^n. Given an (arbitrary) set E in R^n and an arbitrary function f:E->R, we ask: How can we tell whether f extends to a function F \in X? If such an F exists, then how small can we take its norm? What can we say about its derivatives (assuming functions in X have derivatives)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F as above with norm nearly as small as possible? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few data points (x, f(x)) as “outliers”? Which points should we discard?

    The results were obtained jointly with A. Israel, B. Klartag, G.K. Luli and P. Shvartsman over many years.

    Video

    10:15–11:15 amClaire VoisinTitle: Deformations of K-trivial manifolds and applications to hyper-Kähler geometry

    Summary: I will explain the Ran approach via the T^1-lifting principle to the BTT theorem stating that deformations of K-trivial compact Kähler manifolds are unobstructed. I will explain a similar unobstructedness result for Lagrangian submanifolds of hyper-Kähler manifolds and I will describe important consequences on the topology and geometry of hyper-Kähler manifolds.

    Video

    11:30– 2:30 pmVictor GuilleminTitle: Semi-Classical Functions of Isotropic Type

    Abstract: The world of semiclassical analysis is populated by objects of “Lagrangian type.” The topic of this talk however will be objects in semi-classical analysis that live instead on isotropic submanifolds. I will describe in my talk a lot of interesting examples of such objects.

    Video

    12:30–2:30 pmLunch Break
    2:30–3:30 pmTeng FeiTitle: Symplectic deformations and the Type IIA flow

    Abstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong, Picard and Zhang.

    Video

    Speakers Banquet

     

     

     

    Wednesday, May 11, 2022

     

    8:15 amLight breakfast & coffee/tea
    9:00–10:00 amShing-Tung Yau (Zoom)Title: Canonical metrics and stability in mirror symmetry

    Abstract: I will discuss the deformed Hermitian-Yang-Mills equation, its role in mirror symmetry and its connections to notions of stability.  I will review what is known, and pose some questions for the future.

    Video

    10:15–11:15 amDuong H. PhongTitle: $L^\infty$ estimates for the Monge-Ampere and other fully non-linear equations in complex geometry

    Abstract: A priori estimates are essential for the understanding of partial differential equations, and of these, $L^\infty$ estimates are particularly important as they are also needed for other estimates. The key $L^\infty$ estimates were obtained by S.T. Yau in 1976 for the Monge-Ampere equation for the Calabi conjecture, and sharp estimates obtained later in 1998 by Kolodziej using pluripotential theory. It had been a long-standing question whether a PDE proof of these estimates was possible. We provide a positive answer to this question, and derive as a consequence sharp estimates for general classes of fully non-linear equations. This is joint work with B. Guo and F. Tong.

    Video

    11:30–2:30 pmPaul SeidelTitle: The quantum connection: familiar yet puzzling

    Abstract: The small quantum connection on a Fano variety is possibly the most basic piece of enumerative geometry. In spite of being really easy to write down, it is the subject of far-reaching conjectures (Dubrovin, Galkin, Iritani), which challenge our understanding of mirror symmetry. I will give a gentle introduction to the simplest of these questions.

    Video

    12:30–2:30 pmLunch Break
    2:30–3:30 pmMelissa C.C. LiuTitle: Higgs-Coulumb correspondence for abelian gauged linear sigma models

    Abstract: The underlying geometry of a gauged linear sigma model (GLSM) consists of a GIT quotient of a complex vector space by the linear action of a reductive algebraic group G (the gauge group) and a polynomial function (the superpotential) on the GIT quotient. The Higgs-Coulomb correspondence relates (1) GLSM invariants which are virtual counts of curves in the critical locus of the superpotential (Higgs branch), and (2) Mellin-Barnes type integrals on the Lie algebra of G (Coulomb branch). In this talk, I will describe the correspondence when G is an algebraic torus, and explain how to use the correspondence to study dependence of GLSM invariants on the stability condition. This is based on joint work with Konstantin Aleshkin.

    Video

    3:30–4:00 pmCoffee Break 
    4:00–5:00 pmSebastien PicardTitle: Topological Transitions of Calabi-Yau Threefolds

    Abstract: Conifold transitions were proposed in the works of Clemens, Reid and Friedman as a way to travel in the parameter space of Calabi-Yau threefolds with different Hodge numbers. This process may deform a Kahler Calabi-Yau threefold into a non-Kahler complex manifold with trivial canonical bundle. We will discuss the propagation of differential geometric structures such as balanced hermitian metrics, Yang-Mills connections, and special submanifolds through conifold transitions. This is joint work with T. Collins, S. Gukov and S.-T. Yau.

    Video

     

     

     

    Thursday, May 12, 2022

     

    8:15 amLight breakfast & coffee/tea
    9:00 am–10:00 amAkito Futaki (Zoom)Title: Transverse coupled Kähler-Einstein metrics and volume minimization

    Abstract:
    We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kählercone, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.Video
    10:15 am–11:15 amYu-Shen LinTitle: SYZ Mirror Symmetry of Log Calabi-Yau Surfaces

    Abstract: Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admits special Lagrangian fibrations. The conjecture serves as one of the guiding principles in mirror symmetry. In this talk, I will explain the existence of the special Lagrangian fibrations in some log Calabi-Yau surfaces and their dual fibrations in their expected mirrors. The journey leads us to the study of the moduli space of Ricci-flat metrics with certain asymptotics on these geometries and the discovery of new semi-flat metrics. If time permits, I will explain the application to the Torelli theorem of ALH^* gravitational instantons. The talk is based on joint works with T. Collins and A. Jacob.

    Video

    11:30 am – 12:30 pmRobert FriedmanTitle: Deformations of singular Fano and Calabi-Yau varieties

    Abstract: This talk will describe recent joint work with Radu Laza on deformations of generalized Fano and Calabi-Yau varieties, i.e. compact analytic spaces whose dualizing sheaves are either duals of ample line bundles or are trivial. Under the assumption of isolated hypersurface canonical singularities, we extend results of Namikawa and Steenbrink in dimension three and discuss various generalizations to higher dimensions.

    Video

    12:30 pmConcluding Remarks

     

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/6/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Symposium on Foundations of Responsible Computing (FORC)
    9:00 am-5:00 pm
    12/01/2024-06/08/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Screen-Shot-2020-03-05-at-11.54.28-AM-600x338

    On June 6-8, 2022, the CMSA hosted the 3rd annual Symposium on Foundations of Responsible Computing (FORC).

    The Symposium on Foundations of Responsible Computing (FORC) is a forum for mathematical research in computation and society writ large.  The Symposium aims to catalyze the formation of a community supportive of the application of theoretical computer science, statistics, economics and other relevant analytical fields to problems of pressing and anticipated societal concern.

    Organizers: Cynthia Dwork, Harvard SEAS | Omer Reingold, Stanford | Elisa Celis, Yale

    Schedule

    DOWNLOAD PDF

    June 6, 2022

    9:15 am–10:15 amOpening Remarks

    Keynote Speaker: Caroline Nobo, Yale University

    Title: From Theory to Impact: Why Better Data Systems are Necessary for Criminal Legal Reform

    Abstract: This talk will dive into the messy, archaic, and siloed world of local criminal justice data in America. We will start with a 30,000 foot discussion about the current state of criminal legal data systems, then transition to the challenges of this broken paradigm, and conclude with a call to measure new things – and to measure them better! This talk will leave you with an understanding of criminal justice data infrastructure and transparency in the US, and will discuss how expensive case management software and other technology are built on outdated normative values which impede efforts to reform the system. The result is an infuriating paradox: an abundance of tech products built without theoretical grounding, in a space rich with research and evidence.

    10:15 am–10:45 amCoffee Break
    10:45 am–12:15 pmPaper Session 1Session Chair: Ruth Urner
    Georgy Noarov, University of PennsylvaniaTitle: Online Minimax Multiobjective Optimization

    Abstract: We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. The learner’s objective is to minimize the maximum cumulative loss over all coordinates. We give a simple algorithm that lets the learner do almost as well as if she knew the adversary’s actions in advance. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains, ranging from multicalibration to a large set of no-regret algorithms, to a variant of Blackwell’s approachability theorem for polytopes with fast convergence rates. As a new application, we show how to “(multi)calibeat” an arbitrary collection of forecasters — achieving an exponentially improved dependence on the number of models we are competing against, compared to prior work.

    Matthew Eichhorn, Cornell UniversityTitle: Mind your Ps and Qs: Allocation with Priorities and Quotas

    Abstract: In many settings, such as university admissions, the rationing of medical supplies, and the assignment of public housing, decision-makers use normative criteria (ethical, financial, legal, etc.) to justify who gets an allocation. These criteria can often be translated into quotas for the number of units available to particular demographics and priorities over agents who qualify in each demographic. Each agent may qualify in multiple categories at different priority levels, so many allocations may conform to a given set of quotas and priorities. Which of these allocations should be chosen? In this talk, I’ll formalize this reserve allocation problem and motivate Pareto efficiency as a natural desideratum. I’ll present an algorithm to locate efficient allocations that conform to the quota and priority constraints. This algorithm relies on beautiful techniques from integer and linear programming, and it is both faster and more straightforward than existing techniques in this space. Moreover, its clean formulation allows for further refinement, such as the secondary optimization of some heuristics for fairness.

    Haewon Jeong, Harvard UniversityTitle: Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values

    Abstract: We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature, most of them require a complete training set as input. In practice, data can have missing values, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead, we train a tree with missing incorporated as attribute (MIA), which does not require explicit imputation, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset, through several experiments on real-world datasets.

    Emily Diana, University of PennsylvaniaTitle: Multiaccurate Proxies for Downstream Fairness

    Abstract: We study the problem of training a model that must obey demographic fairness conditions when the sensitive features are not available at training time — in other words, how can we train a model to be fair by race when we don’t have data about race? We adopt a fairness pipeline perspective, in which an “upstream” learner that does have access to the sensitive features will learn a proxy model for these features from the other attributes. The goal of the proxy is to allow a general “downstream” learner — with minimal assumptions on their prediction task — to be able to use the proxy to train a model that is fair with respect to the true sensitive features. We show that obeying multiaccuracy constraints with respect to the downstream model class suffices for this purpose, provide sample- and oracle efficient-algorithms and generalization bounds for learning such proxies, and conduct an experimental evaluation. In general, multiaccuracy is much easier to satisfy than classification accuracy, and can be satisfied even when the sensitive features are hard to predict.

    12:15 pm–1:45 pmLunch Break
    1:45–3:15 pmPaper Session 2Session Chair: Guy Rothblum
    Elbert Du, Harvard UniversityTitle: Improved Generalization Guarantees in Restricted Data Models

    Abstract: Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis — even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that, under this assumption, it is possible to “re-use” privacy budget on different portions of the data, significantly improving accuracy without increasing the risk of overfitting.

    Ruth Urner, York UniversityTitle: Robustness Should not be at Odds with Accuracy

    Abstract: The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability and trustworthiness: in many instances an imperceptible perturbation can falsely flip a neural network’s prediction. Applied research in this area has mostly focused on developing novel adversarial attack strategies or building better defenses against such. It has repeatedly been pointed out that adversarial robustness may be in conflict with requirements for high accuracy. In this work, we take a more principled look at modeling the phenomenon of adversarial examples. We argue that deciding whether a model’s label change under a small perturbation is justified, should be done in compliance with the underlying data-generating process. Through a series of formal constructions, systematically analyzing the the relation between standard Bayes classifiers and robust-Bayes classifiers, we make the case for adversarial robustness as a locally adaptive measure. We propose a novel way defining such a locally adaptive robust loss, show that it has a natural empirical counterpart, and develop resulting algorithmic guidance in form of data-informed adaptive robustness radius. We prove that our adaptive robust data-augmentation maintains consistency of 1-nearest neighbor classification under deterministic labels and thereby argue that robustness should not be at odds with accuracy.

    Sushant Agarwal, University of WaterlooTitle: Towards the Unification and Robustness of Perturbation and Gradient Based Explanations

    Abstract: As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method, and a variant of LIME which is a perturbation based method. More specifically, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation, i.e., when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties, such as robustness and linearity, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally, we empirically validate our theory using extensive experimentation on both synthetic and real world datasets.

    Tijana Zrnic, University of California, BerkeleyTitle: Regret Minimization with Performative Feedback

    Abstract: In performative prediction, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time, the learner needs to deploy a model to get feedback about the distribution it induces. We study the problem of finding near-optimal models under performativity while maintaining low regret. On the surface, this problem might seem equivalent to a bandit problem. However, it exhibits a fundamentally richer feedback structure that we refer to as performative feedback: after every deployment, the learner receives samples from the shifted distribution rather than only bandit feedback about the reward. Our main contribution is regret bounds that scale only with the complexity of the distribution shifts and not that of the reward function. The key algorithmic idea is careful exploration of the distribution shifts that informs a novel construction of confidence bounds on the risk of unexplored models. The construction only relies on smoothness of the shifts and does not assume convexity. More broadly, our work establishes a conceptual approach for leveraging tools from the bandits literature for the purpose of regret minimization with performative feedback.

    3:15 pm–3:45 pmCoffee Break
    3:45 pm–5:00 pmPanel DiscussionTitle: What is Responsible Computing?

    Panelists: Jiahao Chen, Cynthia Dwork, Kobbi Nissim, Ruth Urner

    Moderator: Elisa Celis

     

    June 7, 2022

    9:15 am–10:15 amKeynote Speaker: Isaac Kohane, Harvard Medical SchoolTitle: What’s in a label? The case for and against monolithic group/ethnic/race labeling for machine learning

    Abstract: Populations and group labels have been used and abused for thousands of years. The scale at which AI can incorporate such labels into its models and the ways in which such models can be misused are cause for significant concern. I will describe, with examples drawn from experiments in precision medicine, the task dependence of how underserved and oppressed populations can be both harmed and helped by the use of group labels. The source of the labels and the utility models underlying their use will be particularly emphasized.

    10:15 am–10:45 amCoffee Break
    10:45 am–12:15 pmPaper Session 3Session Chair: Ruth Urner
    Rojin Rezvan, University of Texas at AustinTitle: Individually-Fair Auctions for Multi-Slot Sponsored Search

    Abstract: We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from Chawla and Jagadeesan.

    Judy Hanwen Shen, StanfordTitle: Leximax Approximations and Representative Cohort Selection

    Abstract: Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency, exploiting significant utility improvements, and robustness to noise. Among other definitional contributions, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.

    Jiayuan Ye,
    National University of Singapore
    Title: Differentially Private Learning Needs Hidden State (or Much Faster Convergence)

    Abstract: Differential privacy analysis of randomized learning algorithms typically relies on composition theorems, where the implicit assumption is that the internal state of the iterative algorithm is revealed to the adversary. However, by assuming hidden states for DP algorithms (when only the last-iterate is observable), recent works prove a converging privacy bound for noisy gradient descent (on strongly convex smooth loss function) that is significantly smaller than composition bounds after a few epochs. In this talk, we extend this hidden-state analysis to various stochastic minibatch gradient descent schemes (such as under “shuffle and partition” and “sample without replacement”), by deriving novel bounds for the privacy amplification by random post-processing and subsampling. We prove that, in these settings, our privacy bound is much smaller than composition for training with a large number of iterations (which is the case for learning from high-dimensional data). Our converging privacy analysis, thus, shows that differentially private learning, with a tight bound, needs hidden state privacy analysis or a fast convergence. To complement our theoretical results, we present experiments for training classification models on MNIST, FMNIST and CIFAR-10 datasets, and observe a better accuracy given fixed privacy budgets, under the hidden-state analysis.

    Mahbod Majid, University of WaterlooTitle: Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism

    Abstract: We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution from O(d) independent samples (up to logarithmic factors) subject to pure differential privacy.

    Our main technique is a new approach to use the powerful Sum of Squares method (SoS) to design differentially private algorithms. SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics – estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees. We demonstrate a similar proofs to private algorithms phenomenon: instances of the workhorse exponential mechanism which apparently require exponential time but which can be analyzed with low-degree SoS proofs can be automatically turned into polynomial-time differentially private algorithms. We prove a meta-theorem capturing this phenomenon, which we expect to be of broad use in private algorithm design.

    12:15 pm–1:45 pmLunch Break
    1:45–3:15 pmPaper Session 4Session Chair: Kunal Talwar
    Kunal Talwar,
    Apple
    Title: Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

    Abstract: Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation (SMC) protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected.
    In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.

    Giuseppe Vietri, University of MinnesotaTitle: Improved Regret for Differentially Private Exploration in Linear MDP

    Abstract: We study privacy-preserving exploration in sequential decision-making for environments that rely on sensitive data such as medical records. In particular, we focus on solving the problem of reinforcement learning (RL) subject to the constraint of (joint) differential privacy in the linear MDP setting, where both dynamics and rewards are given by linear functions. Prior work on this problem due to Luyo et al. (2021) achieves a regret rate that has a dependence of O(K^{3/5}) on the number of episodes K. We provide a private algorithm with an improved regret rate with an optimal dependence of O(K^{1/2}) on the number of episodes. The key recipe for our stronger regret guarantee is the adaptivity in the policy update schedule, in which an update only occurs when sufficient changes in the data are detected. As a result, our algorithm benefits from low switching cost and only performs O(log(K)) updates, which greatly reduces the amount of privacy noise. Finally, in the most prevalent privacy regimes where the privacy parameter ? is a constant, our algorithm incurs negligible privacy cost — in comparison with the existing non-private regret bounds, the additional regret due to privacy appears in lower-order terms.

    Mingxun Zhou,
    Carnegie Mellon University
    Title: The Power of the Differentially Oblivious Shuffle in Distributed Privacy MechanismsAbstract: The shuffle model has been extensively investigated in the distributed differential privacy (DP) literature. For a class of useful computational tasks, the shuffle model allows us to achieve privacy-utility tradeoff similar to those in the central model, while shifting the trust from a central data curator to a “trusted shuffle” which can be implemented through either trusted hardware or cryptography. Very recently, several works explored cryptographic instantiations of a new type of shuffle with relaxed security, called differentially oblivious (DO) shuffles. These works demonstrate that by relaxing the shuffler’s security from simulation-style secrecy to differential privacy, we can achieve asymptotical efficiency improvements. A natural question arises, can we replace the shuffler in distributed DP mechanisms with a DO-shuffle while retaining a similar privacy-utility tradeoff?
    In this paper, we prove an optimal privacy amplification theorem by composing any locally differentially private (LDP) mechanism with a DO-shuffler, achieving parameters that tightly match the shuffle model. Moreover, we explore multi-message protocols in the DO-shuffle model, and construct mechanisms for the real summation and histograph problems. Our error bounds approximate the best known results in the multi-message shuffle-model up to sub-logarithmic factors. Our results also suggest that just like in the shuffle model, allowing each client to send multiple messages is fundamentally more powerful than restricting to a single message.
    Badih Ghazi,
    Google Research
    Title: Differentially Private Ad Conversion Measurement

    Abstract: In this work, we study conversion measurement, a central functionality in the digital advertising space, where an advertiser seeks to estimate advertiser site conversions attributed to ad impressions that users have interacted with on various publisher sites. We consider differential privacy (DP), a notion that has gained in popularity due to its strong and rigorous guarantees, and suggest a formal framework for DP conversion measurement, uncovering a subtle interplay between attribution and privacy. We define the notion of an operationally valid configuration of the attribution logic, DP adjacency relation, privacy
    budget scope and enforcement point, and provide, for a natural space of configurations, a complete characterization.

    3:15 pm–3:45 pmCoffee Break
    3:45 pm–5:00 pmOpen Poster Session

     

    June 8, 2022

    9:15 am–10:15 amKeynote Speaker: Nuria Oliver, Data-Pop AllianceTitle: Data Science against COVID-19

    Abstract: In my talk, I will describe the work that I have been doing since March 2020, leading a multi-disciplinary team of 20+ volunteer scientists working very closely with the Presidency of the Valencian Government in Spain on 4 large areas: (1) human mobility modeling; (2) computational epidemiological models (both metapopulation, individual and LSTM-based models); (3) predictive models; and (4) citizen surveys via the COVID19impactsurvey with over 600,000 answers worldwide.

    I will describe the results that we have produced in each of these areas, including winning the 500K XPRIZE Pandemic Response Challenge and best paper award at ECML-PKDD 2021. I will share the lessons learned in this very special initiative of collaboration between the civil society at large (through the survey), the scientific community (through the Expert Group) and a public administration (through the Commissioner at the Presidency level). WIRED magazine just published an article describing our story.

    10:15 am–10:45 amCoffee Break
    10:45 am–12:15 pmPaper Session 5Session Chair: Kunal Talwar
    Shengyuan Hu, Carnegie Mellon UniversityTitle: Private Multi-Task Learning: Formulation and Applications to Federated Learning

    Abstract: Many problems in machine learning rely on multi-task learning (MTL), in which the goal is to solve multiple related machine learning tasks simultaneously. MTL is particularly relevant for privacy-sensitive applications in areas such as healthcare, finance, and IoT computing, where sensitive data from multiple, varied sources are shared for the purpose of learning. In this work, we formalize notions of task-level privacy for MTL via joint differential privacy (JDP), a relaxation of differential privacy for mechanism design and distributed optimization. We then propose an algorithm for mean-regularized MTL, an objective commonly used for applications in personalized federated learning, subject to JDP. We analyze our objective and solver, providing certifiable guarantees on both privacy and utility. Empirically, our method allows for improved privacy/utility trade-offs relative to global baselines across common federated learning benchmarks

    Christina Yu,
    Cornell University
    Title: Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve

    Abstract: We consider the problem of dividing limited resources to individuals arriving over T rounds with a goal of achieving fairness across individuals. In general there may be multiple resources and multiple types of individuals with different utilities. A standard definition of `fairness’ requires an allocation to simultaneously satisfy envy-freeness and Pareto efficiency. However, in the online sequential setting, the social planner must decide on a current allocation before the downstream demand is realized, such that no policy can guarantee these desiderata simultaneously with probability 1, requiring a modified metric of measuring fairness for online policies. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to L_T necessarily suffers an efficiency loss of at least 1 / L_T. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. Our result is the first to provide guarantees for fair online resource allocation with high probability for multiple resource and multiple type settings. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.

    Hedyeh Beyhaghi, Carnegie Mellon UniversityTitle: On classification of strategic agents who can both game and improve

    Abstract: In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

    Keegan Harris, Carnegie Mellon UniversityTitle: Bayesian Persuasion for Algorithmic Recourse

    Abstract: When subjected to automated decision-making, decision subjects may strategically modify their observable features in ways they believe will maximize their chances of receiving a favorable decision. In many practical situations, the underlying assessment rule is deliberately kept secret to avoid gaming and maintain competitive advantage. The resulting opacity forces the decision subjects to rely on incomplete information when making strategic feature modifications. We capture such settings as a game of Bayesian persuasion, in which the decision maker offers a form of recourse to the decision subject by providing them with an action recommendation (or signal) to incentivize them to modify their features in desirable ways. We show that when using persuasion, both the decision maker and decision subject are never worse off in expectation, while the decision maker can be significantly better off. While the decision maker’s problem of finding the optimal Bayesian incentive-compatible (BIC) signaling policy takes the form of optimization over infinitely-many variables, we show that this optimization can be cast as a linear program over finitely-many regions of the space of possible assessment rules. While this reformulation simplifies the problem dramatically, solving the linear program requires reasoning about exponentially-many variables, even under relatively simple settings. Motivated by this observation, we provide a polynomial-time approximation scheme that recovers a near-optimal signaling policy. Finally, our numerical simulations on semi-synthetic data empirically illustrate the benefits of using persuasion in the algorithmic recourse setting.

    12:15 pm–1:45 pmLunch Break
    1:45–3:15 pmPaper Session 6Session Chair: Elisa Celis
    Mark Bun, Boston UniversityTitle: Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling

    Abstract: Sampling schemes are fundamental tools in statistics, survey design, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However, in practice, sampling designs are often more complex than the simple, data-independent sampling schemes that are addressed in prior work. In this work, we extend the study of privacy amplification results to more complex, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms, as well as provide some insight into the study of more general sampling designs.

    Samson Zhou, Carnegie Mellon UniversityTitle: Private Data Stream Analysis for Universal Symmetric Norm Estimation

    Abstract: We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular, we focus on releasing the family of symmetric norms, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include L_p norms, k-support norms, top-k norms, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the “heavy” coordinates in important levels and releases approximate level sizes for the “light” coordinates in important levels. Surprisingly, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover, our mechanism permits (1+\alpha)-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.

    Aloni Cohen, University of ChicagoTitle: Attacks on Deidentification’s Defenses

    Abstract: Quasi-identifier-based deidentification techniques (QI-deidentification) are widely used in practice, including k-anonymity, ?-diversity, and t-closeness. We present three new attacks on QI-deidentification: two theoretical attacks and one practical attack on a real dataset. In contrast to prior work, our theoretical attacks work even if every attribute is a quasi-identifier. Hence, they apply to k-anonymity, ?-diversity, t-closeness, and most other QI-deidentification techniques.
    First, we introduce a new class of privacy attacks called downcoding attacks, and prove that every QI-deidentification scheme is vulnerable to downcoding attacks if it is minimal and hierarchical. Second, we convert the downcoding attacks into powerful predicate singling-out (PSO) attacks, which were recently proposed as a way to demonstrate that a privacy mechanism fails to legally anonymize under Europe’s General Data Protection Regulation. Third, we use LinkedIn.com to reidentify 3 students in a k-anonymized dataset published by EdX (and show thousands are potentially vulnerable), undermining EdX’s claimed compliance with the Family Educational Rights and Privacy Act.

    The significance of this work is both scientific and political. Our theoretical attacks demonstrate that QI-deidentification may offer no protection even if every attribute is treated as a quasi-identifier. Our practical attack demonstrates that even deidentification experts acting in accordance with strict privacy regulations fail to prevent real-world reidentification. Together, they rebut a foundational tenet of QI-deidentification and challenge the actual arguments made to justify the continued use of k-anonymity and other QI-deidentification techniques.

    Steven Wu,
    Carnegie Mellon University
    Title: Fully Adaptive Composition in Differential Privacy

    Abstract: Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. The authors introduce two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the tightness of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. We also construct several general families of odometers. These odometers can match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging recent advances in time-uniform martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss, and conjecture that our results are essentially not improvable (even in constants) in general.

    3:15 pm–3:45 pmFORC Reception
    3:45 pm–5:00 pmSocial Hour
  • Workshop
    9:00 am-5:00 pm
    12/01/2024-04/29/2022
    Blockchain,Network,Concept,,,Distributed,Ledger,,Computer,Connection,Technology,,Matrix

    On April 27–29, 2022, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics.

    Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

    In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

    Speakers:

    • Federico Ardila (San Francisco State)
    • Nima Arkani-Hamed (IAS)
    • Madeline Brandt (Brown)
    • Nick Early (Max Planck Institute)
    • Chris Eur (Harvard)
    • Claudia Fevola (Max Planck Institute)
    • Christian Gaetz (Harvard)
    • Yuji Kodama (Ohio State University)
    • Yelena Mandelshtam (Berkeley)
    • Sebastian Mizera (IAS)
    • Matteo Parisi (Harvard CMSA)
    • Emma Previato (Boston University)
    • Anna Seigal (Harvard)
    • Melissa Sherman-Bennett (University of Michigan)
    • Simon Telen (Max Planck Institute)
    • Charles Wang (Harvard)

    Schedule

    Schedule PDF

    Wednesday, April 27, 2022

    9:30 am–10:30 amFederico ArdilaTitle: Nonlinear spaces from linear spaces

    Abstract: Matroid theory provides a combinatorial model for linearity, but it plays useful roles beyond linearity. In the classical setup, a linear subspace V of an n-dimensional vector space gives rise to a matroid M(V) on {1,…,n}. However, the matroid M(V) also knows about some nonlinear geometric spaces related to V. Conversely, those nonlinear spaces teach us things we didn’t know about matroids. My talk will discuss some examples.

    10:30 am–11:00 amCOFFEE BREAK
    11:00 am–11:45 amChris EurTitle: Tautological classes of matroids

    Abstract: Algebraic geometry has furnished fruitful tools for studying matroids, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (K-classes) on permutohedral varieties, which we call “tautological bundles (classes)” of matroids, as a new framework that unifies, recovers, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget, Hunter Spink, and Dennis Tseng.

    11:45 am–2:00 pmLUNCH BREAK
    2:00 pm–2:45 pmNick EarlyTitle: Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes

    Abstract: The associahedron is known to encapsulate physical properties such as the notion of tree-level factorization for one of the simplest Quantum Field Theories, the biadjoint scalar, which has only cubic interactions.  I will discuss novel instances of the associahedron and the biadjoint scalar in a class of generalized amplitudes, discovered by Cachazo, Early, Guevara and Mizera, by taking certain limits thereof. This connection leads to a simple proof of a new realization of the associahedron involving a Minkowski sum of certain positroid polytopes in the second hypersimplex.

    2:45 pm–3:30 pmAnna SeigalTitle: Invariant theory for maximum likelihood estimation

    Abstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

    3:30 pm–4:00 pmCOFFEE BREAK
    4:00 pm–4:45 pmMatteo ParisiTitle: Amplituhedra, Scattering Amplitudes, and Triangulations

    Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – introduced by physicists to encode interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory.
    Triangulations of polygons are encoded in the associahedron, studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes, constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. I will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between Amplituhedra of “m=2” type and a seemingly unrelated object – the Hypersimplex. The latter is a polytope which appears in many contexts, from matroid theory to tropical geometry.
    Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski.

    4:45 pm–5:30 pmMelissa Sherman-BennettTitle: The hypersimplex and the m=2 amplituhedron

    Abstract: In this talk, I’ll continue where Matteo left off. I’ll give some more details about the curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). The hypersimplex decompositions are closely related to matroidal subdivisions. Along the way, we prove a nice description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers, inspired by an analogous triangulation of the hypersimplex into Eulerian-number-many simplices.

     

    Thursday, April 28, 2022

    9:30 am–10:30 amClaudia FevolaTitle: Nonlinear Algebra meets Feynman integrals

    Abstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. They form a finite-dimensional vector space and the elements of a basis are named “master integrals” in the physics literature. The number of master integrals has been interpreted in different ways: it equals the dimension of a twisted de Rham cohomology group, the Euler characteristic of a very affine variety, and the holonomic rank of a D-module. In this talk, we are interested in a more general family of integrals that contains Feynman integrals as a special case. We explore this setting using tools coming from nonlinear algebra. This is an ongoing project with Daniele Agostini, Anna-Laura Sattelberger, and Simon Telen.

    10:30 am–11:00 amCOFFEE BREAK
    11:00 am–11:45 amSimon TelenTitle: Landau discriminants

    Abstract: The Landau discriminant is a projective variety containing kinematic parameters for which a Feynman integral can have singularities. We present a definition and geometric properties. We discuss how to compute Landau discriminants using symbolic and numerical methods. Our methods can be used, for instance, to compute the Landau discriminant of the pentabox diagram, which is a degree 12 hypersurface in 6-space. This is joint work with Sebastian Mizera.

    11:45 am–2:00 pmLUNCH BREAK
    2:00 pm–2:45 pmChristian GaetzTitle: 1-skeleton posets of Bruhat interval polytopes

    Abstract: Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes, despite not being simple, have interesting h-vectors. In a special case, work of Williams shows that Bruhat interval polytopes are isomorphic to bridge polytopes, so that chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs.

    2:45 pm–3:30 pmMadeleine BrandtTitle: Top Weight Cohomology of $A_g$

    Abstract: I will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of $A_g$. Thus, it can be computed combinatorially. This is joint work with Juliette Bruce, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.

    3:30 pm–4:00 pmCOFFEE BREAK
    4:00 pm–5:00 pmEmma PreviatoTitle: Sigma function on curves with non-symmetric semigroup

    Abstract: We start with an overview of the correspondence between spectral curves and commutative rings of differential operators, integrable hierarchies of non-linear PDEs and Jacobian vector fields. The coefficients of the operators can be written explicitly in terms of the Kleinian sigma function: Weierstrass’ sigma function was generalized to genus greater than one by Klein, and is a ubiquitous tool in integrability. The most accessible case is the sigma function of telescopic curves. In joint work with J. Komeda and S. Matsutani, we construct a curve with non-symmetric Weierstrass semigroup (equivalently, Young tableau), consequently non-telescopic, and its sigma function. We conclude with possible applications to commutative rings of differential operators.

    6:00 pmDinner Banquet, Gran Gusto Trattoria

     

    Friday, April 29, 2022

    9:00 am–10:00 amYuji KodamaTitle: KP solitons and algebraic curves

    Abstract: It is well-known that soliton solutions of the KdV hierarchy are obtained by singular limits of hyper-elliptic curves. However, there is no general results for soliton solutions of the KP hierarchy, KP solitons. In this talk, I will show that some of the KP solitons are related to the singular space curves associated with certain class of numerical semigroups.

    10:00 am–10:30 amCOFFEE BREAK
    10:30 am–11:15 amYelena MandelshtamTitle: Curves, degenerations, and Hirota varieties

    Abstract: The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases, Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This talk is based on joint work with Daniele Agostini, Claudia Fevola, and Bernd Sturmfels.

    11:15 am–12:00 pmCharles WangTitle: Differential Algebra of Commuting Operators

    Abstract: In this talk, we will give an overview of the problem of finding the centralizer of a fixed differential operator in a ring of differential operators, along with connections to integrable hierarchies and soliton solutions to e.g. the KdV or KP equations. Given these interesting connections, it is important to be able to compute centralizers of differential operators, and we discuss how to use techniques from differential algebra to approach this question, as well as how having these computational tools can help in understanding the structure of soliton solutions to these equations.

    12:00 pm–2:00 pmLUNCH BREAK
    2:00 pm–3:00 pmSebastian MizeraTitle: Feynman Polytopes

    Abstract: I will give an introduction to a class of polytopes that recently emerged in the study of scattering amplitudes in quantum field theory.

    3:00 pm–3:30 pmCOFFEE BREAK
    3:30 pm–4:30 pmNima Arkani-HamedTitle: Spacetime, Quantum Mechanics and Combinatorial Geometries at Infinity

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Algebraic Statistics with a View towards Physics

    9:00 am-10:00 am
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.

    **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

    All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

    LINK TO FORM

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/13/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.21.22-1583x2048-1

    Abstract:
    Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure, the adoption of MPC in real industry is still very much limited as of today, the biggest obstacle of which boils down to its efficiency.

    My research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal, my research spans both theoretical and applied cryptography. In theory, I develop new techniques for achieving general MPC with the optimal complexity, bringing theory closer to practice. In practice, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice.

    Biography:
    Peihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC, she received her Ph.D. from the University of California, Berkeley in 2019 and had brief stints at Google, Facebook, Microsoft Research, and Visa Research. Her research interests lie broadly in cryptography, theory, and security, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/20/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Workshop
    9:00 am-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series.

    Location: Room G10, 20 Garden Street, Cambridge, MA 02138.

    Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).

    Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory, algebraic geometry, and representation theory.

    At this workshop, we will bring together mathematicians, theoretical physicists, and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.

    Speakers:

    • James Halverson, Northeastern University Dept. of Physics and IAIFI
    • Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI
    • Andrew Sutherland, MIT Department of Mathematics

     

    https://youtu.be/qseSPgHHFtQ

     

     

    https://youtu.be/JN3mVazeP2E

     

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.14.22-1583x2048

    Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.

  • Member Seminar
    9:00 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Farzan Vafa

    Title: Diffusive growth sourced by topological defects

    Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time, and predict that in the presence of a positive defect, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature, we exploit the fact that for axisymmetric surfaces, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry, for polar order and small bending modulus, is a deformed football.
    We apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/27/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    6/3/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Dan Freed (The University of Texas at Austin)

    Title: The Atiyah-Singer Index Theorem

    Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator.

    This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

    Talk chair: Cumrun Vafa

    Video

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Interdisciplinary Science Seminar
    Speaker: Jianfeng Lu, Duke UniversityTitle: Surface hopping algorithms for non-adiabatic quantum systems

    Abstract: Surface hopping algorithm is widely used in chemistry for mixed quantum-classical dynamics. In this talk, we will discuss some of our recent works in mathematical understanding and algorithm development for surface hopping methods. These methods are based on stochastic approximations of semiclassical path-integral representation to the solution of multi-level Schrodinger equations; such methodology also extends to other high-dimensional transport systems.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    7/8/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Big Data Conference 2022
    9:00 am-1:00 pm
    12/01/2024
    Big Data 2022_web

    On August 26, 2022 the CMSA hosted our eighth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The 2022 Big Data Conference took place virtually on Zoom.

    Organizers:

    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Schedule

    9:00 amConference OrganizersIntroduction and Welcome
    9:10 am – 9:55 amXiaohong ChenTitle: On ANN optimal estimation and inference for policy functionals of nonparametric conditional moment restrictions

    Abstract:  Many causal/policy parameters of interest are expectation functionals of unknown infinite-dimensional structural functions identified via conditional moment restrictions. Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional covariates more effectively than linear sieves. In this talk we present ANN optimal estimation and inference on  policy functionals, such as average elasticities or value functions, of unknown structural functions of endogenous covariates. We provide ANN efficient estimation and optimal t based confidence interval for regular policy functionals such as average derivatives in nonparametric instrumental variables regressions. We also present ANN quasi likelihood ratio based inference for possibly irregular policy functionals of general nonparametric conditional moment restrictions (such as quantile instrumental variables models or Bellman equations) for time series data. We conduct intensive Monte Carlo studies to investigate computational issues with ANN based optimal estimation and inference in economic structural models with endogeneity. For economic data sets that do not have very high signal to noise ratios, there are current gaps between theoretical advantage of ANN approximation theory vs inferential performance in finite samples.
    Some of the results are applied to efficient estimation and optimal inference for average price elasticity in consumer demand and BLP type demand.

    The talk is based on two co-authored papers:
    (1) Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators
    (Authors: Jiafeng Chen, Xiaohong Chen and Elie Tamer)
    https://arxiv.org/abs/2110.06763

    (2) Neural network Inference on Nonparametric conditional moment restrictions with weakly dependent data
    (Authors: Xiaohong Chen, Yuan Liao and Weichen Wang).

    View/Download Lecture Slides (pdf)

    10:00 am – 10:45 amJessica JeffersTitle: Labor Reactions to Credit Deterioration: Evidence from LinkedIn Activity

    Abstract: We analyze worker reactions to their firms’ credit deterioration. Using weekly networking activity on LinkedIn, we show workers initiate more connections immediately following a negative credit event, even at firms far from bankruptcy. Our results suggest that workers are driven by concerns about both unemployment and future prospects at their firm. Heightened networking activity is associated with contemporaneous and future departures, especially at financially healthy firms. Other negative events like missed earnings and equity downgrades do not trigger similar reactions. Overall, our results indicate that the build-up of connections triggered by credit deterioration represents a source of fragility for firms.

    10:50 am – 11:35 amMiles CranmerTitle: Interpretable Machine Learning for Physics

    Abstract: Would Kepler have discovered his laws if machine learning had been around in 1609? Or would he have been satisfied with the accuracy of some black box regression model, leaving Newton without the inspiration to discover the law of gravitation? In this talk I will explore the compatibility of industry-oriented machine learning algorithms with discovery in the natural sciences. I will describe recent approaches developed with collaborators for addressing this, based on a strategy of “translating” neural networks into symbolic models via evolutionary algorithms. I will discuss the inner workings of the open-source symbolic regression library PySR (github.com/MilesCranmer/PySR), which forms a central part of this interpretable learning toolkit. Finally, I will present examples of how these methods have been used in the past two years in scientific discovery, and outline some current efforts.

    View/Download Lecture Slides (pdf) 

    11:40 am – 12:25 pmDan RobertsTitle: A Statistical Model of Neural Scaling Laws

    Abstract: Large language models of a huge number of parameters and trained on near internet-sized number of tokens have been empirically shown to obey “neural scaling laws” for which their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model — a joint generative data model and random feature model — that captures this neural scaling phenomenology. By solving this model using tools from random matrix theory, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws (ii) how nonlinear feature maps, i.e the role played by the deep neural network, enable scaling laws when trained on these datasets, and (iii) how such scaling laws can break down, and what their behavior is when they do. A key feature is the manner in which the power laws that occur in the statistics of natural datasets are translated into power law scalings of the test loss, and how the finite extent of such power laws leads to both bottlenecks and breakdowns.

    View/Download Lecture Slides (pdf)

     

    12:30 pmConference OrganizersClosing Remarks

     

    Information about last year’s conference can be found here.

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 09.28.22

    Topological Quantum Matter Seminar

    Speaker: Ruihua Fan, Harvard University

    Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow
    Abstract: One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024
    CMSA QMMP Seminar 09.26.22

    Quantum Matter in Mathematics and Physics

    Speaker: Avner Karasik (University of Cambridge, UK)

    Title: Candidates for Non-Supersymmetric Dualities

    Abstract: In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

     

  • Math Science Literature Lecture Series
    9:00 am-10:30 pm
    12/01/2024

    Maxim Kontsevich  (IHÉS)

    Title: On the History of quantum cohomology and homological mirror symmetry

    Abstract: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry.  First, the usual cup-product on the cohomology of a complex projective variety admits a canonical multi-parameter deformation to so-called quantum product, satisfying a nice system of differential equations (WDVV equations).  The second discovery, even more striking,  is Mirror Symmetry, a duality between families of Calabi-Yau varieties acting as a mirror reflection on the Hodge diamond.

    Later it was realized that the quantum product belongs to the realm of symplectic geometry, and a half of mirror symmetry (called Homological Mirror Symmetry) is a duality between complex algebraic and symplectic varieties. The search of correct definitions and possible generalizations lead to great advances in many domains, giving mathematicians new glasses, through which they can see familiar objects in a completely new way.

    I will review the history of major mathematical advances in the subject of HMS, and the swirl of ideas around it.

    Talk chair: Paul Seidel

    Video

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    4/1/2021 Strongly Correlated Quantum Materials

    9:00 am-10:30 am
    12/01/2024
  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 09.21.22

    Topological Quantum Matter Seminar

    Speaker: Semyon Klevtsov, University of Strasbourg

    Title: Geometric test for topological states of matter

    Abstract: We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the

    degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille).

     

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024-04/27/2021

    In 2021, the CMSA hosted a lecture series on the literature of the mathematical sciences. This series highlights significant accomplishments in the intersection between mathematics and the sciences. Speakers include Edward Witten, Lydia Bieri, Simon Donaldson, Michael Freedman, Dan Freed, and many more.

    Videos of these talks can be found in this Youtube playlist.

    https://youtu.be/vb_JEhUW9t4

    In the Spring 2021 semester, the CMSA hosted a sub-program on this series titled A Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Below is the schedule for talks in that subprogram

    April 6, 2021 | 9:00 – 10:30am ET

    Edward Witten (IAS)

    TitleIsadore Singer’s Work on Analytic Torsion


    April 13, 2021 | 9:00 – 10:30am ET

    Claire Voisin (College de France)

    Title: K-theory and characteristic classes in topology and complex geometry  (a tribute to Atiyah and Hirzebruch)


    April 20, 2021 | 9:00 – 10:30am ET

    Dan Freed (the University of Texas at Austin)

    TitleThe Atiyah-Singer Index Theorem


    April 27, 2021 | 9:00 – 10:30am ET

    Frances Kirwan (University of Oxford)

    TitleMoment maps and the Yang-Mills functional

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Edward Witten (IAS)

    TitleIsadore Singer’s Work on Analytic Torsion

    Abstract:  I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory.

    This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and Singer.

    Talk chair: Cumrun Vafa

    Slides | Video

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Equiangular lines and regular graphs

    9:00 am-10:00 am
    12/01/2024

    Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

    Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
    the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA QMMP Seminar

    Quantum Matter in Mathematics and Physics Seminar

    Speaker: Zhengyan Darius Shi (MIT)
    Title: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
    Abstract: Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity \sigma(mega) \sim mega^{-2/z} (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result \sigma(mega) \sim mega^{-2(z-2)/z}  due to Kim et al. is incorrect for inversion-odd order parameters.
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    7/1/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Interdisciplinary Science Seminar

    Speaker: Yue M. Lu, Harvard University

    Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning

    Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
    In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.

    Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007.  He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.

  • CMSA EVENT: Joint BHI/CMSA Conference on Flat Holography
    9:00 am-5:00 pm
    12/01/2024-06/24/2022

    On June 21–24, 2022, the Harvard Black Hole Initiative and the CMSA hosted the Joint BHI/CMSA Conference on Flat Holography (and related topics).

    The recent discovery of infinitely-many soft symmetries for all quantum theories of gravity in asymptotically flat space has provided a promising starting point for a bottom-up construction of a holographic dual for the real world. Recent developments have brought together previously disparate studies of soft theorems, asymptotic symmetries, twistor theory, asymptotically flat black holes and their microscopic duals, self-dual gravity, and celestial scattering amplitudes, and link directly to AdS/CFT.

    The conference was held in room G10 of the CMSA, 20 Garden Street, Cambridge, MA.

    Organizers:

    • Daniel Kapec, CMSA
    • Andrew Strominger, BHI
    • Shing-Tung Yau, Harvard & Tsinghua

    Confirmed Speakers:

    • Nima Arkani-Hamed, IAS
    • Shamik Banerjee, Bhubaneswar, Inst. Phys.
    • Miguel Campiglia, Republica U., Montevido
    • Geoffrey Compere, Brussels
    • Laura Donnay, Vienna
    • Netta Engelhardt, MIT
    • Laurent Freidel, Perimeter
    • Alex Lupsasca, Princeton
    • Juan Maldacena, IAS
    • Lionel Mason, Oxford
    • Natalie Paquette, U. Washington
    • Sabrina Pasterski, Princeton/Perimeter
    • Andrea Puhm, Ecole Polytechnique
    • Ana-Maria Raclariu, Perimeter
    • Marcus Spradlin, Brown
    • Tomasz Taylor, Northeastern
    • Herman Verlinde, Princeton
    • Anastasia Volovich, Brown
    • Bin Zhu, Northeastern

    Short talks by: Gonçalo Araujo-Regado (Cambridge), Adam Ball (Harvard), Eduardo Casali (Harvard), Jordan Cotler (Harvard), Erin Crawley (Harvard), Stéphane Detournay (Brussels), Alfredo Guevara (Harvard), Temple He (UC Davis), Elizabeth Himwich (Harvard), Yangrui Hu (Brown), Daniel Kapec (Harvard), Rifath Khan (Cambridge), Albert Law (Harvard), Luke Lippstreu (Brown), Noah Miller (Harvard), Sruthi Narayanan (Harvard), Lecheng Ren (Brown), Francisco Rojas (UAI), Romain Ruzziconi (Vienna), Andrew Strominger (Harvard), Adam Tropper (Harvard), Tianli Wang (Harvard), Walker Melton (Harvard)

    Schedule

    Monday, June 20, 2022

    Arrival
    7:00–9:00 pmWelcome Reception at Andy’s residence

     

    Tuesday, June 21, 2022

    9:00–9:30 amBreakfastlight breakfast provided
    Morning SessionChair: Dan Kapec
    9:30–10:00 amHerman VerlindeTitle: Comments on Celestial Dynamics
    10:00–10:30 amJuan MaldacenaTitle: What happens when you spend too much time looking at supersymmetric
    black holes?
    10:30–11:00Coffee break
    11:00–11:30 amMiguel CampigliaTitle: Asymptotic symmetries and loop corrections to soft theorems
    11:30–12:00 pmGeoffrey CompereTitle: Metric reconstruction from $Lw_{1+\infty}$ multipoles

    Abstract: The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be exchanged under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely determined by a set of conserved celestial charges, which uniquely label transitions among non-radiative regions caused by radiative processes. The algebra of the conserved celestial charges is derived from the real $Lw_{1+\infty}$ algebra. The celestial charges are expressed in terms of multipole moments, which allows to holographically reconstruct the metric in de Donder, Newman-Unti or Bondi gauge outside of sources.

    12:00–2:00 pmLunch break
    Afternoon SessionChair: Eduardo Casali
    2:00–2:30 pmNatalie PaquetteTitle: New thoughts on old gauge amplitudes
    2:30–3:00 pmLionel MasonTitle: An open sigma model for celestial gravity

    Abstract: A global twistor construction for conformally self-dual split signature metrics on $S2\times S2$  was developed 15 years ago by Claude LeBrun and the speaker.  This encodes the conformal metric into the location of a finite deformation of the real twistor space inside the flat complex twistor space, $\mathbb{CP}3$. This talk adapts the construction to construct global SD Einstein metrics from conformal boundary data and perturbations around the self-dual sector.  The construction entails determining a family of holomorphic discs in $\mathbb{CP}3$ whose boundaries lie on the deformed real slice and the (chiral) sigma model controls these discs in the Einstein case and provides amplitude formulae.

    3:00–3:30 pmCoffee break
    3:30–4:30 pmShort TalksDaniel Kapec: Soft Scalars and the Geometry of the Space of Celestial CFTs

    Albert Law: Soft Scalars and the Geometry of the Space of Celestial CFTs

    Sruthi Narayanan: Soft Scalars and the Geometry of the Space of Celestial CFTs

    Stéphane Detournay: Non-conformal symmetries and near-extremal black holes

    Francisco Rojas: Celestial string amplitudes beyond tree level

    Temple He: An effective description of energy transport from holography

    4:30–5:00 pmNima Arkani-Hamed(Dual) surfacehedra and flow particles know about strings

     

    Wednesday, June 22, 2022

    9:00–9:30 amBreakfastlight breakfast provided
    Morning SessionChair: Alfredo Guevara
    9:30–10:00 amLaurent FreidelTitle: Higher spin symmetry in gravity

    Abstract: In this talk, I will review how the gravitational conservation laws at infinity reveal a tower of symmetry charges in an asymptotically flat spacetime.
    I will show how the conservation laws, at spacelike infinity, give a tower of soft theorems that connect to the ones revealed by celestial holography.
    I’ll present the expression for the symmetry charges in the radiative phase space, which opens the way to reveal the structure of the algebra beyond the positive helicity sector. Then, if time permits I’ll browse through many questions that these results raise:
    such as the nature of the spacetime symmetry these charges represent, the nature of the relationship with multipole moments, and the insights their presence provides for quantum gravity.

    10:00–10:30 amAna-Maria RaclariuTitle: Eikonal approximation in celestial CFT
    10:30–11:00 amCoffee break
    11:00–11:30 amAnastasia VolovichTitle: Effective Field Theories with Celestial Duals
    11:30–12:00 pmMarcus SpradlinTitle: Loop level gluon OPE’s in celestial holography
    12:00–2:00 pmLunch break
    Afternoon SessionChair: Chiara Toldo
    2:00–2:30 pmNetta EngelhardtTitle: Wormholes from entanglement: true or false?
    2:30–3:00 pmShort TalksLuke Lippstreu: Loop corrections to the OPE of celestial gluons

    Yangrui Hu: Light transforms of celestial amplitudes

    Lecheng Ren: All-order OPE expansion of celestial gluon and graviton primaries from MHV amplitudes

    3:00–3:30 pmCoffee break
    3:30–4:30 pmShort TalksNoah Miller: C Metric Thermodynamics

    Erin Crawley: Kleinian black holes

    Rifath Khan: Cauchy Slice Holography: A New AdS/CFT Dictionary

    Gonçalo Araujo-Regado: Cauchy Slice Holography: A New AdS/CFT Dictionary

    Tianli Wang: Soft Theorem in the BFSS Matrix Model

    Adam Tropper: Soft Theorem in the BFSS Matrix Model

    7:00–9:00 pmBanquetMaharaja Restaurant, 57 JFK Street, Cambridge, MA

     

    Thursday, June 23, 2022

    9:00–9:30 amBreakfastlight breakfast provided
    Morning SessionChair: Jordan Cotler
    9:30–10:00 amLaura DonnayTitle: A Carrollian road to flat space holography
    10:00–10:30 amAndrea PuhmTitle: Celestial wave scattering on Kerr-Schild backgrounds
    10:30–11:00 amCoffee break
    11:00–11:30 amSabrina PasterskiTitle: Mining Celestial Symmetries

    Abstract: The aim of this talk is to delve into the common thread that ties together recent work with H. Verlinde, L. Donnay, A. Puhm, and S. Banerjee exploring, explaining, and exploiting the symmetries encoded in the conformally soft sector.

    Come prepared to debate the central charge, loop corrections, contour prescriptions, and orders of limits!

    11:30–12:00 pmShamik BanerjeeTitle: Virasoro and other symmetries in CCFT

    Abstract:  In this talk I will briefly describe my ongoing work with Sabrina Pasterski. In this work we revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton.  In its original formulation, we find that there is an obstruction to reproducing the expected $TT$ OPE in the double soft limit. This obstruction is related to the existence of the $SL_2$ current algebra symmetry of the CCFT. We propose a modification to the definition of the stress tensor which circumvents this obstruction and also discuss its implications for the existence of other current algebra (w_{1+\infty}) symmetries in CCFT.

    12:00–2:00 pmLunch break
    Afternoon SessionChair: Albert Law
    2:00–2:30 pmTomasz TaylorTitle: Celestial Yang-Mills amplitudes and D=4 conformal blocks
    2:30–3:00 pmBin ZhuTitle:  Single-valued correlators and Banerjee-Ghosh equations

    Abstract:  Low-point celestial amplitudes are plagued with singularities resulting from spacetime translation. We consider a marginal deformation of the celestial CFT which is realized by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators.

    3:00–3:30 pmCoffee break
    3:30–4:00 pmAlex LupsascaTitle: Holography of the Photon Ring
    4:00–5:30 pmShort TalksElizabeth Himwich: Celestial OPEs and w(1+infinity) symmetry of massless and massive amplitudes

    Adam Ball: Perturbatively exact $w_{1+\infty}$ asymptotic symmetry of quantum self-dual gravity

    Romain Ruzziconi: A Carrollian Perspective on Celestial Holography

    Jordan Cotler: Soft Gravitons in 3D

    Alfredo Guevara: Comments on w_1+\inf

    Andrew Strominger: Top-down celestial holograms

    Eduardo Casali: Celestial amplitudes as AdS-Witten diagrams

    Walker Melton: Top-down celestial holograms

     

    Friday, June 24, 2022

    9:00–9:30 amBreakfast
    9:30–12:30 pmOpen Discussion
    12:30–2:30 pmLunch provided at the BHI
    Departure

     

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    Interdisciplinary Science Seminar
    Title: Recent Advances on Maximum Flows and Minimum-Cost Flows

    Abstract: We survey recent advances on computing flows in graphs, culminating in an almost linear time algorithm for solving minimum-cost flow and several other problems to high accuracy on directed graphs. Along the way, we will discuss intuitions from linear programming, graph theory, and data structures that influence these works, and the resulting natural open problems.

    Bio: Yang P. Liu is a final-year graduate student at Stanford University. He is broadly interested in the efficient design of algorithms, particularly flows, convex optimization, and online algorithms. For his work, he has been awarded STOC and ITCS best student papers.

  • Workshop
    9:00 am-5:00 pm
    12/01/2024-08/05/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Phase Transitions_Poster

    On August 2–5, the CMSA hosted a workshop on Phase Transitions and Topological Defects in the Early Universe.

    The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA and online via Zoom webinar.

    The next decade will see a wealth of new cosmological data, which can lead to new insights into fundamental physics. Upcoming facilities (such as LISA) will be able to probe signals of fascinating phenomena in the early universe. These include signals from “Phase Transitions and Topological Defects,” which are ubiquitously given rise to in well-motivated UV models. In-depth studies of such signals requires cross-talks between experts from a wide spectrum of fields.

    The workshop aims to provide a platform for efficient exchange of new ideas related to these topics. It will start with an overview of some of the past and future experimental efforts. Next, there will be a substantial number of talks probing different aspects of phenomenology of phase transitions and topological defects in the early universe. It will finally close with discussions on recent formal development in the field.

    Scientific Advisory: Julian B. Muñoz, Lisa Randall, Matthew Reece, Tracy Slatyer, Shing-Tung Yau

    Organizers:
    Harvard: Nick DePorzio, Katie Fraser, Sam Homiller, Rashmish Mishra, & Aditya Parikh
    MIT: Pouya Asadi, Marianne Moore, & Yitian Sun

    Schedule/Format
    There will be 20+ 10 minute talks, ample discussion time, and lightning chalkboard talks.

    Speakers:

    • Nancy Aggarwal (Northwestern)
    • Jae Hyeok Chang (UMD – JHU)
    • Yanou Cui (UC Riverside)
    • David Dunsky (UC Berkeley)
    • Isabel Garcia-Garcia (KITP – UCSB)
    • Oliver Gould (Nottingham)
    • Yann Gouttenoire (Tel Aviv)
    • Eleanor Hall (UC Berkeley)
    • Sungwoo Hong (Chicago)
    • Anson Hook (UMD)
    • Jessica Howard (UC Irvine)
    • Seth Koren (Chicago)
    • Mrunal Korwar (Wisconsin)
    • Soubhik Kumar (UC Berkeley)
    • Vuk Mandic (Minnesota)
    • Yuto Minami (Osaka)
    • Michael Nee (Oxford)
    • Kai Schmitz (CERN)
    • Stephen R. Taylor (Vanderbilt)
    • Ofri Telem (UC Berkeley)
    • Juven Wang (Harvard)
    • Yikun Wang (Caltech)

    Participants:

    • Manuel Buen Abad (UMD)
    • Pouya Asadi (MIT)
    • Sean Benevedes (MIT)
    • Sandipan Bhattacherjee (Birla Institute of Technology Mesra Ranchi India)
    • Xingang Chen (Harvard University)
    • Nicholas DePorzio (Harvard University)
    • Peizhi Du (Stony Brook University)
    • Nicolas Fernandez (University of Illinois Urbana-Champaign)
    • Joshua Foster (MIT)
    • Katherine Fraser (Harvard University)
    • Sarah Geller (MIT)
    • Aurora Ireland (University of Chicago)
    • Marius Kongsore (New York University)
    • Ho Tat Lam (Massachusetts Institute of Technology)
    • Lingfeng Li (Brown University)
    • Yingying Li (Fermilab)
    • Gustavo Marques-Tavares (UMD)
    • Rashmish Mishra (Harvard University)
    • Siddharth Mishra-Sharma (MIT/Harvard University)
    • Toby Opferkuch (UC Berkeley)
    • Tong Ou (University of Chicago)
    • Aditya Parikh (Harvard University)
    • Yitian Sun (MIT)
    • Juan Sebastian Valbuena-Bermudez (Ludwig Maximilian University of Munich and Max Planck Institute for Physics)
    • Isaac Wang (Rutgers)
    • Wei Xue (University of Florida)
    • Winston Yin (UC Berkeley)
    • Quratulain Zahoor (The Islamia University of Bahwalpur Punjab (Pakistan)

    Schedule

    Tuesday, August 2, 2022

    9:00–9:20 amBreakfast
    9:20–9:30 amRashmish MishraOpening Remarks
    9:30–10:00 amVuk MandicTitle: Searching for the Stochastic Gravitational Wave Background with LISA

    Abstract: The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) will open a window into the milliHertz band of the gravitational wave spectrum. Among the many sources in this band is the stochastic gravitational wave background (SGWB), arising as an incoherent superposition of many uncorrelated gravitational wave sources. The SGWB could be of cosmological origin, carrying unique information about the physical processes that took place within the first minute after the big bang, including possible phase transitions and topological defects. LISA therefore has the potential to illuminate particle physics at very high energy scales that may be inaccessible in laboratories. I will discuss how LISA can be used to search for the SGWB, highlighting a new pipeline developed for this purpose as well as several challenges and limitations that such a search will encounter.

    10:00–10:30 amNancy AggarwalTitle: Gravitational waves at frequencies above 10 kHz

    Abstract: Gravitational waves (GWs) at frequencies higher than the LIGO band can bring us completely new information about the universe. Besides being the most-interesting frequency region for looking at cosmological phenomena, they can also convey signatures of ultralight bosons through blackhole superradiance and light primordial blackholes (PBHs). I will introduce a new global initiative to study GW sources and detectors at ultra-high-frequencies (MHz-GHz), as well as a new experiment at Northwestern University to look for GWs in the frequency band of 10 kHz to 300 kHz using levitated optomechanical sensors. I will summarize the design, the current experimental progress, as well as a path forward for future improvements.

    10:30–11:00 amYuto MinamiTitle: New measurements of the cosmic birefringence

    Abstract: Polarised light of the cosmic microwave background, the remnant light of the Big Bang, is sensitive to parity-violating physics, cosmic birefringence. In this presentation I report on a new measurement of cosmic birefringence from polarisation data of the European Space Agency (ESA)’s Planck satellite released in 2018. The statistical significance of the measured signal is 2.4 sigma. Recently, we found a signal with 3.3 sigma statistical significance when we use the latest Planck data and consider an effect of polarised foreground emission. If confirmed with higher statistical significance in future, it would have important implications for the elusive nature of dark matter and dark energy.

    11:00–1:30 pmBreak
    1:30–3:00 pmLighting Talks 1Lingfeng Li
    Winston Yin
    Marius Kongsore
    Nick DePorzio
    3:00–3:30 pmJae Hyeok ChangTitle: Correlating gravitational wave and gamma-ray signals from primordial black holes

    Abstract: Asteroid-mass primordial black holes (PBHs) can explain the observed dark matter abundance while being consistent with the current indirect detection constraints. These PBHs can produce gamma-ray signals from Hawking radiation that are within the sensitivity of future measurements by the AMEGO and e-ASTROGAM experiments. PBHs which give rise to such observable gamma-ray signals have a cosmic origin from large primordial curvature fluctuations. There must then be a companion, stochastic gravitational wave (GW) background produced by the same curvature fluctuations. I will demonstrate that the resulting GW signals will be well within the sensitivity of future detectors such as LISA, DECIGO, BBO, and the Einstein Telescope. The multimessenger signal from the observed gamma-rays and GWs will allow a precise measurement of the primordial curvature perturbation that produces the PBH. I will also argue that the resulting correlation between the two types of observations can provide a smoking-gun signal of PBHs.

    3:30–4:00 pmAnson Hook
    (Virtual via Zoom)
    Title: Early Universe Cosmology from Stochastic Gravitational Waves

    Abstract:  The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure gstar and beta functions as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the 10^-3 level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to O(1) deviations of gstar and the QCD beta function from their Standard Model value at temperatures ~ 10^5 GeV. In this case, many motivated models such as split SUSY and other solutions to the Electroweak Hierarchy problem would be tested. Future detectors, such as DECIGO, would be 100 times more sensitive than LISA to these effects and be capable of testing other motivated scenarios such as WIMPs and axions. The amazing prospect of using precision gravitational wave measurements to test such well motivated theories provides a benchmark to aim for when developing a precise understanding of the gravitational wave spectrum both experimentally and theoretically.

     

    Wednesday, August 3, 2022

    9:00–9:30 amBreakfast
    9:30–10:00 amKai Schmitz
    (Virtual via Zoom)
    Title: Gravitational waves from metastable cosmic strings

    Abstract: Cosmic strings are predicted by many Standard Model extensions involving the cosmological breaking of an Abelian symmetry and represent a potential source of primordial gravitational waves (GWs). In many Grand Unified Theories (GUTs), cosmic strings especially turn out to be metastable, as the nucleation of GUT monopoles along strings after a finite lifetime eventually leads to the collapse of the entire string network. In this talk, I will discuss the theoretical description of such a network and its individual components as well as the consequences for the emitted GW spectrum. Remarkably, the GW signal from metastable strings may well explain the common-spectrum process recently observed in pulsar timing data, while at the same time and in contrast to stable cosmic strings predicting a signal at higher frequencies that is still within the reach of current-generation ground-based interferometers. On their way to design sensitivity, existing GW experiments will thus have a realistic chance to probe particle physics processes at energies close to the GUT scale via the observation of GWs from metastable strings. This talk is based on 2107.04578 in collaboration with Wilfried Buchmüller and Valerie Domcke.

    10:00–10:30 amOliver Gould
    (Virtual via Zoom)
    Title: Effective field theory for cosmological phase transitions

    Abstract: Phase transitions are driven by thermal loop fluctuations, which modify background fields at leading order. This breaks the loop expansion and leads to large theoretical uncertainties in typical calculations, especially for gravitational wave predictions. I will give an overview of our present understanding of these uncertainties, and of the tools that have been developed to overcome them. Effective field theory has been at the forefront of this development, and I will outline how it can be used to solve a number of decades-long-standing theoretical problems.

    10:30–11:00 amIsabel Garcia-GarciaTitle: The Rocket Science of Expanding Bubbles

    11:00–1:30 pmBreak
    1:30–3:00 pmLightning Talks 2Sarah Geller
    Peizhi Du
    Tong Ou
    Isaac Wang
    Katie Fraser
    3:00–3:30 pmDavid Dunsky
    (Virtual via Zoom)
    Title: Gravitational Wave Gastronomy

    Abstract: The symmetry breaking of grand unified gauge groups in the early universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable and can leave behind unique gravitational wave fingerprints. In this talk, I will discuss the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and “eat” the strings, 2) the collapse and decay of a monopole-string network by strings that “eat” the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and “eat” the wall, and 4) the collapse and decay of a string-bounded wall network by walls that “eat” the strings. We call the gravitational wave signals produced from the “eating” of one topological defect by another “gravitational wave gastronomy”. The gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO(10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects.

    3:30–4:00 pmYanou Cui
    (Virtual via Zoom)
    Title: Cosmic Archaeology with gravitational waves from (axion) cosmic strings

    Abstract: In this talk I will discuss important aspects of cosmology and particle physics that can be probed with GW signals from cosmic strings: probing the pre-BBN primordial dark age and axion physics.  Gravitational waves (GWs) originating from the dynamics of a cosmic string network have the ability to probe many otherwise inaccessible properties of the early universe. In particular, I will discuss how the frequency spectrum of a stochastic GW background (SGWB) from a cosmic string network can be used to probe Hubble expansion rate of the early universe prior to Big Bang Nucleosynthesis (BBN), during the “primordial dark age”. Furthermore I will show that in contrast to the standard expectation, cosmic strings formed before inflation could regrow back into the horizon and leave imprints, with GW bursts potentially being the leading signal. In relation to axion physics I will also demonstrate the detection prospect for SGWB from global/axion strings which may provide a new probe for axion-like dark matter models, considering various scenarios of cosmic history.

    4:00–4:30 pmMichael NeeTitle: The Boring Monopole

    Abstract: First order phase transitions play an important role in the cosmology of many theories of BSM physics. In this talk I will discuss how a population of magnetic monopoles present in the early universe can seed first order phase transitions, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, thus requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. Our results show that monopole-catalysed tunnelling can dominate over the homogeneous decay for a wide range of parameters.

     

    Thursday, August 4, 2022

    9:00–9:30 amBreakfast
    9:30–10:00 amYikun WangTitle: A New Approach to Electroweak Symmetry Non-Restoration

    Abstract: Electroweak symmetry non-restoration up to high temperatures well above the electroweak scale has intriguing implications for (electroweak) baryogenesis and early universe thermal histories. In this talk, I will discuss such a possible fate of the electroweak symmetry in the early universe and a new approach to realize it, via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. Examples of benchmark scenarios that allow for electroweak symmetry non-restoration all the way up to hundreds of TeV temperatures, at the same time featuring suppressed sphaleron washout factors down to the electroweak scale, will be presented. Renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures, have been implemented calculating the thermal history. This method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

    10:00–10:30 amSoubhik KumarTitle: Probing primordial fluctuations through stochastic gravitational wave background anisotropies

    Abstract: Stochastic gravitational wave backgrounds are expected to be anisotropic. While such anisotropies can be of astrophysical origin, a cosmological component of such anisotropies can carry rich information about primordial perturbations. Focusing on the case of a cosmological phase transition, I will talk about how such anisotropies can give us a powerful probe of primordial non-Gaussianities, complementary to current and future CMB and LSS searches. In the scenario where astrophysical foregrounds are also present, I will then discuss some strategies using which we can extract the cosmological signal, focusing on the case of LISA, Taiji and BBO, in particular.

    10:30–11:00 amJessica Howard
    (Virtual via Zoom)
    Title: Dark Matter Freeze-out during SU(2)_L Confinement

    Abstract: We explore the possibility that dark matter is a pair of SU(2)_L doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This phase of confinement causes the Standard Model doublets and dark matter to confine into pion-like objects. Before the weak sector deconfines, the dark pions freezeout and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the observed relic density. We determine which regions of this parameter space evade direct detection and collider bounds.

    11:00–11:30 amJuven WangTitle: Quantum Matter Adventure to Beyond the Standard Model Prediction

    Abstract: Ideas developed from the quantum matter and quantum field theory frontier may guide us to explore new physics beyond the 4d Standard Model. I propose a few such ideas. First, new physics for neutrinos: right-handed neutrinos carry a Z_{16} class mixed gauge-gravitational global anomaly index, which could be replaced by 4d or 5d topological quantum field theory, or 4d interacting conformal field theory. These theories provide possible new neutrino mass mechanisms [arXiv:2012.15860]. Second, deconfined quantum criticality between Grand Unified Theories: dictated by a Z_2 class global anomaly, a gapless quantum critical region can happen between Georgi-Glashow and Pati-Salam models as deformation of the Standard Model, where Beyond the Standard Model physics and Dark Gauge sector occur as neighbor phases [arXiv:2106.16248, arXiv:2112.14765, arXiv:2204.08393]. Third, the Strong CP problem can be solved by a new solution involving Symmetric Mass Generation [arXiv:2204.14271].

    11:30–1:30 pmBreak
    1:30–4:00 pmStephen R. TaylorTitle: Pulsar Timing Arrays: The Next Window onto the Low-frequency Gravitational-wave Universe

    Abstract: The nanohertz-frequency band of gravitational waves should be awash with signals from supermassive black-hole binaries, as well as cosmological signatures of phase transitions, cosmic strings, and other relics of the early Universe. Pulsar-timing arrays (PTAs) like the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and the International Pulsar Timing Array are poised to chart this new frontier of gravitational wave discovery within the next several years. I will present exciting new results from recent cutting-edge searches, discuss some milestones on the road to the next decade of PTA discovery, and take workshop attendees through a guided tutorial of how the broader community can use our production-level analysis pipeline to extract new science with ease.

     

    Friday, August 5, 2022

    9:00–9:30 amBreakfast
    9:30–10:00 amOfri TelemTitle: Charge-Monopole Pairwise Phases from Dressed Quantum States

    10:00–10:30 amSungwoo HongTitle: Coupling a Cosmic String to a TQFT

    Abstract: In the last few years, the notion of symmetry has been enlarged to “generalized symmetry” or “higher-form symmetry” and these more generalized symmetries have played a critical role in deepening our understanding of QFT, notably IR phases of QFT. In this talk, I will discuss a various ways of coupling the axion-Maxwell theory to a topological field theory (TQFT). Contrary to a common wisdom, I will show that such topological modifications can lead to direct changes in the local physics with possible observable consequences. This surprise can be realized by a dimensional reduction, namely, a coupling to a TQFT in 4d leads to a non-trivial and local impact on the 2d string world-sheet QFT. There also exists a topological modification of the theory, i.e. gauging a discrete subgroup of 0-form shift symmetry, and this time it results in a alteration of spectrum of cosmic strings. If time permits, I will also discuss generalized symmetries and associated higher-groups of these theories.

    10:30–11:00 amEleanor Hall
    (Virtual via Zoom)
    Title: Non-perturbative methods for false vacuum decay

    Abstract: Gravitational waves from phase transitions in the early universe are one of our most promising signal channels of BSM physics; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present the quasi-stationary effective action, a new non-perturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. This method opens the door to reliable calculation of gravitational wave signals and false vacuum decay rates for strongly-interacting theories. I will also discuss recent developments and ongoing extensions of the QSEA.

    11:00–1:30 pmBreak
    1:30–2:00 pmMrunal KorwarTitle: Electroweak Symmetric Balls

    Abstract: Electroweak symmetric balls are macroscopic objects with electroweak symmetry restored inside. Such an object can arise in models where dark sectors contain monopole or non-topological soliton with a Higgs portal interaction to the Standard Model. It could be produced in the early universe via phase transition or parametric resonance, accounting for all dark matter. In a scenario where the balls are allowed to evaporate, the observed baryon asymmetry in our universe could be explained by a mechanism of “catalyzed baryogenesis.” In this mechanism, the motion of a ball-like catalyst provides the necessary out-of-equilibrium condition, its outer wall has CP-violating interactions with the Standard Model particles, and its interior has baryon number violating interactions via electroweak Sphaleron. Because of electroweak symmetric cores, such objects have a large geometric cross-section off a nucleus, generating a multi-hit signature in large volume detectors. These objects could radiatively capture a nucleus and release GeV-scale energy for each interaction. The IceCube detector can probe dark matter balls with masses up to a gram.

    2:00–2:30 pmSeth KorenTitle: Discrete Gauged Baryon Minus Lepton Number and the Cosmological Lithium Problem

    Abstract: We study the baryon minus lepton number gauge theory broken by a scalar with charge six. The infrared discrete vestige of the gauge symmetry demands the existence of cosmic string solutions, and their production as dynamical objects in the early universe is guaranteed by causality. These topological defects can support interactions which convert three protons into three positrons, and we argue an `electric’-`magnetic’ interplay can lead to an amplified, strong-scale cross-section in an analogue of the Callan-Rubakov effect.
    The cosmological lithium problem—that theory predicts a primordial abundance thrice as high as that observed—has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We suggest cosmic strings have disintegrated O(1) of the primordial lithium nuclei and estimate the rate in a benchmark scenario. To our knowledge this is the first new physics mechanism with microphysical justification for the abundance of lithium uniquely to be modified after Big Bang Nucleosynthesis.

    2:30–3:00 pmYann GouttenoireTitle: Supercool Composite Dark Matter beyond 100 TeV

     

    Phase-Transitions_Poster

  • CMSA EVENT: Advances in Mathematical Physics
    9:00 am-1:45 pm
    12/01/2024-08/01/2022
    1 Oxford Street, Cambridge MA 02138
    Elliott-Lieb-conference-2022_banner-2-1536x734

    A Conference in Honor of Elliott H. Lieb on his 90th Birthday

    On July 30 – Aug 1, 2022 the Harvard Mathematics Department and the CMSA co-hosted a birthday conference in honor of Elliott Lieb.

    This meeting highlights Elliott’s vast contribution to math and physics. Additionally, this meeting features Prof. Lieb’s more recent impact in strong subadditivity of entropy and integrable systems (ice model, Temperley-Lieb algebra etc.).

    Venue:

    July 30–31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
    August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138

    Schedule (pdf)

    Organizers:
    Michael Aizenman, Princeton University
    Joel Lebowitz, Rutgers University
    Ruedi Seiler, Technische Universität Berlin
    Herbert Spohn, Technical University of Munich
    Horng-Tzer Yau, Harvard University
    Shing-Tung Yau, Harvard University
    Jakob Yngvason, University of Vienna

    SPEAKERS:
    Rafael Benguria, Pontificia Universidad Catolica de Chile
    Eric Carlen, Rutgers University
    Philippe Di Francesco, University of Illinois
    Hugo Duminil-Copin, IHES
    László Erdös, Institute of Science and Technology Austria
    Rupert Frank, Ludwig Maximilian University of Munich
    Jürg Fröhlich, ETH Zurich
    Alessandro Giuliani, Università degli Studi Roma Tre
    Bertrand Halperin, Harvard University
    Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
    Sabine Jansen, Ludwig Maximilian University of Munich
    Mathieu Lewin, Université Paris-Dauphine
    Bruno Nachtergaele, The University of California, Davis
    Yoshiko Ogata, University of Tokyo
    Ron Peled, Tel Aviv University
    Benjamin Schlein, University of Zurich
    Robert Seiringer, Institute of Science and Technology Austria
    Jan Philip Solovej, University of Copenhagen
    Hal Tasaki, Gakushuin University
    Simone Warzel, Technical University of Munich
    Jun Yin, The University of California, Los Angeles

     

    Elliott-Lieb-conference

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    CMSA Interdisciplinary Science Seminar

    Speaker: Sumit Sinha, Harvard University

    Title: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data (https://arxiv.org/abs/2202.10595)

    Abstract: Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.

    Bio: I am a postdoctoral fellow in Harvard SEAS (Applied Mathematics) and Dana Farber Cancer Institute (Data Science) beginning Feb 2022. I finished my PhD in Physics (Theoretical Biophysics) from UT Austin (Jan 2022) on “Theoretical and computational studies of growing tissue”.  I pursued my undergraduate degree in Physics from the Indian Institute of Technology, Kanpur in India (2015). Boradly, I am interested in developing theoretical models, inspired from many-body statistical physics, for biological processes at different length and time scales.

     

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024

    Abstract: The establishment of neural circuitry during early infancy is critical for developing visual, auditory, and motor functions. However, how cortical tissue develops postnatally is largely unknown. By combining T1 relaxation time from quantitative MRI and mean diffusivity (MD) from diffusion MRI, we tracked cortical tissue development in infants across three timepoints (newborn, 3 months, and 6 months). Lower T1 and MD indicate higher microstructural tissue density and more developed cortex. Our data reveal three main findings: First, primary sensory-motor areas (V1: visual, A1: auditory, S1: somatosensory, M1: motor) have lower Tand MD at birth than higher-level cortical areas. However, all primary areas show significant reductions in Tand MD in the first six months of life, illustrating profound tissue growth after birth. Second, significant reductions in Tand MD from newborns to 6-month-olds occur in all visual areas of the ventral and dorsal visual streams. Strikingly, this development was heterogenous across the visual hierarchies: Earlier areas are more developed with denser tissue at birth than higher-order areas, but higher-order areas had faster rates of development. Finally, analysis of transcriptomic gene data that compares gene expression in postnatal vs. prenatal tissue samples showed strong postnatal expression of genes associated with myelination, synaptic signaling, and dendritic processes. Our results indicate that these cellular processes may contribute to profound postnatal tissue growth in sensory cortices observed in our in-vivo measurements. We propose a novel principle of postnatal maturation of sensory systems: development of cortical tissue proceeds in a hierarchical manner, enabling the lower-level areas to develop first to provide scaffolding for higher-order areas, which begin to develop more rapidly following birth to perform complex computations for vision and audition.

    This work is published here: https://www.nature.com/articles/s42003-021-02706-w

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-07.14.22-1583x2048

    Abstract:  Introducing internal degrees of freedom in the description of crystalline insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses. Here, we present a semiclassical approach to transport and accumulation of general spinor degrees of freedom in adiabatically driven, weakly inhomogeneous crystals of dimensions one, two and three under external electromagnetic fields. Our approach shows that spatio-temporal modulations of the system induce a spinor current and density that is related to geometrical and topological objects — the spinor-Chern fluxes and numbers — defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates.

    The results are available here: https://arxiv.org/abs/2203.14902

    Bio: Ioannis Petrides is a postdoctoral fellow at the School of Engineering and Applied Sciences at Harvard University. He received his Ph.D. from the Institute for Theoretical Physics at ETH Zurich. His research focuses on the topological and geometrical aspects of condensed matter systems.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/15/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    Interdisciplinary Science Seminar
    Speaker: Fouad El Baidouri, Broad Institute

    Title: The phenotype of the last universal common ancestor and the evolution of complexity

    Abstract: A fundamental concept in evolutionary theory is the last universal common ancestor (LUCA) from which all living organisms originated. While some authors have suggested a relatively complex LUCA it is still widely assumed that LUCA must have been a very simple cell and that life has subsequently increased in complexity through time. However, while current thought does tend towards a general increase in complexity through time in Eukaryotes, there is increasing evidence that bacteria and archaea have undergone considerable genome reduction during their evolution. This raises the surprising possibility that LUCA, as the ancestor of bacteria and archaea may have been a considerably complex cell. While hypotheses regarding the phenotype of LUCA do exist, all are founded on gene presence/absence. Yet, despite recent attempts to link genes and phenotypic traits in prokaryotes, it is still inherently difficult to predict phenotype based on the presence or absence of genes alone. In response to this, we used Bayesian phylogenetic comparative methods to predict ancestral traits. Testing for robustness to horizontal gene transfer (HGT) we inferred the phenotypic traits of LUCA using two robust published phylogenetic trees and a dataset of 3,128 bacterial and archaeal species.

    Our results depict LUCA as a far more complex cell than has previously been proposed, challenging the evolutionary model of increased complexity through time in prokaryotes. Given current estimates for the emergence of LUCA we suggest that early life very rapidly evolved cellular complexity.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    6/24/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Some new algorithms in statistical genomics

    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-06.23.2022-1583x2048-1

    Abstract: The statistical analysis of genomic data has incubated many innovations for computational method development. This talk will discuss some simple algorithms that may be useful in analyzing such data. Examples include algorithms for efficient resampling-based hypothesis testing, minimizing the sum of truncated convex functions, and fitting equality-constrained lasso problems. These algorithms have the potential to be used in other applications beyond statistical genomics.

    Bio: Hui Jiang is an Associate Professor in the Department of Biostatistics at the University of Michigan. He received his Ph.D. in Computational and Mathematical Engineering from Stanford University. Before joining the University of Michigan, he was a postdoc in the Department of Statistics and Stanford Genome Technology Center at Stanford University. He is interested in developing statistical and computational methods for analyzing large-scale biological data generated using modern high-throughput technologies.

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Peter Shor (MIT)

    TitleQuantum error correcting codes and fault tolerance

    Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field.

    Talk chair: Zhengwei Liu

    Video

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    The number of n-queens configurations

    9:00 am-10:00 am
    12/01/2024

    Speaker: Michael Simkin, Harvard CMSA

    Title: The number of n-queens configurations

    Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

    Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    6/10/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
    9:00 am-12:00 pm
    12/01/2024-01/13/2017
    banner-image-1

    The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

     

    Confirmed Participants:

  • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
    9:00 am-5:00 pm
    12/01/2024-05/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Organizers:

    D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

    Speakers:

    1. Netanel Blaier (MIT)
    2. Kwokwai Chan (CUHK)
    3. Bohan Fang (Peking University)
    4. Amanda Francis (BYU)
    5. Hansol Hong (CUHK)
    6. Heather Lee (Purdue University)
    7. Si Li (Tsinghua University)
    8. Yu-Shen Lin (Stanford University)
    9. Alex Perry (Harvard University)
    10. Hiro Tanaka (Harvard University)
    11. Sara Tukachinsky (HUJ)
    12. Michael Viscardi (MIT)
    13. Eric Zaslow (Northwestern University)
    14. Jingyu Zhao (Columbia University)

    Please click here for the conference Main Website.

    Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Schedule:

    May 6 – Day 1
    9:00amBreakfast
    9:35amOpening remarks
    9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
    10:45am – 11:15amBreak
    11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
    May 7 – Day 2
    9:00amBreakfast
    9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
    10:45am – 11:15amBreak
    11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
    May 8 – Day 3
    9:00amBreakfast
    9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
    10:45am – 11:15amBreak
    11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
    * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

    This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Adventures in Perturbation Theory

    9:00 am-10:00 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-01.25.2022-1

    Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The Amplituhedron BCFW Triangulation

    9:00 am-10:00 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-2.3.2022

    Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

  • CMSA EVENT: Workshop on Optimization in Image Processing
    9:00 am-12:30 pm
    12/01/2024-06/30/2016

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Speakers:

    1. Antonin Chambolle, CMAP, Ecole Polytechnique
    2. Raymond Chan, The Chinese University of Hong Kong
    3. Ke Chen, University of Liverpool
    4. Patrick Louis Combettes, Université Pierre et Marie Curie
    5. Mario Figueiredo, Instituto Superior Técnico
    6. Alfred Hero, University of Michigan
    7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
    8. Mila Nikolova, Ecole Normale Superieure Cachan
    9. Shoham Sabach, Israel Institute of Technology
    10. Martin Benning, University of Cambridge
    11. Jin Keun Seo, Yonsei University
    12. Fiorella Sgallari, University of Bologna
    13. Gabriele Steidl, Kaiserslautern University of Technology
    14. Joachim Weickert, Saarland University
    15. Isao Yamada, Tokyo Institute of Technology
    16. Wotao Yin, UCLA

    Please click Workshop Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

    Schedule:

    June 27 – Day 1
    9:00amBreakfast
    9:20amOpening remarks
    9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
    10:20am – 10:50amBreak
    10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
    11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
    12:30pm – 2:00pmLunch
    2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
    June 28 – Day 2
    9:00amBreakfast
    9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
    10:20am – 10:50amBreak
    10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
    11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 4:40pmDiscussions
    June 29 – Day 3
    9:00amBreakfast
    9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
    10:20am – 10:50amBreak
    10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
    11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
    June 30 – Day 4
    9:00amBreakfast
    9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
    10:20am – 10:50amBreak
    10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
    11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
    * This event is sponsored by CMSA Harvard University.

    Organizers: Raymond Chan and Shing-Tung Yau

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA/Tsinghua Math-Science Literature Lecture: Scott Kominers

    9:00 am-10:30 am
    12/01/2024

    CMSA/Tsinghua Math-Science Literature Lecture

    Prof. Scott Kominers will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

    Date: Monday, November 20, 2023

    Time: 9:00 – 10:30 am ET

    Location: Via Zoom Webinar

    Registration is required.

    Title: 60 Years of Matching: From Gale and Shapley to Trading Networks

    Abstract: Gale and Shapley’s 1962 American Mathematical Monthly paper, “College Admissions and the Stability of Marriage,” is by now one of the most cited articles in the journal’s history, having served as the foundation for an entire branch of the field of market design. This success owes in large part to the beautiful, applicable, and surprisingly general theory of matching mechanisms uncovered in Gale and Shapley’s work. This talk traces the history and evolution of matching theory from that paper forward to the present day, along the way touching on real-world applications to everything from medical residency matching to electricity markets.

    Moderator: Sergiy Verstyuk


    Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

     

    CMSA COVID-19 Policies

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    10/19/2021 Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    Title: Ising model, total positivity, and criticality

    Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
    The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
    I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model

  • Workshop
    9:00 am-5:00 pm
    12/01/2024-05/19/2023
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    GRAMSIAcover-600x338

    On May 16 – May 19, 2023 the CMSA hosted a four-day workshop on GRAMSIA: Graphical Models, Statistical Inference, and Algorithms. The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop was organized by David Gamarnik (MIT), Kavita Ramanan (Brown), and Prasad Tetali  (Carnegie Mellon).

    The purpose of this workshop is to highlight various mathematical questions and issues associated with graphical models and message-passing algorithms, and to bring together a group of researchers for discussion of the latest progress and challenges ahead. In addition to the substantial impact of graphical models on applied areas, they are also connected to various branches of the mathematical sciences. Rather than focusing on the applications, the primary goal is to highlight and deepen these mathematical connections.

    Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

     

    Speakers:
    • Jake Abernethy (Georgia Tech)
    • Guy Bresler (MIT)
    • Florent Krzakala (Ecole Polytechnique Federale de Lausanne)
    • Lester Mackey (Microsoft Research New England)
    • Theo McKenzie (Harvard)
    • Andrea Montanari (Stanford)
    • Elchanan Mossel (MIT)
    • Yury Polyanskiy (MIT)
    • Patrick Rebeschini (Oxford)
    • Subhabrata Sen (Harvard)
    • Devavrat Shah (MIT)
    • Pragya Sur (Harvard)
    • Alex Wein (UC Davis)
    • Yihong Wu (Yale)
    • Sarath Yasodharan (Brown)
    • Horng-Tzer Yau (Harvard)
    • Christina Lee Yu (Cornell)
    • Ilias Zadik (MIT)
    Schedule:

    Tuesday, May 16, 2023

    9:00 amBreakfast
    9:15 – 9:30 amIntroductory remarks by organizers
    9:30 – 10:20 amSubhabrata Sen (Harvard)

    Title: Mean-field approximations for high-dimensional Bayesian regression

    Abstract: Variational approximations provide an attractive computational alternative to MCMC-based strategies for approximating the posterior distribution in Bayesian inference. The Naive Mean-Field (NMF) approximation is the simplest version of this strategy—this approach approximates the posterior in KL divergence by a product distribution. There has been considerable progress recently in understanding the accuracy of NMF under structural constraints such as sparsity, but not much is known in the absence of such constraints. Moreover, in some high-dimensional settings, the NMF is expected to be grossly inaccurate, and advanced mean-field techniques (e.g. Bethe approximation) are expected to provide accurate approximations. We will present some recent work in understanding this duality in the context of high-dimensional regression. This is based on joint work with Sumit Mukherjee (Columbia) and Jiaze Qiu (Harvard University).

    10:30 – 11:00 amCoffee break 
    11:00 – 11:50 amElchanan Mossel (MIT)

    Title: Some modern perspectives on the Kesten-Stigum bound for reconstruction on trees.

    Abstract: The Kesten-Stigum bound is a fundamental spectral bound for reconstruction on trees. I will discuss some conjectures and recent progress on understanding when it is tight as well as some conjectures and recent progress on what it signifies even in cases where it is not tight.

    12:00 – 2:00 pmLunch
    2:00 – 2:50 pmChristina Lee Yu (Cornell)

    Title: Exploiting Neighborhood Interference with Low Order Interactions under Unit Randomized Design

    Abstract: Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in many real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we utilize knowledge of the network structure to provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. Central to our contribution is a new framework for balancing between model flexibility and statistical complexity as captured by this low order interactions structure.

    3:00 – 3:30 pmCoffee break
    3:30 – 4:20 pmTheo McKenzie (Harvard)

    Title: Spectral statistics for sparse random graphs

    Abstract: Understanding the eigenvectors and eigenvalues of the adjacency matrix of random graphs is fundamental to many algorithmic questions; moreover, it is related to longstanding questions in quantum physics. In this talk we focus on random models of sparse graphs, giving some properties that are unique to these sparse graphs, as well as some specific obstacles. Based on this, we show some new results on spectral statistics of sparse random graphs, as well as some conjectures.

    4:40 – 6:30 pmLightning talk session + welcome reception

     

    Wednesday, May 17, 2023

    9:00 amBreakfast
    9:30 – 10:20Ilias Zadik (MIT)

    Title: Revisiting Jerrum’s Metropolis Process for the Planted Clique Problem

    Abstract: Jerrum in 1992 (co-)introduced the planted clique model by proving the (worst-case initialization) failure of the Metropolis process to recover any o(sqrt(n))-sized clique planted in the Erdos-Renyi graph G(n,1/2). This result is classically cited in the literature of the problem, as the “first evidence” the o(sqrt(n))-sized planted clique recovery task is “algorithmically hard”.
    In this work, we show that the Metropolis process actually fails to work (under worst-case initialization) for any o(n)-sized planted clique, that is the failure applies well beyond the sqrt(n) “conjectured algorithmic threshold”. Moreover we also prove, for a large number of temperature values, that the Metropolis process fails also under “natural initialization”, resolving an open question posed by Jerrum in 1992.

    10:30 – 11:00Coffee break
    11:00 – 11:50Florent Krzakala (Ecole Polytechnique Federale de Lausanne)

    Title: Are Gaussian data all you need for machine learning theory?

    Abstract: Clearly, no! Nevertheless, the Gaussian assumption remains prevalent among theoreticians, particularly in high-dimensional statistics and physics, less so in traditional statistical learning circles. To what extent are Gaussian features merely a convenient choice for certain theoreticians, or genuinely an effective model for learning? In this talk, I will review recent progress on these questions, achieved using rigorous probabilistic approaches in high-dimension and techniques from mathematical statistical physics. I will demonstrate that, despite its apparent limitations, the Gaussian approach is sometimes much closer to reality than one might expect. In particular, I will discuss key findings from a series of recent papers that showcase the Gaussian equivalence of generative models, the universality of Gaussian mixtures, and the conditions under which a single Gaussian can characterize the error in high-dimensional estimation. These results illuminate the strengths and weaknesses of the Gaussian assumption, shedding light on its applicability and limitations in the realm of theoretical statistical learning.

    12:00 – 2:00 pmLunch
    2:00 – 2:50 pmAndrea Montanari (Stanford)

    Title: Dimension free ridge regression

    Abstract: Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we revisit ridge regression. We allow the feature vector to be high-dimensional, or even infinite-dimensional, in which case it belongs to a separable Hilbert space and assume it to satisfy a certain convex concentration property. Within this setting, we establish non-asymptotic bounds that approximate the bias and variance of ridge regression in terms of the bias and variance of an ‘equivalent’ sequence model (a regression model with diagonal design matrix). Previously, such an approximation result was known only in the proportional regime and only up to additive errors: in particular, it did not allow to characterize the behavior of the excess risk when this converges to 0. Our general theory recovers earlier results in the proportional regime (with better error rates). As a new application, we obtain a completely explicit and sharp characterization of ridge regression for Hilbert covariates with regularly varying spectrum. Finally, we analyze the overparametrized near-interpolation setting and obtain sharp ‘benign overfitting’ guarantees.

    [Based on joint work with Chen Cheng]

    3:00 – 3:50 pmYury Polyanskiy (MIT)

    Title: Recent results on broadcasting on trees and stochastic block model

    Abstract: I will survey recent results and open questions regarding the q-ary stochastic block model and its local version (broadcasting on trees, or BOT). For example, establishing uniqueness of non-trivial solution to distribution recursions (BP fixed point) implies a characterization for the limiting mutual information between the graph and community labels. For q=2 uniqueness holds in all regimes. For q>2 uniqueness is currently only proved above a certain threshold that is asymptotically (for large q) is close to Kesten-Stigum (KS) threshold. At the same time between the BOT reconstruction and KS we show that uniqueness does not hold, at least in the presence of (arbitrary small) vertex-level side information. I will also discuss extension of the robust reconstruction result of Janson-Mossel’2004.

    Based on joint works with Qian Yu (Princeton) and Yuzhou Gu (MIT).

    4:00 – 4:30 pmCoffee break
    4:30 – 5:20 pmAlex Wein (UC Davis)

    Title: Is Planted Coloring Easier than Planted Clique?

    Abstract: The task of finding a planted clique in the random graph G(n,1/2) is perhaps the canonical example of a statistical-computational gap: for some clique sizes, the task is statistically possible but believed to be computationally hard. Really, there are multiple well-studied tasks related to the planted clique model: detection, recovery, and refutation. While these are equally difficult in the case of planted clique, this need not be true in general. In the related planted coloring model, I will discuss the computational complexity of these three tasks and the interplay among them. Our computational hardness results are based on the low-degree polynomial model of computation.By taking the complement of the graph, the planted coloring model is analogous to the planted clique model but with many planted cliques. Here our conclusion is that adding more cliques makes the detection problem easier but not the recovery problem.

     

    Thursday, May 18, 2023

    9:00Breakfast
    9:30 – 10:20Guy Bresler (MIT)

    Title: Algorithmic Decorrelation and Planted Clique in Dependent Random Graphs

    Abstract: There is a growing collection of average-case reductions starting from Planted Clique (or Planted Dense Subgraph) and mapping to a variety of statistics problems, sharply characterizing their computational phase transitions. These reductions transform an instance of Planted Clique, a highly structured problem with its simple clique signal and independent noise, to problems with richer structure. In this talk we aim to make progress in the other direction: to what extent can these problems, which often have complicated dependent noise, be transformed back to Planted Clique? Such a bidirectional reduction between Planted Clique and another problem shows a strong computational equivalence between the two problems.  We develop a new general framework for reasoning about the validity of average-case reductions based on low sensitivity to perturbations. As a concrete instance of our general result, we consider the planted clique (or dense subgraph) problem in an ambient graph that has dependent edges induced by randomly adding triangles to the Erdos-Renyi graph G(n,p), and show how to successfully eliminate dependence by carefully removing the triangles while approximately preserving the clique (or dense subgraph). Joint work with Chenghao Guo and Yury Polyanskiy.

    10:30 – 11:00Coffee break 
    11:00 – 11:50Sarath Yasodharan (Brown)

    Title: A Sanov-type theorem for unimodular marked random graphs and its applications

    Abstract: We prove a Sanov-type large deviation principle for the component empirical measures of certain sequences of unimodular random graphs (including Erdos-Renyi and random regular graphs) whose vertices are marked with i.i.d. random variables. Specifically, we show that the rate function can be expressed in a fairly tractable form involving suitable relative entropy functionals. As a corollary, we establish a variational formula for the annealed pressure (or limiting log partition function) for various statistical physics models on sparse random graphs. This is joint work with I-Hsun Chen and Kavita Ramanan.

    12:00 – 12:15 pm

    12:15 – 2:00 pm

    Group Photo

    Lunch

    2:00 – 2:50 pmPatrick Rebeschini (Oxford)

    Title: Implicit regularization via uniform convergence

    Abstract: Uniform convergence is one of the main tools to analyze the complexity of learning algorithms based on explicit regularization, but it has shown limited applicability in the context of implicit regularization. In this talk, we investigate the statistical guarantees on the excess risk achieved by early-stopped mirror descent run on the unregularized empirical risk with the squared loss for linear models and kernel methods. We establish a direct link between the potential-based analysis of mirror descent from optimization theory and uniform learning. This link allows characterizing the statistical performance of the path traced by mirror descent directly in terms of localized Rademacher complexities of function classes depending on the choice of the mirror map, initialization point, step size, and the number of iterations. We will discuss other results along the way.

    3:00 – 3:50 pmPragya Sur (Harvard)

    Title: A New Central Limit Theorem for the Augmented IPW estimator in high dimensions

    Abstract: Estimating the average treatment effect (ATE) is a central problem in causal inference. Modern advances in the field studied estimation and inference for the ATE in high dimensions through a variety of approaches. Doubly robust estimators such as the augmented inverse probability weighting (AIPW) form a popular approach in this context. However, the high-dimensional literature surrounding these estimators relies on sparsity conditions, either on the outcome regression (OR) or the propensity score (PS) model. This talk will introduce a new central limit theorem for the classical AIPW estimator, that applies agnostic to such sparsity-type assumptions. Specifically, we will study properties of the cross-fit version of the estimator under well-specified OR and PS models, and the proportional asymptotics regime where the number of confounders and sample size diverge proportional to each other. Under assumptions on the covariate distribution, our CLT will uncover two crucial phenomena among others: (i) the cross-fit AIPW exhibits a substantial variance inflation that can be quantified in terms of the signal-to-noise ratio and other problem parameters, (ii) the asymptotic covariance between the estimators used while cross-fitting is non-negligible even on the root-n scale. These findings are strikingly different from their classical counterparts, and open a vista of possibilities for studying similar other high-dimensional effects. On the technical front, our work utilizes a novel interplay between three distinct tools—approximate message passing theory, the theory of deterministic equivalents, and the leave-one-out approach.

    4:00 – 4:30 pmCoffee break
    4:30 – 5:20 pmYihong Wu (Yale)

    Title: Random graph matching at Otter’s threshold via counting chandeliers

    Abstract: We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erdős–Rényi graphs G(n,q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nq\to\infty and the edge correlation coefficient ρ satisfies ρ^2>α≈0.338, where α is Otter’s tree-counting constant. Moreover, this almost exact matching can be made exact under an extra condition that is information-theoretically necessary. This is the first polynomial-time graph matching algorithm that succeeds at an explicit constant correlation and applies to both sparse and dense graphs. In comparison, previous methods either require ρ=1−o(1) or are restricted to sparse graphs. The crux of the algorithm is a carefully curated family of rooted trees called chandeliers, which allows effective extraction of the graph correlation from the counts of the same tree while suppressing the undesirable correlation between those of different trees. This is joint work with Cheng Mao, Jiaming Xu, and Sophie Yu, available at https://arxiv.org/abs/2209.12313

     

    Friday, May 19, 2023

    9:00Breakfast
    9:30 – 10:20Jake Abernethy (Georgia Tech)

    Title: Optimization, Learning, and Margin-maximization via Playing Games

    Abstract: A very popular trick for solving certain types of optimization problems is this: write your objective as the solution of a two-player zero-sum game, endow both players with an appropriate learning algorithm, watch how the opponents compete, and extract an (approximate) solution from the actions/decisions taken by the players throughout the process. This approach is very generic and provides a natural template to produce new and interesting algorithms. I will describe this framework and show how it applies in several scenarios, including optimization, learning, and margin-maximiation problems. Along the way we will encounter a number of novel tools and rediscover some classical ones as well.

    10:30 – 11:00Coffee break 
    11:00 – 11:50Devavrat Shah (MIT)

    Title: On counterfactual inference with unobserved confounding via exponential family

    Abstract: We are interested in the problem of unit-level counterfactual inference with unobserved confounders owing to the increasing importance of personalized decision-making in many domains: consider a recommender system interacting with a user over time where each user is provided recommendations based on observed demographics, prior engagement levels as well as certain unobserved factors. The system adapts its recommendations sequentially and differently for each user. Ideally, at each point in time, the system wants to infer each user’s unknown engagement if it were exposed to a different sequence of recommendations while everything else remained unchanged. This task is challenging since: (a) the unobserved factors could give rise to spurious associations, (b) the users could be heterogeneous, and (c) only a single trajectory per user is available.

    We model the underlying joint distribution through an exponential family. This reduces the task of unit-level counterfactual inference to simultaneously learning a collection of distributions of a given exponential family with different unknown parameters with single observation per distribution. We discuss a computationally efficient method for learning all of these parameters with estimation error scaling linearly with the metric entropy of the space of unknown parameters – if the parameters are an s-sparse linear combination of k known vectors in p dimension, the error scales as O(s log k/p).  En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality.

    Based on a joint work with Raaz Dwivedi, Abhin Shah and Greg Wornell (all at MIT) with manuscript available here: https://arxiv.org/abs/2211.08209

    12:00 – 2:00 pmLunch 
    2:00 – 2:50 pmLester Mackey  (Microsoft Research New England)

    Title: Advances in Distribution Compression

    Abstract: This talk will introduce two new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning:
    1. Given an initial n-point summary (for example, from independent sampling or a Markov chain), kernel thinning finds a subset of only square-root n-points with comparable worst-case integration error across a reproducing kernel Hilbert space.
    2. If the initial summary suffers from biases due to off-target sampling, tempering, or burn-in, Stein thinning simultaneously compresses the summary and improves the accuracy by correcting for these biases.
    These tools are especially well-suited for tasks that incur substantial downstream computation costs per summary point like organ and tissue modeling in which each simulation consumes 1000s of CPU hours.
    Based on joint work with Raaz Dwivedi, Marina Riabiz, Wilson Ye Chen, Jon Cockayne, Pawel Swietach, Steven A. Niederer, Chris. J. Oates, Abhishek Shetty, and Carles Domingo-Enrich.

    3:00 – 3:30 pmCoffee break
    3:30 – 4:20 pmHorng-Tzer Yau (Harvard)

    Title: On the spectral gap of mean-field spin glass models.

    Abstract: We will discuss recent progress regarding spectral gaps for the Glauber dynamics of spin glasses at high temperature. In addition, we will also report on estimating the operator norm  of the covariance matrix for the SK model.

     

    Moderators: Benjamin McKenna, Harvard CMSA & Changji Xu, Harvard CMSA


     

    CMSA COVID-19 Policies

     

  • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
    9:00 am-5:00 pm
    12/01/2024-12/04/2016

    The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

    The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

    Please click here to register for this event.

    Speakers:

    1. Cliff Taubes (Harvard University)
    2. Valentino Tosatti (Northwestern University)
    3. Pengfei Guan (McGill University)
    4. Jared Speck (MIT)

    Schedule:

    December 3rd – Day 1
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
    December 4th – Day 2
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

    Please click Mini-School Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • CMSA EVENT: Mirror symmetry, gauged linear sigma models, matrix factorizations, and related topics
    9:00 am-4:30 pm
    12/01/2024-03/06/2020
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Mirror-Symmetry-poster-1

    On March 4-6, 2020 the CMSA will be hosting a three-day workshop on Mirror symmetry, Gauged linear sigma models, Matrix factorizations, and related topics as part of the Simons Collaboration on Homological Mirror Symmetry. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    Speakers: 

    Schedule

    Videos from the workshop are available in the Youtube playlist.

  • CMSA EVENT: Quantum Matter Workshop
    9:00 am-5:00 pm
    12/01/2024-12/04/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Quantum Matter Workshop

    On December 2-4, 2019 the CMSA will be hosting a workshop on Quantum Matter as part of our program on Quantum Matter in Mathematics and Physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Pictures can be found here.

    Organizers: Juven Wang (CMSA), Xiao-Gang Wen (MIT), and Shing-Tung Yau (Harvard)

    Confirmed Speakers: 

     

  • CMSA EVENT: Workshop on Coding and Information Theory
    9:00 am-3:30 pm
    12/01/2024-04/13/2018

    The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

    Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    Click here for a list of registrants. 

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

  • Workshop
    9:00 am-6:00 pm
    12/01/2024-05/12/2023
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    The CMSA will be hosting a Workshop on Global Categorical Symmetries from May 7 – 12, 2023

    Participation in the workshop is by invitation.

    Public Lectures

    There will be three lectures on Thursday, May 11, 2023, which are open to the public.
    Location:  Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
    Note: The public lectures will be held in-person only.

    2:00 – 2:50 pm
    Speaker: Kantaro Ohmori (U Tokyo )
    Title: Fusion Surface Models: 2+1d Lattice Models from Higher Categories
    Abstract: Generalized symmetry in general dimensions is expected to be described by higher categories. Conversely, one might expect that, given a higher category with appropriate structures, there exist models that admit the category as its symmetry. In this talk I will explain a construction of such 2+1d lattice models for fusion 2-categories defined by Douglas and Reutter, generalizing the work of Aasen, Fendley and Mong on anyon chains. The construction is by decorating a boundary of a topological Freed-Teleman-Moore sandwich into a non-topological boundary. In particular we can construct a family of candidate lattice systems for chiral topological orders.

     

    3:00 – 3:50 pm
    Speaker: David Jordan (Edinburgh)
    Title: Langlands duality for 3-manifolds
    Abstract: Originating in number theory, and permeating representation theory, algebraic geometry, and quantum field theory, Langlands duality is a pattern of predictions relating pairs of mathematical objects which have no clear a priori mathematical relation. In this talk I’ll explain a new conjectural appearance of Langlands duality in the setting of 3-manifold topology, I’ll give some evidence in the form of special cases, and I’ll survey how the conjecture relates to both the arithmetic and geometric Langlands duality conjectures.

    3:50 – 4:30 pm
    Tea/Snack Break

    4:30 – 5:30 pm
    Speaker: Ken Intriligator (UCSD)
    Colloquium
    Title: QFT Aspects of Symmetry
    Abstract: Everything in the Universe, including the photons that we see and the quarks and electrons in our bodies, are actually ripples of quantum fields. Quantum field theory (QFT) is the underlying mathematical framework of Nature, and in the case of electrons and photons it is the most precisely tested theory in science. Strongly coupled aspects, e.g. the confinement of quarks and gluons at long distances, remain challenging. QFT also describes condensed matter systems, connects to string theory and quantum gravity, and describes cosmology. Symmetry has deep and powerful realizations and implications throughout physics, and this is especially so for the study of QFT. Symmetries play a helpful role in characterizing the phases of theories and their behavior under renormalization group flows (zooming out). Quantum field theory has also been an idea generating machine for mathematics, and there has been increasingly fruitful synergy in both directions. We are currently exploring the symmetry-based interconnections between QFT and mathematics in our Simons Collaboration on Global Categorical Symmetry, which is meeting here this week. I will try to provide an accessible, colloquium-level introduction to aspects of symmetries and QFT, both old and new.


  • CMSA EVENT: Big Data Conference 2023
    9:00 am-5:00 pm
    12/01/2024-09/01/2023
    1 Oxford Street, Cambridge MA 02138

    On August 31-Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    Location: Harvard University Science Center Hall D & via Zoom.

    Directions and Recommended Lodging

    Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

    Registration is required.

    Note: In-person registration is at capacity. Please sign up for the Zoom Webinar (registration link).

     

    Speakers:

     

    Organizers:

    • Michael Douglas, CMSA, Harvard University
    • Yannai Gonczarowski, Economics and Computer Science, Harvard University
    • Lucas Janson, Statistics and Computer Science, Harvard University
    • Tracy Ke, Statistics, Harvard University
    • Horng-Tzer Yau, Mathematics and CMSA, Harvard University
    • Yue Lu, Electrical Engineering and Applied Mathematics, Harvard University

    Schedule

    (PDF download)

    Thursday, August 31, 2023

    9:00 AMBreakfast
    9:30 AMIntroductions
    9:45–10:45 AMAlbert-László Barabási (Northeastern, Harvard)

    Title: From Network Medicine to the Foodome: The Dark Matter of Nutrition

    Abstract: A disease is rarely a consequence of an abnormality in a single gene but reflects perturbations to the complex intracellular network. Network medicine offer a platform to explore systematically not only the molecular complexity of a particular disease, leading to the identification of disease modules and pathways, but also the molecular relationships between apparently distinct (patho) phenotypes. As an application, I will explore how we use network medicine to uncover the role individual food molecules in our health. Indeed, our current understanding of how diet affects our health is limited to the role of 150 key nutritional components systematically tracked by the USDA and other national databases in all foods. Yet, these nutritional components represent only a tiny fraction of the over 135,000 distinct, definable biochemicals present in our food. While many of these biochemicals have documented effects on health, they remain unquantified in any systematic fashion across different individual foods. Their invisibility to experimental, clinical, and epidemiological studies defines them as the ‘Dark Matter of Nutrition.’ I will speak about our efforts to develop a high-resolution library of this nutritional dark matter, and efforts to understand the role of these molecules on health, opening novel avenues by which to understand, avoid, and control disease.

    https://youtu.be/UmgzUwi6K3E

    10:45–11:00 AMBreak
    11:00 AM–12:00 PMRachel Cummings (Columbia)

    Title: Differentially Private Algorithms for Statistical Estimation Problems

    Abstract: Differential privacy (DP) is widely regarded as a gold standard for privacy-preserving computation over users’ data.  It is a parameterized notion of database privacy that gives a rigorous worst-case bound on the information that can be learned about any one individual from the result of a data analysis task. Algorithmically it is achieved by injecting carefully calibrated randomness into the analysis to balance privacy protections with accuracy of the results.
    In this talk, we will survey recent developments in the development of DP algorithms for three important statistical problems, namely online learning with bandit feedback, causal interference, and learning from imbalanced data. For the first problem, we will show that Thompson sampling — a standard bandit algorithm developed in the 1930s — already satisfies DP due to the inherent randomness of the algorithm. For the second problem of causal inference and counterfactual estimation, we develop the first DP algorithms for synthetic control, which has been used non-privately for this task for decades. Finally, for the problem of imbalanced learning, where one class is severely underrepresented in the training data, we show that combining existing techniques such as minority oversampling perform very poorly when applied as pre-processing before a DP learning algorithm; instead we propose novel approaches for privately generating synthetic minority points.

    Based on joint works with Marco Avella Medina, Vishal Misra, Yuliia Lut, Tingting Ou, Saeyoung Rho, and Ethan Turok.

    https://youtu.be/0cPE6rb1Roo

    12:00–1:30 PMLunch
    1:30–2:30 PMMorgane Austern (Harvard)

    Title: To split or not to split that is the question: From cross validation to debiased machine learning

    Abstract: Data splitting is a ubiquitous method in statistics with examples ranging from cross-validation to cross-fitting. However, despite its prevalence, theoretical guidance regarding its use is still lacking. In this talk, we will explore two examples and establish an asymptotic theory for it. In the first part of this talk, we study the cross-validation method, a ubiquitous method for risk estimation, and establish its asymptotic properties for a large class of models and with an arbitrary number of folds. Under stability conditions, we establish a central limit theorem and Berry-Esseen bounds for the cross-validated risk, which enable us to compute asymptotically accurate confidence intervals. Using our results, we study the statistical speed-up offered by cross-validation compared to a train-test split procedure. We reveal some surprising behavior of the cross-validated risk and establish the statistically optimal choice for the number of folds. In the second part of this talk, we study the role of cross-fitting in the generalized method of moments with moments that also depend on some auxiliary functions. Recent lines of work show how one can use generic machine learning estimators for these auxiliary problems, while maintaining asymptotic normality and root-n consistency of the target parameter of interest. The literature typically requires that these auxiliary problems are fitted on a separate sample or in a cross-fitting manner. We show that when these auxiliary estimation algorithms satisfy natural leave-one-out stability properties, then sample splitting is not required. This allows for sample reuse, which can be beneficial in moderately sized sample regimes.

    https://youtu.be/L_pHxgoQSgU

    2:30–2:45 PMBreak
    2:45–3:45 PMAnkur Moitra (MIT)

    Title: Learning from Dynamics

    Abstract: Linear dynamical systems are the canonical model for time series data. They have wide-ranging applications and there is a vast literature on learning their parameters from input-output sequences. Moreover they have received renewed interest because of their connections to recurrent neural networks.
    But there are wide gaps in our understanding. Existing works have only asymptotic guarantees or else make restrictive assumptions, e.g. that preclude having any long-range correlations. In this work, we give a new algorithm based on the method of moments that is computationally efficient and works under essentially minimal assumptions. Our work points to several missed connections, whereby tools from theoretical machine learning including tensor methods, can be used in non-stationary settings.

    https://youtu.be/UmgzUwi6K3E

    3:45–4:00 PMBreak
    4:00–5:00 PMMark Sellke (Harvard)

    Title: Algorithmic Thresholds for Spherical Spin Glasses

    Abstract: High-dimensional optimization plays a crucial role in modern statistics and machine learning. I will present recent progress on non-convex optimization problems with random objectives, focusing on the spherical p-spin glass. This model is related to spiked tensor estimation and has been studied in probability and physics for decades. We will see that a natural class of “stable” optimization algorithms gets stuck at an algorithmic threshold related to geometric properties of the landscape. The algorithmic threshold value is efficiently attained via Langevin dynamics or by a second-order ascent method of Subag. Much of this picture extends to other models, such as random constraint satisfaction problems at high clause density.

    https://youtu.be/JoghiwiIbT8

    6:00 – 8:00 PMBanquet for organizers and speakers

     

    Friday, September 1, 2023

    9:00 AMBreakfast
    9:30 AMIntroductions
    9:45–10:45 AMJacob Andreas (MIT)

    Title: What Learning Algorithm is In-Context Learning?

    Abstract: Neural sequence models, especially transformers, exhibit a remarkable capacity for “in-context” learning. They can construct new predictors from sequences of labeled examples (x,f(x)) presented in the input without further parameter updates. I’ll present recent findings suggesting that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context, using in-context linear regression as a model problem. First, I’ll show by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, I’ll show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Finally, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners’ late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. This work is joint with Ekin Akyürek at MIT, and Dale Schuurmans, Tengyu Ma and Denny Zhou at Stanford.

    https://youtu.be/UNVl64G3BzA

    10:45–11:00 AMBreak
    11:00 AM–12:00 PMTommi Jaakkola (MIT)

    Title: Generative modeling and physical processes

    Abstract: Rapidly advancing deep distributional modeling techniques offer a number of opportunities for complex generative tasks, from natural sciences such as molecules and materials to engineering. I will discuss generative approaches inspired from physical processes including diffusion models and more recent electrostatic models (Poisson flow), and how they relate to each other in terms of embedding dimension. From the point of view of applications, I will highlight our recent work on SE(3) invariant distributional modeling over backbone 3D structures with ability to generate designable monomers without relying on pre-trained protein structure prediction methods as well as state of the art image generation capabilities (Poisson flow). Time permitting, I will also discuss recent analysis of efficiency of sample generation in such models.

    https://youtu.be/GLEwQAWQ85E

    12:00–1:30 PMLunch
    1:30–2:30 PMMarinka Zitnik (Harvard Medical School)

    Title: Multimodal Learning on Graphs

    Abstract: Understanding biological and natural systems requires modeling data with underlying geometric relationships across scales and modalities such as biological sequences, chemical constraints, and graphs of 3D spatial or biological interactions. I will discuss unique challenges for learning from multimodal datasets that are due to varying inductive biases across modalities and the potential absence of explicit graphs in the input. I will describe a framework for structure-inducing pretraining that allows for a comprehensive study of how relational structure can be induced in pretrained language models. We use the framework to explore new graph pretraining objectives that impose relational structure in the induced latent spaces—i.e., pretraining objectives that explicitly impose structural constraints on the distance or geometry of pretrained models. Applications in genomic medicine and therapeutic science will be discussed. These include TxGNN, an AI model enabling zero-shot prediction of therapeutic use across over 17,000 diseases, and PINNACLE, a contextual graph AI model dynamically adjusting its outputs to contexts in which it operates. PINNACLE enhances 3D protein structure representations and predicts the effects of drugs at single-cell resolution.

    https://youtu.be/hjt4nsN_8iM

    2:30–2:45 PMBreak
    2:45–3:45 PMJianqing Fan (Princeton)

    Title: UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

    Abstract: Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts. Numerous methods are available for constructing prediction intervals, such as quantile regression and conformal predictions, among others. Nevertheless, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this work, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions.  Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics. (Joint work Jiawei Ge and Debarghya Mukherjee).

    https://youtu.be/WY6dr1oEOrk

    3:45–4:00 PMBreak
    4:00–5:00 PMMelissa Dell (Harvard)

    Title: Efficient OCR for Building a Diverse Digital History

    Abstract: Many users consult digital archives daily, but the information they can access is unrepresentative of the diversity of documentary history. The sequence-to-sequence architecture typically used for optical character recognition (OCR) – which jointly learns a vision and language model – is poorly extensible to low-resource document collections, as learning a language-vision model requires extensive labeled sequences and compute. This study models OCR as a character-level image retrieval problem, using a contrastively trained vision encoder. Because the model only learns characters’ visual features, it is more sample-efficient and extensible than existing architectures, enabling accurate OCR in settings where existing solutions fail. Crucially, it opens new avenues for community engagement in making digital history more representative of documentary history.

    https://youtu.be/u0JY9vURUAs

     


    Information about the 2022 Big Data Conference can be found here.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Invariant theory for maximum likelihood estimation

    9:00 am-10:00 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-2.8.2022

    Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

  • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
    9:00 am-1:30 pm
    12/01/2024-02/09/2018

    The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

    There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

    The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The n-queens problem

    9:00 am-10:00 am
    12/01/2024

    Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

    In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

    This is joint work with Peter Keevash.

  • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
    9:00 am-6:15 pm
    12/01/2024-03/26/2018
    GIC-Poster-2-e1520002551865

    On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

    The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

    Please click here to register for the event.

    Confirmed Speakers:

  • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
    9:00 am-11:55 am
    12/01/2024-03/29/2019
    Machine-Learning-Poster

    The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Speakers:

  • CMSA EVENT: The 2017 Charles River Lectures
    9:15 am-5:30 pm
    12/01/2024

    The 2017 Charles River Lectures

    Charles River with Bench at Sunset

    Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

    The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


    ***************************************************

    UPDATED LOCATION

    Harvard University

    Harvard Science Center (Halls C & E)

    1 Oxford Street, Cambridge, MA 02138 (Map)

    Monday, October 2, 2017

    9:15 AM – 5:30 PM

    **************************************************

    Please note that registration has closed.

    Speakers:

    Agenda:

    In Harvard Science Center Hall C:

    8:45 am – 9:15 amCoffee/light breakfast

    9:15 am – 10:15 am: Ofer Zeitouni

    Title: Noise stability of the spectrum of large matrices

    Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

    The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

    10:20 am – 11:20 am: Andrea Montanari

    Title: Algorithms for estimating low-rank matrices 

    Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

    11:20 am – 11:45 amBreak

    11:45 am – 12:45 pm: Paul Bourgade

    Title: Random matrices, the Riemann zeta function and trees

    Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

    1:00 pm – 2:30 pm: Lunch

    In Harvard Science Center Hall E:

    2:45 pm – 3:45 pm: Roman Vershynin

    Title: Deviations of random matrices and applications

    Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

    3:45 pm – 4:15 pm: Break

    4:15 pm – 5:15 pm: Massimiliano Gubinelli

    Title: Weak universality and Singular SPDEs

    Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

    Poster:

    2017 Charles River Lectures Poster

    Organizers:

     Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

  • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
    9:15 am-3:25 pm
    12/01/2024-09/11/2019
    Topology-Poster

    On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

    New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

    Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

    This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Click here for a list of restaurants in the area. 

    Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

    Partial list of speakers:

    Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

  • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
    9:15 am-10:00 am
    12/01/2024-04/17/2019

    As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

    This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

    In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Videos

    Tentative Speaker List:

    Schedule:

    Monday, April 15

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:15amWelcome and Introduction
    9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

    Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

    10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

    Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

    In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

    I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

    10:45 – 11:15amCoffee Break
    11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

    12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    12:45 – 2:00pmLunch
    2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

    My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

    2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

    Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

    Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

    4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

    Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

    5:30 – 6:30pmReception

     

    Tuesday, April 16

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

    9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

    Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

    11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

    Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

    12:30 – 2:00pmLunch
    2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

    Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

    2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

    Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

    4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

    Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


    Wednesday, April 17

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

    Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

    Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

    (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

    (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

    (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

    University of Jerusalem, Jerusalem, 91904, Israel

    9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

    Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

    This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

    Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

    11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

    Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

    12:30 – 1:30pmLunch
    1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

    Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

    2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

    Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

    3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

    Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

    3:45 – 4:00pmL Mahadevan – summary
  • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
    9:20 am-3:15 pm
    12/01/2024-08/28/2018
    Topological-1

    Screen-Shot-2018-08-13-at-2.28.22-PM

    On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

    This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please register here

    Speakers: 

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Max Wiesner

    Title: Light strings, strong coupling, and the Swampland

    Abstract: In this talk, I will start by reviewing central ideas of the so-called Swampland Program. The Swampland Program aims to identify criteria that distinguish low-energy effective field theories, that can be consistently coupled to quantum gravity, from those theories that become inconsistent in the presence of quantum gravity.

    In my talk I will specialize to four-dimensional effective field theories with N=2 and N=1 supersymmetry. In weakly-coupled regions of the scalar field space of such theories, it has been shown that light strings are crucial to realize certain Swampland criteria. Complementary to that, the focus of this talk will be on the role of such light strings away from these weak-coupling regimes. In this context, I will first discuss a relation between light perturbative strings and strong coupling singularities in the Kähler moduli space of 4d N=1 compactifications of F-theory. More precisely, in regions of moduli space, in which a critical string classically becomes light, I will show that non-perturbative corrections yield to strong coupling singularities for D7-brane gauge theories which obstruct weak-coupling limits. Moreover, I will demonstrate that in the vicinity of this strong coupling singularity, the critical, light string in fact leaves the spectrum of BPS strings thereby providing an explanation for the obstruction of the weak coupling limit.

    I will then move on and discuss the backreaction of perturbative strings in 4d EFTs. Away from the string core, the backreaction of such strings necessarily leads to strong coupling regions where naively the energy stored in the backreaction diverges. I will show how the introduction of additional non-critical strings can regulate this backreaction and how this can be used to study the spectrum of BPS strings and their tensions even beyond weak coupling regions. In this context, I will demonstrate how the requirement, that the total string tension should not exceed the Planck scale, constrains the possible BPS string charges.

  • Special Seminar
    9:30 am-11:00 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Speaker: Bong Lian

    Title: Singular Calabi-Yau mirror symmetry

    Abstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors, including Matsumoto, Sasaki, Yoshida and others, mainly from the viewpoint of their moduli spaces and their comparisons.  I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono, Tsung-Ju Lee, Hiromichi Takagi, Shing-Tung Yau.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Tsung-Ju Lee

    Title: Periods for singular CY families and Riemann–Hilbert correspondence

    Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and mirror symmetry. In this talk, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.

  • Member Seminar
    9:30 am-11:30 am
    12/01/2024

    Member Seminar

    Speaker: Chuck Doran

    Title: The Greene-Plesser Construction Revisited

    Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The threshold for stacked triangulations

    9:30 am-10:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10
    CMSA-Combinatorics-Physics-and-Probability-Seminar-05.03.22

    Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{[n]}3$, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle.
    Suppose that every triangle is initially infected independently with probability p=p(n), what is the threshold probability for percolation — the event that all triangles get infected? How many new triangles do get infected in the subcritical regime?

    This notion of percolation can be viewed as a simplification of simple-connectivity. Namely, a stacked triangulation of a triangle is obtained by repeatedly subdividing an inner face into three faces.
    We ask: for which $p$ does the random simplicial complex Y_2(n,p) contain, for every triple $xyz$, the faces of a stacked triangulation of $xyz$ whose internal vertices are arbitrarily labeled in [n].

    We consider this problem in every dimension d>=2, and our main result identifies a sharp probability threshold for percolation, showing it is asymptotically (c_d*n)^(-1/d), where c_d is the growth rate of the Fuss–Catalan numbers of order d.

    The proof hinges on a second moment argument in the supercritical regime, and on Kalai’s algebraic shifting in the subcritical regime.

    Joint work with Eyal Lubetzky.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-Seminar-09.13.22

    Quantum Matter in Mathematics and Physics

    Speaker: Yichul Cho (SUNY Stony Brook)

    Title: Non-invertible Symmetries in Nature

    Abstract: In this talk, I will discuss non-invertible symmetries in
    familiar 3+1d quantum field theories describing our Nature. In
    massless QED, the classical U(1) axial symmetry is not completely
    broken by the ABJ anomaly. Instead, it turns into a discrete,
    non-invertible symmetry. The non-invertible symmetry operator is
    obtained by dressing the naïve U(1) axial symmetry operator with a
    fractional quantum Hall state. We also find a similar non-invertible
    symmetry in the massless limit of QCD, which provides an alternative
    explanation for the neutral pion decay. In the latter part of the
    talk, I will discuss non-invertible time-reversal symmetries in 3+1d
    gauge theories. In particular, I will show that in free Maxwell
    theory, there exists a non-invertible time-reversal symmetry at every
    rational value of the theta angle.

    Based on https://arxiv.org/abs/2205.05086 and https://arxiv.org/abs/2208.04331.

     

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Mathlit_WOODIN

    CMSA/Tsinghua Math-Science Literature Lecture

    woodin_portait_books

    Prof. Hugh Woodin will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

    Date: Wednesday, November 9, 2022

    Time: 9:30 – 11:00 am ET

    Location: Via Zoom Webinar and Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

    Directions and Recommended Lodging

    Registration is required.

     

    Title: Large cardinals and small sets: The AD+ Duality Program

    Abstract: The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers.  The modern view is that determinacy axioms concern generalizations of the borel sets, and deep connections with large cardinal axioms have emerged.

    The study of determinacy axioms has led to a specific technical refinement of AD, this is the axiom AD+. The further connections with large axioms have in turn implicitly led to a duality program, this is the AD+ Duality Program.

    The main open problems here are intertwined with those of the Inner Model Program, which is the central program in the study of large cardinal axioms.

    This has now all been distilled into a series of specific conjectures.

     

    Talk chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)

    Moderator: Alejandro Poveda Ruzafa (Harvard CMSA)

     

    Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

     

    CMSA COVID-19 Policies

  • Member Seminar
    9:30 am-11:00 am
    12/01/2024

    Member Seminar

    Speaker: Sergiy Verstyuk

    Title: Machine Learning the Gravity Equation for International Trade

    Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 11.10.22

    General Relativity Seminar

    Speaker: Pierre Heidmann (Johns Hopkins)

    Title: Schwarzschild-like Topological Solitons in Gravity

    Abstract: We present large classes of non-extremal solitons in gravity that are asymptotic to four-dimensional Minkowski spacetime plus extra compact dimensions. They correspond to smooth horizonless geometries induced by topology in spacetime and supported by electromagnetic flux, which characterize coherent states of quantum gravity. We discuss a new approach to deal with Einstein-Maxwell equations in more than four dimensions, such that they decompose into a set of Ernst equations. We generate the solitons by applying different techniques associated with the Ernst formalism. We focus on solitons with zero net charge yet supported by flux, and compare them to Schwarzschild black holes. These are also ultra-compact geometries with very high redshift but differ in many aspects. At the end of the talk, we discuss the stability properties of the solitons and their gravitational signatures.

  • Algebraic Geometry in String Theory Seminar
  • CMSA EVENT: Math-Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024
    Math-Science Literature Lecture Series

    Mathematics & Literature Lecture Series

    Beginning in Spring 2020, the CMSA will be hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars. Talks will take place throughout the semester. All talks will take place virtually. You must register to attend. Recordings will be posted to this page.

    Written articles will accompany each lecture in this series and be available as part of the publication “The Literature and History of Mathematical Science

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry, transforming Calabi-Yau 3-folds between A- and B-models. In this talk, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X, detail the change of derived categories from its smoothing to its small resolution.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Pok Man Tam (University of Pennsylvania)

    Title: Topology of the Fermi sea: Ordinary metals as topological materials

    Abstract: It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F  to experimental observables, namely: (i) equal-time density/number correlations [1], and (ii) Andreev state transport along a planar Josephson junction [2]. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.

    [1] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)

    [2] P. M. Tam and C. L. Kane, arXiv:2210.08048

     

    https://www.youtube.com/watch?v=AXHLAo8kMHQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=25

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Title: Asymptotic localization, massive fields, and gravitational singularities

    Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-03.09.2022

    Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Prague dimension of random graphs

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-11.23.21

    Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    General Relativity Seminar

    Speaker: Semyon Dyatlov (MIT)

    Title: Ringdown and geometry of trapping for black holes

    Abstract: Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of a black hole merger when the dynamics is expected to be driven by linear effects. In this talk I give an overview of various results in pure mathematics which relate asymptotic behavior of quasi-normal modes at high frequency to the geometry of the set of trapped null geodesics, such as the photon sphere in Schwarzschild (-de Sitter). These trapped geodesics have two kinds of behavior: the geodesic flow is hyperbolic in directions normal to the trapped set (a feature stable under perturbations) and it is completely integrable on the trapped set. It turns out that normal hyperbolicity gives information about the rate of decay of quasi-normal modes, while complete integrability gives rise to a quantization condition.

  • Colloquium
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Elliptic chiral homology and chiral index

    9:30 am-10:30 am
    12/01/2024
    20220330_Si-LI_poster

    Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture – Karen Uhlenbeck

    9:30 am-2:26 pm
    12/01/2024
    Lecture_Uhlenbeck_12921

    Karen Uhlenbeck (Institute for Advanced Study)

    Title: The Noether Theorems in Geometry: Then and Now

    Abstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature.

    Talk Chair: Laura DeMarco

    VIDEO

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Gabriel Wong (Harvard CMSA)

    Title: 3D gravity and gravitational entanglement entropy

    Abstract: Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime. Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge modes.

     

    https://www.youtube.com/watch?v=xD0hWdS-OAc&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=24

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Changji Xu

    Title: On the solution space of the Ising perceptron model

    Abstract:  Consider the discrete cube $\{-1,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk, we will talk about its sharp threshold phenomenon, the frozen structure of the solution space, and the Gardner formula.

  • Joint Harvard-CUHK-YMSC Differential Geometry
    9:30 am-10:30 am
    12/01/2024
    Jim-Bryan_poster_3Nov2021

    Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g,h) which are conjectured to be equivalent, one in terms of a version of PT theory, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface, the specialization of n_beta(g,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-04.27.22

    Speaker: Venkatesan Guruswami, UC Berkeley

    Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

    Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.
    We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

    Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

    This is joint work with Xiaoyu He and Ray Li.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Michael Simkin

    Title: Threshold phenomena in random graphs and hypergraphs

    Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields.

    The model is defined as follows: Given a natural number $n$ and a parameter $p \in [0,1]$, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$, independent of all others. Despite their apparent simplicity, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena.

    A central feature is the appearance of threshold phenomena: For all monotone properties (e.g., connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e., with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Speaker: Freid Tong

    Title: The complex Monge-Ampere equation in Kahler geometry

    Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry, with a particular focus on the a priori C^0 estimates and their various applications. In the end, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.

  • Colloquium
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Gradient flows on totally nonnegative flag varieties

    9:30 am-10:30 am
    12/01/2024

    Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Kan Lin

    Title: China’s financial regulatory reform, financial opening-up, and Central Bank Digital Currency (CBDC)

    Abstract: In this talk, I will explain the overall situation of China’s financial industry and review the development of China’s financial regulatory system reform from 1949 to 2021. Then, I will explain the policies of the 3 stages of financial opening-up, 2001–08, 2008–18, 2018≠present. In particular, the latest round of opening-up from 2018 has brought great opportunities for foreign institutions. China has the world’s largest banking industry with assets totaling $53 trillion, and accounts for 1/3 of the growth in global insurance premiums over the next 10 years. I will also introduce the progress of research & development of China’s Central Bank Digital Currency (CBDC, or E-CNY). By October 2021, 140 million people had opened E-CNY wallets, and 1.6 million merchants could accept payments using eCNY wallets, including utilities, catering services, transportation, retail, and government services.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-03.24.2022-1583x2048

    Youtube Video

     

    Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.16.21-1-1

    Abstract: I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine (arxiv:2109.13323).

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 09.30.2022

    Algebraic Geometry in String Theory Seminar

    Speaker:  Mauricio Romo, Tsinghua University

    Title: GLSM, Homological projective duality and nc resolutions
    Abstract: Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.
  • Algebraic Geometry in String Theory Seminar
  • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
    9:30 am-5:00 pm
    12/01/2024-03/01/2019

    From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

    Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
    The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-05.18.22

    Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.07.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Sam Bardwell-Evans, Boston University
    Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
    Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.
  • Algebraic Geometry in String Theory Seminar
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Flip processes

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1

    Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by  $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.

    Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).

    These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).

    We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
    A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Gabriel Wong 

    Title: Universal relations between entanglement, symmetries, and entropy

    Abstract: Entanglement is an essential property of quantum systems that distinguishes them from classical ones.   It is responsible for the nonlocal character of quantum information and provides a resource for quantum teleportation and quantum computation. In this talk I will provide an introduction to quantum entanglement and explain the essential role it plays in two seemingly unrelated subjects: implementation of measurement-based quantum computation and microstate counting of black holes in quantum gravity.   Time permitting, I will also discuss attempts to characterize entanglement in string theory. A unifying theme that illuminates the entanglement structure of these diverse systems is the role of surface symmetries and (entanglement) edge modes. We will explain how these universal aspects of entanglement are captured in the framework of extended topological quantum field theory.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Hypergraph Matchings Avoiding Forbidden Submatchings

    9:30 am-10:30 am
    12/01/2024

    Abstract:  In 1973, Erdős conjectured the existence of high girth (n,3,2)-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős’ conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős’ conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth (n,q,r)-Steiner systems. We prove the approximate version of their conjecture.  This result follows from our general main results which concern finding perfect or almost perfect matchings in a hypergraph G avoiding a given set of submatchings (which we view as a hypergraph H where V(H)=E(G)). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when H is a hypergraph with small codegrees (for which high girth designs is a specific instance). Indeed, the coloring version of our result even yields an almost partition of K_n^r into approximate high girth (n,q,r)-Steiner systems.  If time permits, I will explain some of the other applications of our main results such as to rainbow matchings.  This is joint work with Luke Postle.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.14.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Daniel Pomerleano, UMass Boston

    Title: Singularities of the quantum connection on a Fano variety

    Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty.

    I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M, D).

  • Member Seminar
    9:30 am-11:00 am
    12/01/2024

    Member Seminar

    Speaker: Juven Wang

    Title: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass

    Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1,2,3,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765arXiv:2204.08393arXiv:2202.13498 and references therein.

  • Colloquium
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Daniel Junghans

    Title: AdS with Scale Separation

    Abstract: I will talk about Anti-de Sitter solutions in string theory with a parametric separation between the AdS curvature scale and the Kaluza-Klein scale. In particular, I will discuss recent progress on computing backreaction corrections in such solutions, and I will explain how to construct solutions without Romans mass that can be lifted to M-theory.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.28.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Ahsan Khan, IAS

    Title: 2-Categories and the Massive 3d A-Model

    Abstract: I will outline the construction of a 2-category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two, and three dimensions combined with a three-dimensional version of the Gaiotto-Moore-Witten web formalism.

     

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-GR-Seminar-03.24.22

    Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Vitor Cardoso, IST, Lisbon and The Niels Bohr Institute, Copenhagen

    Title: Testing GR with GWs

    Abstract: One of the most remarkable possibilities of General Relativity concerns gravitational collapse to black holes, leaving behind a geometry with light rings, ergoregions and horizons. These peculiarities are responsible for uniqueness properties and energy extraction mechanisms that turn black holes into ideal laboratories of strong gravity, of particle physics (yes!) and of possible quantum-gravity effects. I will discuss some of the latest progress in tests of General Relativity with black holes.

  • Colloquium
  • Seminars

    Seminars Colloquia & Seminar
    4/18/2019 General Relativity Seminar

    9:30 am-10:30 am
    12/01/2024
  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)
    3/2/2022Richard Kenyon (Yale University)
    3/9/2022Richard Tsai (UT Austin)
    3/23/2022Joel Cohen (University of Maryland)
    3/30/2022Rob Leigh (UIUC)
    4/6/2022Johannes Kleiner (LMU München)
    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
    4/20/2022TBA
    4/27/2022TBA
    5/4/2022Melody Chan (Brown University)
    5/11/2022TBA
    5/18/2022TBA
    5/25/2022Heeyeon Kim (Rutgers University)

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-03.17.2022-1-1544x2048-1

    Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)Title: Learning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    3/2/2022Richard Kenyon (Yale University)Title: Dimers and webs

    Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

    This is joint work with Dan Douglas and Haolin Shi.

    3/9/2022Yen-Hsi Richard Tsai (UT Austin)Title: Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space

    Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

    3/23/2022Joel Cohen (University of Maryland)Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths

    Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

    3/30/2022Rob Leigh (UIUC)Title: Edge Modes and Gravity

    Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

    4/6/2022Johannes Kleiner (LMU München)Title: What is Mathematical Consciousness Science?

    Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)Title: Quantisation in monoidal categories and quantum operads

    Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure.  But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups.

    The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

    In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts

    4/27/2022Venkatesan Guruswami (UC Berkeley)Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

    Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.

    We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

    Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

    This is joint work with Xiaoyu He and Ray Li.

    5/18/2022 David Nelson (Harvard)TitleStatistical Mechanics of Mutilated Sheets and Shells

    Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-01.26.2022

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Yingying Wu

    Title: Moduli Space of Metric SUSY Graphs

    Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties, followed by a discussion on the connection with the classical case.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Dan Kapec

    Title: Black Holes, 2D Gravity, and Random Matrices

    Abstract: I will discuss old and new connections between black hole physics, 2D quantum gravity, and random matrix theory. Black holes are believed to be very complicated, strongly interacting quantum mechanical systems, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model, but this result raises more questions than it answers. If time permits, I will discuss some extensions of these results and possible future directions.

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Cohomology of the moduli of Higgs bundles via positive characteristic

    9:30 am-8:30 pm
    12/01/2024

    Abstract: In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the character variety of the curve.  I will then explain how certain symmetries of this cohomology, which are predictions of this conjecture, can be constructed using techniques from non-abelian Hodge theory in positive characteristic.  Based on joint work with Mark de Cataldo, Junliang Shen, and Siqing Zhang.

  • Colloquium
  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.21.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Nicolo Piazzalunga, Rutgers

    Title: The index of M-theory

    Abstract: I’ll introduce the higher-rank Donaldson-Thomas theory for toric Calabi-Yau threefolds, within the setting of equivariant K-theory. I’ll present a factorization conjecture motivated by Physics. As a byproduct, I’ll discuss some novel properties of equivariant volumes, as well as their generalizations to the genus-zero Gromov-Witten theory of non-compact toric varieties.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The singularity probability of random symmetric matrices

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-12.07.2021

    Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-03.30.2022

    Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 12.08.22

    General Relativity Seminar

    Speaker: Allen Fang (Princeton)

    Title: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

    Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vector field techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-04.26.2022

    Abstract:   In “Mirror symmetry for log Calabi–Yau surfaces I,” given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y,D) with at worst du Val singularities. As a corollary, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 03.30.23

    General Relativity Seminar

    Speaker: Alejandra Castro (University of Cambridge)

    Title: Gravitational perturbations near to extreme Kerr

    Abstract: Gravitational perturbations of a black hole illustrate the invaluable synergy between theory, experiment, and numerical simulations in general relativity. A recent development in the theory side has been the identification of the relevant degrees of freedom describing the low energy physics driving a black hole away from extremality.  For simple cases, this low energy sector determines important aspects of the gravitational backreaction, and several properties that are key to our microscopic (quantum) understanding of black hole physics.
    In this talk I will discuss these developments in the context of the (near-)extreme Kerr black hole. In particular, I will revisit the spectrum of linear axisymmetric gravitational perturbations of this black hole. The aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. I will show that for Kerr the low-lying mode sector is subtle and intricate—features that their charged spherical symmetric cousins do not display. This unveils new clues on how to decode a microscopic, and holographic, understanding of the Kerr black hole.
  • Seminars

    Seminars Colloquia & Seminar
    8/4/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Sifan Yu, Vanderbilt University

    Title: Rough solutions of the relativistic Euler equations

    Abstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.

  • Seminars

    Seminars Colloquia & Seminar
    8/11/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/18/2020 Geometry and Physics Seminar

    9:30 am-11:30 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/19/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Conference
    9:30 am-5:00 pm
    12/01/2024-04/08/2022

    General Relativity Conference

    This conference will be held virtually on Zoom. Registration is required.
    Webinar Registration

    A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
    In-Person Registration

    Schedule | April 4–8, 2022

    Schedule (PDF)

    Monday, April 4, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amPieter Blue, University of Edinburgh, UK
    (virtual)
    Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge

    Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of the Einstein equation in this gauge, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975, Chrzanowski introduced the “outgoing radiation gauge”, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently, using a flow along null geodesics, we have constructed a new gauge such that, in this gauge, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge.

    This is joint work with Lars Andersson, Thomas Backdahl, and Siyuan Ma.

    10:30 am–11:30 amPeter Hintz, ETH Zürich
    (virtual)
    Title: Mode stability and shallow quasinormal modes of Kerr-de Sitter
    black holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe, such as our own, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question), mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which, depending on the scaling, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.
    11:30 am–12:30 pmLars Andersson, Albert Einstein Institute, Germany
    (virtual)
    Title: Gravitational instantons and special geometry

    Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

    12:30 pm–1:30 pmbreak
    1:30 pm–2:30 pmMartin Taylor, Imperial College London
    (virtual)
    Title: The nonlinear stability of the Schwarzschild family of black holes

    Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

    2:30 pm–3:30 pmPo-Ning Chen, University of California, Riverside
    (virtual)
    Title: Angular momentum in general relativity

    Abstract:
    The definition of angular momentum in general relativity has been a subtle issue since the 1960s, due to the ‘supertranslation ambiguity’. In this talk, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.
    3:30 pm–4:00 pmbreak
    4:00 pm–5:00 pmDan Lee, Queens College (CUNY)
    (hybrid: in person & virtual)
    Title: Stability of the positive mass theorem

    Abstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem, focusing on recent work with Kazaras and Khuri, in which we proved that if one assumes a lower Ricci curvature bound, then stability holds with respect to pointed Gromov-Hausdorff convergence.

     

    Tuesday, April 5, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amXinliang An, National University of Singapore
    (virtual)
    Title: Anisotropic dynamical horizons arising in gravitational collapse

    Abstract: Black holes are predicted by Einstein’s theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk, we will present several results in these directions. First, in a joint work with Qing Han, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second, in joint works with Dejan Gajic and Ruixiang Zhang, for the spherically symmetric Einstein-scalar field system, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism. If time permits, some results on fluid dynamics will also be addressed.

    10:30 am–11:30 amSergiu Klainerman, Princeton
    (virtual)
    Title: Nonlinear stability of slowly rotating Kerr solutions

    Abstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.

    11:30 am–12:30 pmSiyuan Ma, Sorbonne University
    (virtual)
    Title: Sharp decay for Teukolsky master equation

    Abstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmJonathan Luk, Stanford
    (virtual)
    Title: A tale of two tails

    Abstract: Motivated by the strong cosmic censorship conjecture, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).

    2:30 pm–3:30 pmGary Horowitz, University of California Santa Barbara
    (virtual)
    Title: A new type of extremal black hole

    Abstract: I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero, if quantum matter is added, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmLydia Bieri, University of Michigan
    (virtual)
    Title: Gravitational radiation in general spacetimes

    Abstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

     

    Wednesday, April 6, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amGerhard Huisken, Mathematisches Forschungsinstitut Oberwolfach
    (virtual)
    Title: Space-time versions of inverse mean curvature flow

    Abstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.

    10:30 am–11:30 amCarla Cederbaum, Universität Tübingen, Germany
    (virtual)
    Title: Coordinates are messy

    Abstract: Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M,g,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.

    11:30 am–12:30 pmStefanos Aretakis, University of Toronto
    (virtual)
    Title: Observational signatures for extremal black holes

    Abstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmJared Speck, Vanderbilt University
    (virtual)
    Title: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow

    Abstract: In the last two decades, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia, M. Disconzi, and J. Luk.

    2:30 pm–3:30 pmLan-Hsuan Huang, University of Connecticut
    (virtual)
    Title: Null perfect fluids, improvability of dominant energy scalar, and Bartnik mass minimizers

    Abstract: We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture.

    Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmDemetre Kazaras, Duke University
    (virtual)
    Title: Comparison geometry for scalar curvature and spacetime harmonic functions

    Abstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

     

    Thursday, April 7, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amPiotr Chrusciel, Universitat Wien
    (virtual)
    Title: Maskit gluing and hyperbolic mass

    Abstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.

    10:30 am–11:30 amGreg Galloway, University of Miami (virtual)Title:  Initial data rigidity and applications

    Abstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP, 2021), and look at some consequences.  In a note with Piotr Chruściel (CQG 2021), we showed how to use this result, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.

    11:30 am–12:30 pmPengzi Miao, University of Miami
    (virtual)
    Title: Some remarks on mass and quasi-local mass

    Abstract: In the first part of this talk, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello, and with H.C. Jang.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmYakov Shlapentokh Rothman, Princeton
    (hybrid: in person & virtual)
    Title: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations

    Abstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.

    2:30 pm–3:30 pmMarcelo Disconzi, Vanderbilt University
    (virtual)
    Title: General-relativistic viscous fluids.

    Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmMaxime van de Moortel, Princeton
    (hybrid: in person & virtual)
    Title: Black holes: the inside story of gravitational collapse

    Abstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models, the global structure of the black hole interior has largely remained unexplored.
    These questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.
    I will present my recent resolution of these problems in spherical gravitational collapse, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.

     

    Friday, April 8, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amYe-Kai Wang, National Cheng Kun University, Taiwan
    (virtual)
    Title: Supertranslation invariance of angular momentum at null infinity in double null gauge

    Abstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing
    how Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen, Jordan Keller, Mu-Tao Wang, and Shing-Tung Yau.

    10:30 am–11:30 amZoe Wyatt, King’s College London
    (virtual)
    Title: Global Stability of Spacetimes with Supersymmetric Compactifications

    Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in
    supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.

    11:30 am–12:30 pmElena Giorgi, Columbia University
    (hybrid: in person & virtual)
    Title: The stability of charged black holes

    Abstract: Black hole solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmMarcus Khuri, Stony Brook University
    (virtual)
    Title: The mass-angular momentum inequality for multiple black holes

    Abstract
    : Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected, axisymmetric, maximal, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain, Chrusciel-Li-Weinstein, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from
    R^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han, G. Weinstein, and J. Xiong.
    2:30 pm–3:30 pmMartin Lesourd, Harvard
    (hybrid: in person & virtual)
    Title:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature

    Abstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau, Prof. D. A. Lee, and R. Unger.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmGeorgios Moschidis, Princeton
    (virtual)
    Title: Weak turbulence for the Einstein–scalar field system.

    Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
    In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams.

  • Seminars

    Seminars Colloquia & Seminar
    8/20/2020 Quantum Matter

    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/23/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    BCFW recursion relations and non-planar positive geometry

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-04.12.22-1583x2048-1

    Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.

    **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

    All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

    LINK TO FORM

  • Seminars

    Seminars Colloquia & Seminar
    8/25/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/26/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/27/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Special Seminar
    9:30 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Michael Douglas

    Title: Knowledge Graph Embeddings and Inference

    Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.
    A popular KG representation method is graph embedding, which facilitates question answering, inferring missing edges, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning, network learning, and unstructured statistical inference, and describe experiments to measure the contributions of each mechanism.

    Joint work with M. Simkin, O. Ben-Eliezer, T. Wu, S. P. Chin, T. V. Dang and A. Wood.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/30/2020 Condensed Matters Seminar

    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/22/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker:An Huang

    Title: Quadratic reciprocity from a family of adelic conformal field theories

    Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories, and ensures that these Green’s functions satisfy an adelic product formula. In particular, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place, the desired holomorphic factorization follows from the global conformal symmetry.

  • Seminars

    Seminars Colloquia & Seminar
    6/24/2020 Quantum Matter Seminar

    9:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-02.10.2022-1544x2048-1

    Speaker: Mohamed Anber (Durham University)

    Title: The global structure of the Standard Model and new nonperturbative processes

    Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Matteo Parisi

    Title: Amplituhedra, Scattering Amplitudes and Triangulations

    Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

  • Geometry and Physics Seminar

    Geometry and Physics Seminar
    Geometry and Physics Seminar

    9:30 am-9:30 pm
    12/01/2024-12/22/2020
    unnamed-537x338

    During the summer of 2020, the CMSA will be hosting a new Geometry Seminar. Talks will be scheduled on Mondays at 9:30pm or Tuesdays at 9:30am, depending on the location of the speaker. This seminar is organized by Tsung-Ju Lee, Yoosik Kim, and Du Pei.

    To learn how to attend this seminar, please contact Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu).

    DateSpeakerTitle/Abstract
    6/2/2020
    9:30am ET
    Siu-Cheong Lau
    Boston University
    This meeting will be taking place virtually on Zoom.

    Speaker: Equivariant Floer theory and SYZ mirror symmetry

    Abstract: In this talk, we will first review a symplectic realization of the SYZ program and some of its applications. Then I will explain some recent works on equivariant Lagrangian Floer theory and disc potentials of immersed SYZ fibers. They are joint works with Hansol Hong, Yoosik Kim and Xiao Zheng.

    6/8/2020
    9:30pm ET
    Youngjin Bae (KIAS)This meeting will be taking place virtually on Zoom.

    TitleLegendrian graphs and their invariants

    Abstract: Legendrian graphs naturally appear in the study of Weinstein manifolds with a singular Lagrangian skeleton, and a tangle decomposition of Legendrian submanifolds. I will introduce various invariant of Legendrian graphs including DGA type, polynomial type, sheaf theoretic one, and their relationship. This is joint work with Byunghee An, and partially with Tamas Kalman and Tao Su.

    6/16/2020
    9:30am ET
    Michael McBreen (CMSA)This meeting will be taking place virtually on Zoom.

    Title: Loops in hypertoric varieties and symplectic duality

    Abstract: Hypertoric varieties are algebraic symplectic varieties associated to graphs, or more generally certain hyperplane arrangements. They make many appearances in modern geometric representation theory. I will discuss certain infinite dimensional or infinite type generalizations of hypertoric varieties which occur in the study of enumerative invariants, focusing on some elementary examples. Joint work with Artan Sheshmani and Shing-Tung Yau.

    6/22/2020
    9:30pm ET
    Ziming Ma (CUHK)This meeting will be taking place virtually on Zoom.

    Title: The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties

    Abstract: In this talk, we construct a \(dgBV algebra PV*(X)\) associated to a possibly degenerate Calabi–Yau variety X equipped with local thickening data. This gives a version of the Kodaira–Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi–Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi–Yau varieties X satisfying Hodge–deRham degeneracy property for cohomology of X, in the spirit of Kontsevich–Katzarkov–Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.

    6/30/2020
    9:30pm ET
    Sunghyuk Park (Caltech)This meeting will be taking place virtually on Zoom.

    Title: 3-manifolds, q-series, and topological strings

    Abstract: \(\hat{Z}\) is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients), which has interesting modular properties. While originally from physics, this invariant has been mathematically constructed for a big class of 3-manifolds, and conjecturally it can be extended to all 3-manifolds. In this talk, I will give a gentle introduction to \(\hat{Z}\) and what is known about it, as well as highlighting some recent developments, including the use of R-matrix, generalization to higher rank, large N-limit and interpretation as open topological string partition functions.

    7/7/2020
    9:30am ET
    Jeremy Lane  (McMaster University)This meeting will be taking place virtually on Zoom.

    TitleCollective integrable systems and global action-angle coordinates

    Abstract: A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates.  Moreover, the image of the moment map is a (non-simple) convex polytope.

    7/13/2020
    9:30pm ET
    Po-Shen Hsin (Caltech)This meeting will be taking place virtually on Zoom.

    TitleBerry phase in quantum field theory

    Abstract: We will discuss Berry phase in family of quantum field theories using effective field theory. The family is labelled by parameters which we promote to be spacetime-dependent sigma model background fields. The Berry phase is equivalent to Wess-Zumino-Witten action for the sigma model. We use Berry phase to study diabolic points in the phase diagram of the quantum field theory and discuss applications to deconfined quantum criticality and new tests for boson/fermion dualities in \((2+1)d\).

    7/20/2020
    9:30pm ET
    Sangwook Lee (KIAS)This meeting will be taking place virtually on Zoom.

    Title: A geometric construction of orbifold Jacobian algebras

    Abstract: We review the definition of a twisted Jacobian algebra of a Landau-Ginzburg orbifold due to Kaufmann et al. Then we construct an A-infinity algebra of a weakly unobstructed Lagrangian submanifold in a symplectic orbifold. We work on an elliptic orbifold sphere and see that above two algebras are isomorphic, and furthermore their structure constants are related by a modular identity which was used to prove the mirror symmetry of closed string pairings. This is a joint work with Cheol-Hyun Cho.

    7/27/2020 9:30pm ETMao Sheng (USTC)This meeting will be taking place virtually on Zoom.

    Title: Parabolic de Rham bundles: motivic vs periodic

    Abstract: Let \($C$\) be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over \($C$\) (with rational weights in parabolic structure). Many examples arise from geometry: let \($f: X\to U$\) be a smooth projective morphism over some nonempty Zariski open subset \($U\subset C$\). Then the Deligne–Iyer–Simpson canonical parabolic extension of the Gauss–Manin systems associated to \($f$\) provides such examples. We call a parabolic de Rham bundle \emph{motivic}, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory, to get a characterization of motivic parabolic de Rham bundles. In this talk, I introduce another subcategory of parabolic de Rham bundles, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan–Sheng–Zuo on Higgs-de Rham flows, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus–Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck–Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz’s work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture, we would like to single out the conjectural arithmetic Simpson correspondence, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.

    8/4/2020
    9:30am Et
    Pavel Safronov (University of Zurich)This meeting will be taking place virtually on Zoom.

    TitleKapustin–Witten TFT on 3-manifolds and skein modules

    Abstract: Kapustin and Witten have studied a one-parameter family of topological twists of \(4d N=4\) super Yang–Mills. They have shown that the categories of boundary conditions on a surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid–Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.

    8/11/2020
    9:30am
    Xujia Chen (Stonybrook)This meeting will be taking place virtually on Zoom.

    TitleLifting cobordisms and Kontsevich-type recursions for counts of real curves

    Abstract: Kontsevich’s recursion, proved in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger’s invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon’s recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon’s approach).

    8/18/2020
    9:30am ET
    Dongmin Gang (Asia Pacific Center for Theoretical Physics)This meeting will be taking place virtually on Zoom.

    Title: M-theoretic genesis of topological phases

    Abstract:  I will talk about a novel way of constructing \((2+1)d\) topological phases using M-theory. They emerge as macroscopic world-volume theories of M5-branes wrapped on non-hyperbolic 3-manifolds. After explaining the algorithm of extracting modular structures of the topological phase  from topological data of the 3-manifold, I will discuss the possibility of full classification of topological orders via the geometrical construction.

    8/25/2020
    9:30pm ET
    Mykola Dedushenko (Caltech)This meeting will be taking place virtually on Zoom.

    TitleAlgebras and traces at the boundary of \(4d N=4\) SYM

    Abstract: I will describe how the structure of supersymmetric boundary correlators in \(4d N=4\) SYM can be encoded in a class of associative algebras equipped with twisted traces. In the case of interfaces, this yields a new connection to integrability.

  • Seminars

    Seminars Colloquia & Seminar
    6/2/2020 Geometry Seminar

    9:30 am-10:30 am
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: In this talk, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian, over the torus fixed points, this representation is a Verma module. The vertex function, a K-theoretic enumerative invariant introduced by A. Okounkov, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application, this gives a proof of the invariance of the quantum q-difference module under variation of GIT.

  • Colloquium
    9:30 am-10:00 am
    12/01/2024

    Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Juven Wang

    Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model

    Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT), or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320.

    In the second part of my talk, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-02.17.2022-1544x2048

    Speaker: Andrea Grigoletto (SISSA & INFN)

    Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

    Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

  • Seminars

    Seminars Colloquia & Seminar
    6/25/2020 Condensed Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-04.06.2022

    Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

  • Seminars

    Seminars Colloquia & Seminar
    7/7/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-04.07.2022-1583x2048-1

    Youtube Video

     

    Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.

    References:
    [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021)
    [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022)
    [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation.
    [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Shahar Hadar (University of Haifa)

    Title: Resolving the photon ring

    Abstract: In the past few years, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes, M87* and SgrA*. It is believed that within these images is embedded a fine, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of strong lensing by the black hole and thereby conveys information on its spacetime geometry, potentially providing a new independent avenue for tests of general relativity in the strong-field regime. In the talk I will briefly review the theory of the photon ring and its corresponding spacetime region, the photon shell, which governs the universal lensing structure. I will then describe some current efforts and future prospects for resolving the ring, which include both the construction of transformative new instruments and the development of novel analysis methods. Focusing on the latter, I will present an upcoming proposal to use spectro-temporal autocorrelations in signals emitted from black hole environs as a probe of strong lensing effects.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024

    This is the Fall 2020 – Spring 2022 Quantum Matter in Mathematics and Physics Archive page.

    To view current seminars, please visit the Fall 2022-Spring 2023 Quantum Matter Seminar Page

    As part of the program on Quantum Matter in Mathematics and Physics, the CMSA hosted two weekly seminars. The Quantum Matter/Quantum Field Theory seminar took place on Wednesdays from 10:30 – 12:00pm on Zoom.

    The Condensed Matter/Math Seminar took place on  Thursdays from 10:30 – 12:00pm on Zoom.  In addition to the Quantum Matter seminar, the CMSA  also hosted a related seminar series on  Strongly Correlated Quantum Materials and High-Temperature Superconductors.

    Videos are available at the Quantum Matter in Mathematics and Physics  Youtube Playlist

    Spring 2022

    DateSpeakerTitle/Abstract
    1/18/2022
    2:30–4:00 pm ET
    Aavishkar Patel (UC Berkeley)Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

    Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

    Video

    1/28/2022 2:30–4:00 pm ETMaria Tikhanovskaya (Harvard)Title: Maximal quantum chaos of the critical Fermi surface

    Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

    2/2/2022
    8:00 -9:30 pm ET
    Yunqin Zheng (IPMU & ISSP, U Tokyo)Title: Kramers-Wannier-like duality defects in higher dimensions

    Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

    2/3/2022
    11:30 – 1:00 pm ET
    Lu Li (U Michigan)Title:  Quantum Oscillations of Electrical Resistivity in an Insulator

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    2/9/2022
    8:00 –9:30 pm ET
    Yuji Tachikawa (Kavli IPMU, U Tokyo)Title: On the absence of global anomalies of heterotic string theories

    Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
    2/10/2022Mohamed Anber (Durham University)Title: The global structure of the Standard Model and new nonperturbative processes

    Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

    2/16/2022
    10:30 am–12:00 pm ET
    Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part I

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    2/17/2022
    9:30–11:00 am ET
    Andrea Grigoletto (SISSA & INFN)Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

    Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

    2/23/2022
    10:30 am–12:00 pm ET
    Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part II

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    2/24/2022
    8:00–9:30 pm ET
    Yohei Fuji (U Tokyo)Title: Bridging three-dimensional coupled-wire models and cellular topological states

    Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/1/2021Keisuke HarigayaTitle: Naturalness and muon anomalous magnetic moment

    Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

    Watch Video on Youtube

    9/2/2021Joseph Maciejko (University of Alberta)Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

    Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

    Watch Video on Youtube

    9/8/2021William Witczak-Krempa (U Montreal)Title: Cornering the universal shape of fluctuations and entanglement

    Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

    Ref: arXiv:2102.06223

    Watch Video on Youtube

    9/9/2021Sung-Sik Lee (McMaster University, Perimeter Institute)Title: Quantum gravity from quantum matter

    Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

    Watch Video on Youtube

    9/10/2021

    *special time: 3:30pm – 5:00pm ET*

    Ofri Telem (UC Berkeley)Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

    Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
    Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

    Watch Video on Youtube

    9/15/2021Liang Fu (MIT)Title: Three-particle mechanism for pairing and superconductivity

    Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

    [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
    [2] V. Crepel and L. Fu, arXiv:2103.12060
    [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

    Watch Video on Youtube

    9/16/2021Shiraz Minwalla (Tata Institute of Fundamental Research)Title: The Hilbert Space of large N Chern-Simons matter theories

    Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of  this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to  a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

    Watch Video on Youtube

    9/17/2021

    *special time 3:30 pm- 5 pm ET*

    Eslam Khalaf (Harvard)Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

    Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

    Watch Video on Youtube

    9/22/2021Daniel S Freed (U Texas)Title: Symmetry types in QFT and the CRT theorem

    Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

    Watch Video on Youtube

    9/23/2021Edward Shuryak (Stony Brook University)Title: Applications of instantons, sphalerons and instanton-dyons in QCD

    Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

    Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

    Watch Video on Youtube

    9/29/2021

    *special time 11:30 am- 1 pm ET*

    Nai Phuan Ong (Princeton University)Title: Oscillations in the thermal conductivity of a spin liquid*

    Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

    *Czajka et al., Nature Physics 17, 915 (2021).

    Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

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    10/06/2021Gabriel Cuomo (SCGP)Title: Line defects in CFTs: renormalization group flows and semiclassical limits

    Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

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    10/07/2021Ryan Thorngren (Harvard CMSA)Title: A tour of categorical symmetry

    Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

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    10/07/2021

    *special time 8:30 pm- 10 pm ET*

    Nima Arkani-Hamed (IAS Princeton)Title: UV/IR and Effective Field Theory

    Watch Video on Youtube

    10/21/2021

    *special time 13:30 – 15:00 ET*

    Anton Kapustin (Caltech)Title: Electric-magnetic duality and the Geometric Langlands duality

    Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

    Watch Video on Youtube

    10/22/2021

    *special time 10:30am – 12:00 noon ET*

    Netta Engelhardt (MIT)Title:  Recent Holographic Developments on the Black Hole Information Problem

    Watch Video on Youtube

    10/29/2021

    *special time 2:15pm – 3:45pm ET*

    Eric Sharpe (Virginia Tech)Title: Anomaly resolution via decomposition

    Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

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    10/29/2021

    *special time 4:00pm – 5:30pm*

    Biao Lian (Princeton)Title: Integrability and chaos of 1+1d chiral edge states

    Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

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    11/03/2021
    *special time 2:00pm – 3:30pm ET*
    Clay Cordova (U Chicago)Title: Non-Invertible Duality Defects in 3+1 Dimensions

    Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

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    11/04/2021Yifan Wang (NYU)Title: Fusion Category Symmetries in Quantum Field Theory

    Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

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    11/10/21
    *special time 10–11:30 am ET*
    Michael Stone (UIUC)Title: Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT

    Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature.  I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.

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    11/12/21
    *special time 2:30–4:00 pm ET*
    Jeongwan Haah (Microsoft)Title: A degeneracy bound for homogeneous topological order

    Watch Video on Youtube

    11/16/21
    *special time 3–4:30 pm ET*
    Jie Wang
    (Center for Computational Quantum Physics, Flatiron Institute, Simons Foundation)
    Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

    Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

    [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
    [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
    [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

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    11/18/2021 2:30–4:00 pm ETB. Andrei Bernevig (Princeton University)Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

    Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

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    11/24/21Shinsei Ryu (Princeton University)Title: Multipartitioning topological phases and quantum entanglement

    Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

    Watch Video on Youtube

    12/1/21
    10:00–11:30 am ET
    Daniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 1

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
    12/2/21 10:30–12:00 pm ETDaniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 2

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

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    12/8/21 10:30–12:00 pm ETFei Yan (Rutgers)Title: Defects, link invariants and exact WKB

    Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

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    12/10/21 2:30–4:00 pm ETLukasz Fidkowski (U Washington)Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

    Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

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    Summer 2021:

    DateSpeakerTitle/Abstract
    6/2/2021Juven Wang (Harvard CMSA)

    Video

    TitleUltra Unification:
    Quantum Fields Beyond the Standard Model
    Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
    6/3/2021Tian Lan (CUHK & U Waterloo)

    Video

    TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

    Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
    6/9/2021Yizhi You (Princeton U)

    Video

    TitleFracton critical point and Topological phase transition beyond renormalization

    Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
    6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)

    Video

    TitleMinimal nondegenerate extensions and an anomaly indicator

    Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

    6/16/2021Arkady Vainshtein (UMN)

    Video

    TitleUses of Wilson Operator Expansion in Gauge Theories

    Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

    It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

    6/17/2021Mikhail Shifman (UMN)

    Video

    TitleWhat can supersymmetry do that other field theory cannot
    7/7/2021Dung Nguyen (Brown)

    Video

    TitleFrom Fractional Quantum Hall to higher rank symmetry

    Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of  W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems.  Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
    7/8/2021

    8:00 – 9:30pm

    Jing-Yuan Chen (Tsinghua)

    Video

    TitleSolvable Lattice Hamiltonians with Fractional Hall Conductivity

    Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]

    7/14/2021Liujun Zou (Perimeter Institute)

    Video

    TitleStiefel liquids: Possible non-Lagrangian quantum criticality from intertwined orders

    Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.

    Ref: arXiv: 2101.07805.

    7/15/2021Nathanan Tantivasadakarn (Harvard)

    Video

    TitleHybrid Fracton Orders

    Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

    Based on 2102.09555 and 2106.03842

    7/21/2021Daniel Bulmash (UMD)TitleAnomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs

    Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.

    Ref: arXiv:2104.14567

    7/22/2021
    8:00pm ET
    Hong Yao (Tsinghua)TitleEmergent spacetime supersymmetry in topological phases of matter

    Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators.
    References:
    [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015)
    [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017)
    [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017)
    [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)

    7/28/2021Max Metlitski (MIT)Title: Boundary criticality of the O(N) model in d = 3 critically revisited.

    Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry.
    Based on arXiv:2009.05119.

    7/29/2021Ady Stern & David Mross (Weizmann)TitleThe nu=5/2 enigma: Recent insights from theory and experiment

    Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

    8/4/2021Nathan Benjamin (Princeton & Caltech)Title: Harmonic analysis of 2d CFT partition functions

    Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.

    8/5/2021Hans-Werner Hammer (TU Darmstadt)Title: Un-nuclear physics: conformal symmetry in nuclear reactions

    Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.

    8/11/2021Piers Coleman (Rutgers)Title: Order Fractionalization*

    Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

    8/12/2012Beni Yoshida (Perimeter Institute)Title: On the firewall puzzle

    Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.

    8/18/2021Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics
    Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
    8/19/2021Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)Title: “Probing the Standard Model of Particle Physics Using the Muon
    Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
    8/25/2021Hitoshi Murayama  (UC Berkely & IPMU)Title: Some Exact Results in QCD-like and Chiral Gauge Theories

    Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/20/2021Thomas Peter Devereaux (Stanford University)

    Video

    Title:  Numerical investigations of models of the cuprates

    Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

    I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

    1/21/2021
    8:30-10:00pm ET
    Masahito Yamazaki (IPMU)

    Video

    TitleConfinement as Analytic Continuation Beyond Infinity
    1/27/2021Luigi Tizzano  (SCGP)

    Video

    TitleInstantons, symmetries and anomalies in five dimensions

    Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

    1/28/2021Simon Catterall (Syracuse University)

    Video

    TitleChiral Fermions from Staggered Fields

    Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.

    2/3/2020Philip Phillips (University of Illinois Urbana-Champaign)

    Video

    TitleBeyond BCS: An Exact Model for Superconductivity and Mottness

    Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
    [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

    2/4/2021Diego Delmastro (Perimeter PI)

    Video

    Title: Domain Walls in 4d N=1 Supersymmetric Yang-Mills

    Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).

    2/10/2021Senthil Todadri (MIT)

    Video

    TitleStrange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

    Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.

    [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789
    [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

    2/11/2021Michael Hermele (University of Colorado Boulder)

    Video

    TitleFamilies of gapped systems and quantum pumps

    Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.

    2/17/2021Jaume Gomis (Perimeter PI)

    Video

    TitleGlobal Anomalies on the Hilbert Space

    Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

    2/18/2021Xiao-Gang Wen (MIT)

    Video

    TitleA solution to the chiral fermion problem

    Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

    2/24/2021Zhenghan Wang (Microsoft Station Q)

    Video

    Title:  A Riemann sum of quantum field theory:  lattice Hamiltonian realization of TQFTs

    Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics.  I will start with the conceptual origin of this model as requested by the organizer.  Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds.  In the end, I will mention lattice models that generalize the Haah codes in two directions:  general three manifolds and more than two qubits per site.

    If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum.  New lattice models in fracton physics raise an interesting question:  what kinds of quantum field theories are they approximating if their continuous limits exist?  Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.

    2/25/2021Justin Kaidi (SCGP)

    Video

    TitleExploring Non-Supersymmetric String Theory

    Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.

    3/3/2021Tim Hsieh (Perimeter PI)

    Video

    Title: Symmetry-protected sign problem and magic in quantum phases of matter

    Abstract:  We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
    3/4/2021Mohamed Anber (Clark University)

    Video

    TitleGeneralized ‘t Hooft anomalies in vector-like theories

    Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories.  Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics.  In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls.  This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.

    3/10/2021

    7:30pm ET

    Satoshi Yamaguchi (Osaka U)

    Video

    TitleSupersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases

    Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.

    3/11/2021Chao-Ming Jian (Cornell)

    Video

    Title: Entanglement Criticality in Random Gaussian Quantum Circuits

    Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.

    3/17/2021Silviu S. Pufu (Princeton)

    Video

    Title:  Exact symmetries and threshold states in two-dimensional models for QCD

    Abstract:  Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

    3/18/2021
    12:00 – 1:30pm ET
    Thomas Dumitrescu (UCLA)

    Video

    Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD

    Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint

    3/24/2021Emily Nardoni (UCLA)

    Video

    Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD: Part 2

    Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.

    3/25/2021Michael Levin (U Chicago)

    Video

    TitleAn introduction to string-net models

    Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.

    3/31/2021Dam Thanh Son (U Chicago)

    Video

    TitleSpin of the fractional quantum Hall magnetoroton through polarized Raman scattering

    Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.

    4/1/2021

    9:00am ET

    Naoto Nagaosa (Tokyo U.)

    Video

    Title: Applied physics of high-Tc theories

    Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

    4/7/2021Sakura Schafer-Nameki (University of Oxford)

    Video

    Title: Higher Form Symmetries in string/M-theory

    Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.

    4/8/2020

    1:00pm ET

    Anton Kapustin (Caltech)

    Video

    TitleChiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics
    Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
    4/14/2021Lakshya Bhardwaj (University of Oxford)

    Video

    TitleConfinement and 1-form Symmetries in 4d from 6d (2,0)

    Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
    4/15/2021Michael Creutz (Brookhaven National Laboratory)

    Video

    TitleQCD without diagrams

    Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.

    4/21/2021Sergei Gukov (Caltech)

    Video

    TitleExotic new animals in the CFT zoo: quasiparticles and anisotropic scaling
    4/22/2021Dung-Hai Lee (UC Berkeley)

    Video

    Title Non-abelian bosonization in two and three spatial dimensions and some applications
    Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
    4/28/2021Dominic Williamson (Stanford)

    Video

    Title1-form symmetry-protected topological phases and measurement-based quantum computation

    Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
    4/29/2021Fiona Burnell (University of Minnesota)

    Video

    TitleSubsystem-Symmetry protected phases of matter

    Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter.  These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states.  After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries.  I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.

    5/5/2021

    8:00pm ET

    Ioannis Papadimitriou (KIAS)

    Video

    TitleAnomalies and Supersymmetry

    Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.

    5/6/2021Weslei Bernardino Fontana (Boston University & Estadual)

    Video

    TitleChern-Simons-like theories for fracton phases

    Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.

    5/12/2021André-Marie Tremblay (University of Sherbrooke)

    Video

    Title: A unified theoretical perspective on the cuprate phase diagram

    Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

    5/13/2021Masataka Watanabe (Weizmann Institute of Science)

    Video

    TitleQuantum Information Theory of the Gravitational Anomaly

    Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].

    5/19/2021Herbert Neuberger (Rutgers)

    Video

    Title:  Construction of Lattice Chiral Gauge Theory

    Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided.
    The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.

    5/20/2021Steven Weinberg (UT Austin)

    Video

    TitleMassless Particles
    6/2/2021Juven Wang (Harvard CMSA)

    Video

    TitleUltra Unification:
    Quantum Fields Beyond the Standard Model
    Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
    6/3/2021Tian Lan (CUHK & U Waterloo)TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

    Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
    6/9/2021Yizhi You (Princeton U)TitleFracton critical point and Topological phase transition beyond renormalization

    Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
    6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)TitleMinimal nondegenerate extensions and an anomaly indicator

    Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

    6/16/2021Arkady Vainshtein (UMN)TitleUses of Wilson Operator Expansion in Gauge Theories

    Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

    It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

    6/17/2021Mikhail Shifman (UMN)TitleWhat can supersymmetry do that other field theory cannot
    8/11/2021Piers Coleman (Rutgers)TBA
    8/26/2021Daniel Harlow (MIT)Title: Symmetries in quantum field theory and quantum gravity
    TBAAdy Stern & David Mross (Weizmann)TBA

    Fall 2020:

    DateSpeakerTitle/Abstract
    9/2/2020Subir Sachdev (Harvard University)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

    Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
    describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

    9/3/2020
    9:30 – 11:00am
    Janet Ling Yan Hung (Fudan University)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleGapped Boundaries, Junctions via (fermionic) anyon condensation

    Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.

    9/9/2020Ying-Hsuan Lin (Caltech)

    Video

    This meeting will be taking place virtually on Zoom.

    Title:  Exotic Consistent (1+1)d Anomalies: A Ghost Story

    Abstract:  We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions.  On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm.  For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection.  Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines.  The holomorphic bc ghost system realizes all the exotic consistent anomalies.

    9/10/2020Maissam Barkeshli (Maryland)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleAbsolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions

    Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553

    9/16/2020Andreas Karch (UT Austin)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleBranes, Black Holes and Islands

    Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.

    9/17/2020Roger Mong (University of Pittsburgh)

    Video

    TitleUniversal multipartite entanglement in quantum spin chains

    Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems.  Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations.  Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment.  The measures are based off of the entanglement of purification and the reflected entropy popular among holography.  For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases.  We conclude with a few remarks regarding applications to 2D phases.

    9/23/2020Subir Sachdev (Harvard University)

    Video

    TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders II

    Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

    9/24/2020
    12:00 – 2:30pm ET
    Inna Vishik (University of California, Davis)

    Video

    TitleUniversality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201

    Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.

    9/30/2020Jordan Cotler (Harvard)

    Video

    Title: Gravitational Constrained Instantons and Random Matrix Theory

    Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action.  We find these instantons in all spacetime dimensions, for AdS and dS.  Many can be written in closed form and are quadratically stable.  In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes.  We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.

    10/1/2020Omri Golan (Weizmann Institute of Science)

    Video

    Title: Intrinsic sign problems in topological matter

    Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions.  Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.

    10/7/2020Romain Vasseur (UMass Amherst)

    Video

    Title“Symmetry-enriched random critical points and topological phase transitions“

    Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.

    10/8/2020Justin Kulp (Perimeter Institute)

    Video

    TitleOrbifold Groupoids

    Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
    10/14/2020Yin-Chen He (Perimeter Institute)

    Video

    TitleNon-Wilson-Fisher Kinks of Conformal Bootstrap: Deconfined Phase Transition and Beyond

    Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.

    10/15/2020Louis Taillefer (University of Sherbrooke)

    Video

    TitleNew signatures of the pseudogap phase of cuprate superconductors

    Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

    10/21/2020Oleg Dubinkin (University of Illinois at Urbana–Champaign)

    Video

    Title: Multipole Insulators and Higher-Form symmetries

    Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.

    10/22/2020Paul Fendley (University of Oxford)

    Video

    TitleThe uses of lattice topological defects

    Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains.
    These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion.  One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.  I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.

    10/28/2020Patrick Lee (MIT)

    Video

    Title: The not-so-normal normal state of underdoped Cuprate

    Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

    10/29/2020Biao Lian (Princeton University)

    Video

    TitleSymmetry, Insulating States and Excitations of Twisted Bilayer Graphene with Coulomb Interaction

    Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.

    11/5/2020Zohar Ringel (Racah Institute of Physics)TitleThe information bottleneck: A numerical microscope for order parameters.

    Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.

    11/6/2020
    12:30pm
    Zhi-Xun Shen (Stanford University)

    Video

    TitleEssential Ingredients for Superconductivity in Cupper Oxide Superconductors

    Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
    Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
    magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
    (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
    experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

    [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
    [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
    [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
    [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
    [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
    [6] A. Lanzara et al., Nature 412, 510 (2001)
    [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
    [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
    [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
    [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
    [11] A.G. Loeser et al., Science 273, 325 (1996)
    [12] S. Chen et al., Science, 366, 6469 (2019)
    [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
    [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
    [15] Yu He et al., Science, 362, 62 (Oct. 2018)
    [16] Z. Chen, Y. Wang et al., preprint, 2020

    11/11/2020Abhishodh Prakash (ICTS)

    Video

    TitleAspects of fermionic SPT phases: boundary supersymmetry and unwinding

    Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
    11/12/2020Chandra Varma (University of California, Riverside)

    Video

    TitleLoop-Current Order and Quantum-Criticality in Cuprates

    This talk is organized as follows:
    1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
    2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
    3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
    4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.

    Time permitting,
    (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
    (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
    (iii) Problems.

    11/18/2020Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

    Video

    Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

    Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

    11/19/2020Eduardo Fradkin (University of Illinois at Urbana-Champaign)

    Video

    TitlePair Density Waves and Intertwined Orders in High Tc Superconductors

    Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

    11/25/2020Qimiao Si (Rice University)

    Video

    Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

    Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

    12/2/2020Andrey Chubukov (University of Minnesota)

    Video

    TitleInterplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

    Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

    12/3/2020David B. Kaplan  (University of Washington)

    Video

    Title: Domain Wall Fermions and Chiral Gauge theories: Topological Insulators in Particle Physics

    Abstract:  Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics.  I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter.  How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!)  remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
    12/9/2020David Hsieh (Caltech)

    Video

    Title:  Signatures of anomalous symmetry breaking in the cuprates 

    Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
    [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

    [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516
    .

    12/10/2020Xinan Zhou (Princeton PCTS)

    Video

    Title: An analytic bootstrap approach for CFTs on RP^d and CFTs with boundaries

    Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
    12/16/2020Zheng-Yu Weng (Tsinghua University)

    Video

    TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

    Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

    12/17/2020Steven Kivelson (Stanford University)

    Video

    Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

    Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
    12/22/2020David Tong (University of Cambridge)

    Video

    TitleGapped Chiral Fermions

    Abstract: I’ll describe some quantum field theories that gap fermions without breaking chiral symmetries.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-04.13.22

    Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure. But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

    In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    3/2/2022Richard Kenyon (Yale University)
    3/9/2022Richard Tsai (UT Austin)
    3/23/2022Joel Cohen (University of Maryland)
    3/30/2022Rob Leigh (UIUC)
    4/6/2022Johannes Kleiner (LMU München)
    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
    4/20/2022TBA
    4/27/2022TBA
    5/4/2022Melody Chan (Brown University)
    5/11/2022TBA
    5/18/2022TBA
    5/25/2022Heeyeon Kim (Rutgers University)

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024

    Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

    April 20, 2022 | 9:30 – 11:00 am ET

    Title: Mechanism Design

    Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

    Talk chairs: Scott Kominers, Sergiy Verstyuk

    SLIDES | VIDEO

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. Higgs-Coulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wall-crossing results for GLSM and generalizes Landau- Ginzburg/Calabi-Yau correspondence. The talk is based on a joint work in progress with Melissa Liu.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-03.02.2022

    Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

    This is joint work with Dan Douglas and Haolin Shi.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Title: Stable Big Bang formation for the Einstein equations

    Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Itamar Shamir

    Title: Geometry, Entanglement and Quasi Local Data

    Abstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Tropical Lagrangian multi-sections and locally free sheaves

    9:30 am-10:30 am
    12/01/2024

    Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-03.03.2022-1544x2048-1

    Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138

    Member Seminar

    Speaker: Martin Lesourd

    Title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds

    Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, and Prof. D. A. Lee.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Some combinatorics of Wilson loop diagrams

    9:30 am-10:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands.

    **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

    All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

    LINK TO FORM

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 02.03.23

    General Relativity Seminar

    Speaker: Chiara Toldo (Harvard)

    Title: Near extremal de Sitter black holes and JT gravity

    Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

  • Quantum Matter
    9:30 am-10:30 am
    12/01/2024
    CMSA QMMP 1.30.23

    Quantum Matter Seminar

    Title: Group Invariant States as Many-Body Scars

    Speaker: Igor R. Klebanov (Princeton University)

    Abstract: Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies.  The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

     

    https://www.youtube.com/watch?v=O4xizOTzpL4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=18

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024

    Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

    April 22, 2022 | 9:30 – 11:00 am ET

    Title: Auction Theory

    Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

    Talk chairs: Scott Kominers, Sergiy Verstyuk

    SLIDES | VIDEO Answers to Questions from Talks 2 and 3

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Prashant Kocherlakota (BHI)

    Title: Testing spacetime geometry with images of supermassive compact objects: Current status and the future

    Abstract: Astrophysical black holes (BHs) are expected to be described by the Kerr solution of the Einstein equations. Several frameworks have recently been developed to parametrically deform the Kerr metric in significantly different ways, to enable formulations of tests of the no-hair theorems. Testing the viability status of alternative models – such as non-Kerr BHs from general relativity, BHs from alternative theories, wormholes, and other exotic objects – as descriptors of astrophysical objects has been of longstanding interest. The Event Horizon Telescope (EHT) recently imaged Sagittarius A* (Sgr A*), the supermassive compact object at the center of the Galaxy, making such tests possible. In such tests, the shadow critical curve (or simply shadow boundary), defined on the observer’s image plane, has gained prominence as the observable of interest. We will discuss how the EHT is able to extract information regarding the shadow of Sgr A* and the status of associated tests of the spacetime geometry in the strong-field regime. Future imaging measurements expect to detect the so-called photon ring, a strong-gravitational lensing feature that appears in the close vicinity of the critical curve, which houses higher-order images of the emission source. Time permitting, we will also discuss how these can be used to set up more stringent tests of the spacetime metric and gravity in the future.

     

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Strominger-Yau-Zaslow conjecture is one of the guiding principles in mirror symmetry, which not only predicts the geometric structures of Calabi-Yau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricci-flat metrics. In this talk, we will explain how SYZ fibrations on log Calabi-Yau surfaces detect the non-standard semi-flat metric which generalized the semi-flat metrics of Greene-Shapere-Vafa-Yau. Furthermore, we will use the SYZ fibration on log Calabi-Yau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Dan Lee

    Title: Survey on stability of the positive mass theorem

    Abstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk, I will discuss various results related to this question.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The longest induced path in a sparse random graph

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-12.14.2021

    Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Speaker: Du Pei

    Title: Wall-crossing from Higgs bundles to vortices

    Abstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks.  In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.

  • Combinatorics Physics and Probability
    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-11.30.2021

    Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
    In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
    Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
    This work was done in collaboration with Renaud Lambiotte.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-04.19.2022

    Abstract:  In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong.

    In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

  • Combinatorics Physics and Probability
    9:30 am-10:30 am
    12/01/2024

    Speaker: Nima Arkani-Hamed, IAS

    Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    3/2/2022Richard Kenyon (Yale University)
    3/9/2022Richard Tsai (UT Austin)
    3/23/2022Joel Cohen (University of Maryland)
    3/30/2022Rob Leigh (UIUC)
    4/6/2022Johannes Kleiner (LMU München)
    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
    4/20/2022TBA
    4/27/2022TBA
    5/4/2022Melody Chan (Brown University)
    5/11/2022TBA
    5/18/2022TBA
    5/25/2022Heeyeon Kim (Rutgers University)

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures.

    The talk is partially based on joint works with Si Li.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Puskar Mondal

    Title: Stability and convergence issues in mathematical cosmology

    Abstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized, one needs to study its stability properties. Therefore, I will briefly discuss the stability issue and its consequences (e.g., structure formation, etc).

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-02.01.2022

    Abstract: We will consider the following problem: if (C,x_1,…,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,…,y_n, then how many maps f:C -> X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory, the answer may be expressed in terms of the quantum cohomology of X, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle, though in the presence of sufficient positivity, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem, including joint work with Farkas, Pandharipande, and Cela, as well as work of other authors.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 03.09.23

    General Relativity Seminar

    Speaker: Jose Luis Jaramillo (Bourgogne U.)

    Title: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture

    Abstract: Can we measure the ‘effective regularity’ of spacetime from the perturbation of quasi-normal mode (QNM) overtones? Black hole (BH) QNMs encode the resonant response of black holes under linear perturbations, their associated complex frequencies providing an invariant probe into the background spacetime geometry. In the late nineties, Nollert and Price found evidence of a BH QNM instability phenomenon, according to which perturbed QNMs of Schwarzschild spacetime migrate to new perturbed branches of different qualitative behaviour and asymptotics. Here we revisit this BH QNM instability issue by adopting a pseudospectrum approach. Specifically, we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator by adopting a hyperboloidal formulation of spacetime. Non-selfadjoint (more generally non-normal) operators suffer potentially of spectral instabilities, the notion of pseudospectrum providing a tool suitable for their study. We find evidence that perturbed Nollert & Price BH QNMs track the pseudospectrum contour lines, therefore probing the analytic structure of the resolvent, showing the following (in)stability behaviour: i) the slowest decaying (fundamental) mode is stable, whereas ii) (all) QNM overtones are ultraviolet unstable (for sufficiently high frequency). Building on recent work characterizing Burnett’s conjecture as a low-regularity problem in general relativity, we conjecture that (in the infinite-frequency limit) generic ultraviolet spacetime perturbations make BH QNMs migrate to ‘Regge QNM branches’ with a precise universal logarithmic pattern. This is a classical general relativity (effective) low-regularity phenomenon, agnostic to possible detailed (quantum) descriptions of gravity at higher-energies and potentially observationally accessible.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Jue Liu

    Title: Instability of naked singularities in general relativity

    Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, which are called by naked singularities, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method, and it is this wild method that helps us to extend some results to the asymmetric cases.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 02.23.23

    General Relativity Seminar

    Speaker: Nikolaos Athanasiou (University of Crete, Greece)

    Title: Formation of trapped surfaces in the Einstein-Yang-Mills system

    Abstract: The purpose of this talk is to give an overview of a semi-global existence result and a trapped surface formation results in the context of the Einstein-Yang-Mills system. Adopting a “signature for decay rates” approach first introduced by An, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yield the desired semi-global existence result. Once semi-global existence has been established, we will explain how the formation of a trapped surface follows from a standard ODE argument. This is joint work with Puskar Mondal and Shing-Tung Yau.

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024

    Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

    April 18, 2022 | 9:30 – 11:00 am ET

    Title: Game Theory Basics and Classical Existence Theorems

    Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

    Talk chairs: Scott Kominers, Sergiy Verstyuk

    SLIDES | VIDEO

     

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-Seminar-04.14.22-1583x2048-1

    Youtube video

     

    Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields.  Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos.  Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).

    As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role.  Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times.  Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime.  This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole).  It also makes a number of testable predictions.

    (Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Title: On the Observable Shape of Black Hole Photon Rings

    Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

  • Special Seminar
    9:50 am-10:50 am
    12/01/2024-04/26/2016

    The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

    DayNameTitle
    09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
    09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
    09-22-2015Teng FeiSome new solutions to the Strominger system
    09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
    10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
    10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
    10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
    10-27-2015Tom IlmanenFlow of curves by curvature in R^n
    11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
    11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
    11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
    11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
    12-01-2015Tom Ilmanen
    01-26-2016Mao ShengUniformization of p-adic curves
    02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
    02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
    02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
    02-23-2016Junbin LiConstruction of black hole formation spacetimes
    03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
    03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
    03-15-2016Spring Break 
    03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
    03-29-2016Piotr ChruscielMass of characteristic surfaces
    04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
    04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
    04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
    04-26-2016Andre NevesA path to Yau’s conjecture
  • Seminars
    9:50 am-10:50 am
    12/01/2024

    The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

    DateNameTitle
    09-03-2015Long JinScattering Resonances for Convex Obstacles
    09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
    09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
    09-24-2015Felix FinsterCausal fermion systems and the causal action principle
    10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
    10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
    10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
    10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
    10-29-2015Pin YuShock formations for 3 dimensional wave equations
    11-05-2015No talk 
    11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
    11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
    11-26-2015ThanksgivingNo seminar
    12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
    01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
    02-04-2016Pranav PanditCategorical Kähler Geometry
    02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
    02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
    02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
    03-03-2016Piotr ChruscielSingularities in general relativity
    03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
    03-17-2016Spring BreakNo Talk
    03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
    03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
    04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
    04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
    04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
    04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
    05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
    05-12-2016Stefano Bianchini
  • General Relativity Seminar
    10:00 am-11:00 am
    12/01/2024

    Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

  • Workshop
    10:00 am-5:00 pm
    12/01/2024-05/08/2022

    On May 6–8, 2022, the CMSA  hosted a second NSF FRG Workshop.

    This project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology), Computer Science (Scientific Computing and Complexity Theory), and domain sciences, from Data Sciences to Computational Biology.

    Scientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time, however, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing, searching, simulating, analyzing, and comparing shapes. These methods and tools can be applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition, and satellite image analysis.

    This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

    The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.


    Workshop on Discrete Shapes
    May 6–8, 2022

    Organizers:

    • David Glickenstein (University of Arizona)
    • Joel Hass (University of California, Davis)
    • Patrice Koehl (University of California, Davis)
    • Feng Luo (Rutgers University, New Brunswick)
    • Maria Trnkova (University of California, Davis)
    • Shing-Tung Yau (Harvard)

    Speakers:

    • Miri Ben-Chen (Technion)
    • Alexander Bobenko (TU Berlin)
    • John Bowers (James Madison)
    • Steven Gortler (Harvard)
    • David Gu (Stony Brook)
    • Anil Hirani (UIUC)
    • Yanwen Luo (Rutgers)
    • Peter Schroeder (Caltech)
    • Justin Solomon (MIT)
    • Tianqi Wu (Clark University)

    Contributed Talk Speakers:

    • Oded Stein (MIT)
    • Bohan Zhou (Dartmouth)

    Schedule
    Schedule (PDF)

    Friday, May 6, 2022

    10:00–10:05 amWelcome Opening
    10:05–10:55 amAnil N. HiraniTitle: Discrete vector bundles with connection

    Abstract: We have recently initiated a generalization of discrete exterior calculus to differential forms with values in a vector bundle. A discrete vector bundle with connection over a simplicial complex has fibers at vertices and transport maps on edges, just as in lattice gauge theory. The first part of this work involves defining and examining properties of a combinatorial exterior covariant derivative and wedge product. We find that these operators commute with pullback under simplicial maps of the base space. From these definitions emerges a combinatorial curvature. In the second part of this work we showed that the curvature behaves as one expects: it measures failure of parallel transport to be independent of the path, and is the local obstruction to a trivialization. For a bundle with metric, metric compatibility of the discrete connection is equivalent to a Leibniz rule.  Vanishing curvature is indeed equivalent to an appropriately defined discrete flat connection, and curvature obstructs trivializability. In this talk I will focus on just the first part, and talk about naturality of the discrete exterior covariant derivative and discrete wedge product using simple examples. Joint work with Daniel Berwick-Evans (UIUC) and Mark Schubel (Apple, Inc.).

    11:10–12:00 pmDavid GuTitle: Surface Quadrilateral Meshing Based on Abel-Jacobi Theory

    Abstract: Surface quadrilateral meshing plays an important role in many fields. For example, in CAD (computer-aided design), all shapes are represented as Spline surfaces, which requires structured quad-meshing; in CAE (computer-aided engineering), the surface tessellation greatly affects the accuracy and efficiency of numerical simulations. Although the research on mesh generation has a long history, it remains a great challenge to automatically generate structured quad-meshes with high qualities. The key is to find the governing equation for the singularities of the global structured quad-meshes.

    In this talk, we introduce our recent discovery:  the singularities of a quad-mesh are governed by the Abel theorem. We show that each quad-mesh determines a conformal structure and a meromorphic quadratic differential, the configuration of the mesh singularities can be described as the divisor of the differential. The quad-mesh divisor minus four times of the divisor of a holomorphic one-form is principal and satisfies the Abel theorem: its image under the Jacobi map is zero in the Jacobi variety.

    This leads to a rigorous and efficient algorithm for surface structured quadrilateral meshing. After determining the singularities, the metric induced by the quad-mesh can be computed using the discrete Yambe flow, and the meromorphic quartic differential can be constructed, the trajectories of the differentials give the quad-mesh. The method can be applied directly for geometric modeling and computational mechanics.

    12:00–2:00 pmLunch Break
    2:00–2:50 pm Justin SolomonTitle:  Geometry Processing with Volumes

    Abstract:  Many algorithms in geometry processing are restricted to two-dimensional surfaces represented as triangle meshes.  Drawing inspiration from simulation, medical imaging, and other application domains, however, there is a substantial demand for geometry processing algorithms targeted to volumes represented as tetrahedral meshes or grids.  In this talk, I will summarize some efforts in our group to develop a geometry processing toolkit specifically for volumes.  Specifically, I will cover our recent work on hexahedral remeshing via cuboid decomposition, volumetric correspondence, and minimal surface computation via geometric measure theory.

    3:00–3:20 pmOded SteinTitle: Optimization for flip-free parametrization

    Abstract: Parametrizations without flipped elements are desirable in a variety of applications such as UV mapping and surface/volume correspondence. Computing flip-free parametrizations can be challenging, and there are many different approaches to the problem. In this talk we will look at multiple strategies for flip-free parametrizations that are based on the optimization of continuous energies. Due to the nature of the problem, these energies are often nonconvex and unbounded, which is a challenge for optimization methods. We will also take a closer look at our recently developed method for computing flip-free parametrizations using the Alternating Direction Method of Multipliers (ADMM).

    3:20–4:00 pmBreak
    4:00–4:50 pmJohn BowersTitle: Koebe-Andre’ev-Thurston Packings via Flow

    Abstract: Recently, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation, flip-and-flow, that allows two tangency packings whose contact graphs differ by a combinatorial edge flip to be continuously deformed from one to the other while maintaining tangencies across all of their common edges. Starting from a canonical tangency circle packing with the desired number of circles a finite sequence of flip-and-flow operations may be applied to obtain a circle packing for any desired (proper) contact graph with the same number of circles.

    The full Koebe-Andre’ev-Thurston theorem generalizes the circle packing theorem to allow for neighboring circles to overlap by angles up to $\pi/2$. In this talk I will show that the Connelly-Gortler method can be extended to allow for circles to overlap to angles up to $\pi/2$. This results in a new proof of the general Koebe-Andre’ev-Thurston theorem for disk patterns on $\mathbb{S}^2$ as well as a numerical algorithm for computing them. The proof involves generalizing a notion of convexity for circle polyhedra that was recently used to prove the global rigidity of certain circle packings, which is then used to show that all convex circle polyhedra are infinitesimally rigid, a result of independent interest.

    5:00–5:30 pmMovies “conform!” & ”Koebe polyhedra”

     

    Saturday, May 7, 2022

    9:30–10:20 amAlexander BobenkoTitle: The Bonnet problem: Is a surface characterized by its metric and curvatures?

    Abstract: We consider a classical problem in differential geometry, known as the Bonnet problem, whether a surface is characterized by a metric and mean curvature function. Generically, the answer is yes. Special cases when it is not the case are classified. In particular, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas

    10:20–11:00 amBreak
    11:00–11:50 amMiri Ben ChenTitle: Surface Multigrid via Intrinsic Prolongation

    Abstract: The solution of a linear system is a required ingredient in many geometry processing applications, and multigrid methods are among the most efficient solution techniques. However, due to the unstructured nature of triangle meshes, mapping functions between different multigrid levels is challenging. In this talk I will present our recent work that uses an intrinsic prolongation operator as the main building block in a multigrid solver for curved triangle meshes. Our solver can be used as a black-box in any triangle-mesh based system that requires a linear solve, and leads to order of magnitude time-efficiency improvement compared to direct solvers.

    12:00–2:00 pmLunch Break
    2:00–2:50 pmSteven GortlerTitle: Reconstructing configurations and graphs from unlabeled distance measurements

    Abstract: Place a configuration of n  points (vertices) generically in R^d. Measure the Euclidean lengths of m point-pairs (edges). When is the underlying graph determined by these $m$ numbers (up to isomorphism)? When is the point configuration determined by these $m$ numbers (up to congruence)? This question is motivated by a number of inverse problem applications. In this talk, I will review what is known about this question.

    3:00–3:20 pmBohan ZhouTitle: Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs

    Abstract: Optimal transport has profound and wide applications since its introduction in 1781 by Monge. Thanks to the Benamou-Brenier formulation, it provides a meaningful functional in the image science like image and shape registrations. However, exact computation through LP or PDE is in general not practical in large scale, while the popular entropy-regularized method introduces additional diffusion noise, deteriorating shapes and boundaries. Until the recent work [Jacobs and Leger, A Fast Approach to Optimal Transport: the back-and-forth method, Numerische Mathematik, 2020], solving OT in a both accurate and fast fashion finally becomes possible. Multiple marginal optimal transport is a natural extension from OT but has its own interest and is in general more computationally expensive. The entropy method suffers from both diffusion noise and high dimensional computational issues. In this work with Matthew Parno, we extend from two marginals to multiple marginals, on a wide class of cost functions when those marginals have a graph structure. This new method is fast and does not introduce diffusion. As a result, the new proposed method can be used in many fields those require sharp boundaries. If time allows, we will illustrate by examples the faithful joint recover via MMOT of images with sharp boundaries, with applications on sea ice prediction.

    3:20–4:00 pmBreak
    4:00–4:50 pmPeter SchroederTitle: Constrained Willmore Surfaces

    Abstract: The Willmore energy of a surface is a canonical example of a squared curvature bending energy. Its minimizers are therefore of interest both in the theory of surfaces and in practical applications from physical and geometric modeling. Minimizing the bending energy alone however is insufficient. Taking a cue from univariate splines which incorporate an isometry constraint we consider Willmore minimizers subject to a conformality constraint. In this talk I will report on a numerical algorithm to find such constrained minimizers for triangle meshes.

    Joint work with Yousuf Soliman (Caltech), Olga Diamanti (UGraz), Albert Chern (UCSD), Felix Knöppel (TU Berlin), Ulrich Pinkall (TU Berlin).

    5:00–5:50 pmProblems and Application discussions

     

    Sunday, May 8, 2022

    9:00–9:50 amTianqi WuTitle: Convergence of discrete uniformizations

    Abstract: The theory of discrete conformality, based on the notion of vertex scaling, has been implemented in computing conformal maps or uniformizations of surfaces. We will show that if a Delaunay triangle mesh approximates a smooth surface, then the related discrete uniformization will converge to the smooth uniformization, with an error bounded linearly by the size of the triangles in the mesh.

    10:10–11:00 amYanwen LuoTitle:  Recent Progress in Spaces of Geodesic Triangulations of Surfaces

    Abstract:
    Spaces of geodesic triangulations of surfaces are natural discretization of the groups of surface diffeomorphisms isotopy to the identity. It has been conjectured that these spaces have the same homotopy type as their smooth counterparts. In this talk, we will report the recent progress in this problem. The key ingredient is the idea in Tutte’s embedding theorem. We will explain how to use it to identify the homotopy types of spaces of geodesic triangulations. This is joint work with Tianqi Wu and Xiaoping Zhu.
    11:10–12:00 pmProblems and Application discussions
    12:00–1:00 pmMovie“The Discrete Charm of Geometry”

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Meng Cheng (Yale)

    Title: Symmetry and many-body topology in mixed states

    Abstract: It is by now well-understood that gapped ground states of local Hamiltonians can be classified topologically, and the nontrivial states exhibit many interesting topological phenomena. In this talk I’ll discuss recent developments in generalizing the topological classification to mixed states. Global symmetry plays a key role in understanding phases in pure states. For mixed states, certain “weak” symmetries may hold “on average” for the entire ensemble, in contrast to “strong” symmetries respected by each state in the ensemble. I will show that the interplay between these two kinds of symmetries lead to a rich landscape of symmetry-protected mixed states, and can also be used to characterize mixed state topological order.

     

  • CMSA EVENT: Computational Biology Symposium
    10:00 am-4:00 pm
    12/01/2024
    Compbiotextlessfeature-600x338

    On May 3, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo.

    The symposium will begin at 10:00am ET. There will be a morning and afternoon session, with an hour break for lunch.

    Videos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.

    Confirmed participants:

    Schedule:

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/19/2021 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Swampland Seminar
    10:00 am-11:00 am
    12/01/2024

    Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Aleksey Cherman (UMN)

    Title: Exact lattice chiral symmetry in 2d gauge theory

    Abstract: Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory.  I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

  • Swampland Seminar
    10:00 am-11:00 am
    12/01/2024

    Swampland Seminar

    Speakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech)

    Title: Causality constraints on corrections to Einstein gravity

    Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

  • Quantum Matter
  • Seminars

    Seminars Colloquia & Seminar
    13/3/2018 Topology Seminar

    10:00 am-11:30 am
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/26/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/22/2018 Topology Seminar

    10:00 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 05.05.23 (2)

    Quantum Matter Seminar

    Speaker: Sona Najafi (IBM Quantum)

    Title: Detecting central charge in a superconducting quantum processor

    Abstract: Physical systems at the continuous phase transition point exhibit conformal symmetry rendering local scaling invariance. In two dimensions, the conformal group possesses infinite generators described by Virasoro algebra with an essential parameter known as a central charge. While the central charge manifests itself in a variety of quantities, its detection in experimental setup remains elusive. In this work, we utilize Shannon-Renyi entropy on a local basis of a one-dimensional quantum spin chain at a critical point. We first use a simulated variational quantum eigen solver to prepare the ground state of the critical transfer field Ising model and XXZ model with open and periodic boundary conditions and perform local Pauli X and Z basis measurements. Using error mitigation such as probabilistic error cancellation, we extract an estimation of the local Pauli observables needed to determine the Shannon-Renyi entropy with respect to subsystem size. Finally, we obtain the central charge in the sub-leading term of Shannon-Renyi entropy.

    https://www.youtube.com/watch?v=Os26XRahD0c&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=5

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024

    Speaker: Haoyu Guo (Harvard)

    Title: Transport in large-N critical Fermi surface

    Abstract:
     A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermion-scalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and show that a previously proposed mega^{-2/3} contribution to the optical conductivity at frequency mega has vanishing co-efficient. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity behaves like a Fermi liquid. Arxiv references: 2203.04990, 2207.08841

  • Topological Quantum Matter Seminar
    10:00 am-11:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 12.07.22

    Topological Quantum Matter Seminar

    Speaker: Vasil Rokaj (Harvard)

    Title: Controlling Quantum Matter with Quantum Cavity Fields

    Abstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free electron gas [5]. The exact analytic solution of the Sommerfeld model in the cavity will be presented as well as its fundamental properties. Then, in the second part of the talk, I will focus on a many-particle system of cold ions in a harmonic trap coupled to the cavity field. I will show how this system couples collectively to the cavity and that hybrid states between light and matter, known as polaritons, emerge. The formation of polaritons leads to the modification of the properties of the cold ions and enhances the localization of the many-body wave function [6]. Connections to experiments will be discussed as well.

    [1] F. Garcia-Vidal, C. Ciuti, T. W. Ebbesen, Science, 373, 178 (2021)

    [2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)

    [3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)

    [4] T. W. Ebbesen, Acc. Chem. Res. 49, 11, 2403–2412 (2016)

    [5] V. Rokaj, M. Ruggenthaler, F. G. Eich, A. Rubio, Phys. Rev. Research 4, 013012 (2022)

    [6] V. Rokaj, S.I. Mistakidis, H.R. Sadeghpour, arXiv:2207.03436 (2022)

  • Algebraic Geometry in String Theory Seminar
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Pre-talk Speaker: David Wu (Harvard Physics): 10:00-10:30 am

    Speaker: Damian van de Heisteeg, CMSA

    Title: Species Scale across String Moduli Spaces

    Abstract: String theories feature a wide array of moduli spaces. We propose that the energy cutoff scale of these theories – the so-called species scale – can be determined through higher-curvature corrections. This species scale varies with the moduli; we use it both asymptotically to bound the diameter of the field space, as well as in the interior to determine a “desert point” where it is maximized.

  • Joint Harvard-CUHK-YMSC Differential Geometry
    10:00 am-11:00 am
    12/01/2024

    Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or, Neumann) eigenvalues. Using the results on the Birkhoff conjecture, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks, which Kac proved to be uniquely determined, these are the only domains for which it is known that one can hear their shape.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Andreas Bauer  (Freie Universität Berlin)

    Title: Tensorial TQFT and disentangling modular Walker-Wang models

    Abstract: I will introduce simple “tensorial” definitions for many algebraic and categorical structures appearing in the classification of topological phases of matter. Such “tensorial TQFTs” will be defined as maps that associate tensors to geometric/topological objects of some type, subject to gluing axioms. Tensorial TQFTs are very directly related to microscopic physical models in terms of discrete path integrals. I will use those tensorial definitions to construct invertible boundaries which disentangle modular Walker-Wang models.

     

    https://www.youtube.com/watch?v=MJ8NRSrvihQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=12

  • Topological Quantum Matter Seminar
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 11.16.22

    Topological Quantum Matter Seminar

    Speaker: Jérôme Faist  (ETH Zurich)

    Title: Vacuum fluctuations in cavities: breakdown of the topological protection in the integer Quantum Hall effect

    Abstract: When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling ΩR is such that the coupling energy becomes close to the one of the bare matter resonance ω0. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian.

    In a microcavity, the strength of the electric field caused by the vacuum fluctuations, to which the strength of the light-matter coupling ΩR is proportional, scales inversely with the cavity volume. One very interesting feature of the circuit-based metamaterials is the fact that this volume can be scaled down to deep subwavelength values in all three dimension of space.1 Using metamaterial coupled to two-dimensional electron gases under a strong applied magnetic field, we have now explored to which extend this volume can be scaled down and reached a regime where the stability of the polariton is limited by diffraction into a continuum of plasmon modes2.

    We have also used transport to probe the ultra-strong light-matter coupling3, and show now that the latter can induce a breakdown of the integer quantum Hall effect4. The phenomenon is explained in terms of cavity-assisted hopping, an anti-resonant process where an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity5. We are also evaluating a proposal suggesting that the value of the quantization voltage can be renormalized by the cavity6.

     

    1. Scalari, G. et al. Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial. Science 335, 1323–1326 (2012).
    2. Rajabali, S. et al. Polaritonic Nonlocality in Light Matter Interaction. Nat Photon 15, 690–695 (2021).
    3. Paravicini-Bagliani, G. L. et al. Magneto-Transport Controlled by Landau Polariton States. Nat. Phys. 15, 186–190 (2019).
    4. Appugliese, F. et al. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science 375, 1030–1034 (2022).
    5. Ciuti, C. Cavity-mediated electron hopping in disordered quantum Hall systems. Phys. Rev. B 104, 155307 (2021).
    6. Rokaj, V., Penz, M., Sentef, M. A., Ruggenthaler, M. & Rubio, A. Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance. Phys. Rev. B 105, 205424 (2022).

     

  • Quantum Matter
    10:00 am-11:00 am
    12/01/2024
    CMSA QMMP 03.10.23

    Quantum Matter Seminar

    Speaker: Yichen Huang (Harvard)

    Title: Quantum entropy thermalization

    Abstract: In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization.

    References: arXiv:2302.10165, 2209.09826; Joint work with Aram W. Harrow

     

    https://www.youtube.com/watch?v=8b4g9SEFn_Y&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=13

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Scalable Dynamic Graph Algorithms

    10:00 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    CMSA Interdisciplinary Science Seminar

    Speaker: Quanquan Liu, Northwestern University

    Title: Scalable Dynamic Graph Algorithms

    Abstract: The field of dynamic graph algorithms seeks to understand and compute statistics on real-world networks that undergo changes with time. Some of these networks could have up to millions of edge insertions and deletions per second. In light of these highly dynamic networks, we propose various scalable and accurate graph algorithms for a variety of problems. In this talk, I will discuss new algorithms for various graph problems in the batch-dynamic model in shared-memory architectures where updates to the graph arrive in multiple batches of one or more updates. I’ll also briefly discuss my work in other dynamic models such as distributed dynamic models where the communication topology of the network also changes with time (ITCS 2022). In these models, I will present efficient algorithms for graph problems including k-core decomposition, low out-degree orientation, matching, triangle counting, and coloring.

    Specifically, in the batch-dynamic model where we are given a batch of B updates, I’ll discuss an efficient O(B log^2 n) amortized work and O(log^2 n log log n) depth algorithm that gives a (2+\epsilon)-approximation on the k-core decomposition after each batch of updates (SPAA 2022). We also obtain new batch-dynamic algorithms for matching, triangle counting, and coloring using techniques and data structures developed in our k-core decomposition algorithm. In addition to our theoretical results, we implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyper-threading on 11 graphs of varying densities and sizes. Our experiments show improvements over state-of-the-art algorithms even on machines with only 4 cores (your standard laptop). I’ll conclude with a discussion of some open questions and potential future work that these lines of research inspire.

    Bio: Quanquan C. Liu is a postdoctoral scholar at Northwestern University under the mentorship of Prof. Samir Khuller. She completed her PhD in Computer Science at MIT where she was advised by Prof. Erik Demaine and Prof. Julian Shun. Before that, she obtained her dual bachelor’s degree in computer science and math also at MIT. She has worked on a number of problems in algorithms and the intersection between theory and practice. Her most recent work focuses on scalable dynamic and static graph algorithms as well as differentially private graph algorithms for problems including k-core decomposition, densest subgraphs, subgraph counting, matching, maximal independent set and coloring. She has earned the Best Paper Award at SPAA 2022, a NSF Graduate Research Fellowship, and participated in the 2021 EECS Rising Stars workshop. Outside of research, she is extensively involved in programming outreach as a coach for the USA Computing Olympiad (USACO) and as a trainer for the North America Programming Camp (NAPC).

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Margarita Davydova (MIT)

    Title: Floquet codes, automorphisms, and quantum computation

    Abstract: In this talk, I will introduce a new kind of measurement-based quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of low-weight measurements which simultaneously encode logical information and enable error correction.  We introduce a new class of quantum error-correcting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes.

    As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of time-like domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model.  This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes.

    The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two- and, rarely three-body measurements. Using adaptive two-body measurements, we can achieve a non-Clifford gate in 3+1d, making the first step towards universal quantum computation in this model.

    The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].

  • CMSA EVENT: Frontiers in Applied Mathematics and Computation
    10:00 am-2:00 pm
    12/01/2024-04/29/2020
    Frontiers In Applied Mathematics And Computation

    Together with the School of Engineering and Applied Sciences, the CMSA will be hosting a lecture series on the Frontiers in Applied Mathematics and Computation. Talks in this series will aim to highlight current research trends at the interface of applied math and computation and will explore the application of these trends to challenging scientific, engineering, and societal problems.

    Lectures will take place on March 25, April 1, and April 29, 2021.

    Speakers:

    • George Biros (U.T. Austin)
    • Laura Grigori (INRIA Paris)
    • Samory K. Kpotufe (Columbia)
    • Jonas Martin Peters (University of Copenhagen)
    • Joseph M. Teran (UCLA)

    The schedule below will be updated as talks are confirmed.

     

    Date/TimeSpeakerTitle/Abstract
    3/25/2021
    10:00 – 11:00am ET
    Joseph M. TeranTitle: Affine-Particle-In-Cell with Conservative Resampling and Implicit Time Stepping for Surface Tension Forces

    Abstract: The Particle-In-Cell (PIC) method of Harlow is one of the first and most widely used numerical methods for Partial Differential Equations (PDE) in computational physics. Its relative efficiency, versatility and intuitive implementation have made it particularly popular in computational incompressible flow, plasma physics and large strain elastoplasticity. PIC is characterized by its dual particle/grid (Lagrangian/Eulerian) representation of material where particles are generally used to track material transport in a Lagrangian way and a structured Eulerian grid is used to discretize remaining spatial derivatives in the PDE. I will discuss the importance of conserving linear and angular momentum when switching between these two representations and the recent Affine-Particle-In-Cell (APIC) extension to PIC designed for this conservation. I will also discuss a recent APIC technique for discretizing surface tension forces and their linearizations needed for implicit time stepping. This technique is characterized by a novel surface resampling strategy and I will discuss a generalization of the APIC conservation to this setting.

    4/1/2021
    9:00 – 10:00am ET
    George BirosTitle: Inverse biophysical modeling and its application to neurooncology

    Abstract: A predictive, patient-specific, biophysical model of tumor growth would be an invaluable tool for causally connecting diagnostics with predictive medicine. For example, it could be used for tumor grading, characterization of the tumor microenvironment, recurrence prediction, and treatment planning,  e.g., chemotherapy protocol or enrollment eligibility for clinical trials. Such a model also would provide an important bridge between molecular drivers of tumor growth and imaging-based phenotypic signatures, and thus,  help identify and quantify mechanism-based associations between these two. Unfortunately, such a predictive biophysical model does not exist. Existing models undergoing clinical evaluation are too simple–they do not even capture the MRI phenotype. Although many highly complex models have been proposed, the major hurdle in deploying them clinically is their calibration and validation.

    In this talk, I will discuss the challenges related to the calibration and validation of biophysical models, and in particular the mathematical structure of the underlying inverse problems. I will also present a new algorithm that localizes the tumor origin within a few millimeters.

    4/1/2021
    10:00 – 11:00am ET
    Samory K. KpotufeTitle: From Theory to Clustering

    Abstract: Clustering is a basic problem in data analysis, consisting of partitioning data into meaningful groups called clusters. Practical clustering procedures tend to meet two criteria: flexibility in the shapes and number of clusters estimated, and efficient processing. While many practical procedures might meet either of these criteria in different applications, general guarantees often only hold for theoretical procedures that are hard if not impossible to implement. A main aim is to address this gap.
    We will discuss two recent approaches that compete with state-of-the-art procedures, while at the same time relying on rigorous analysis of clustering. The first approach fits within the framework of density-based clustering, a family of flexible clustering approaches. It builds primarily on theoretical insights on nearest-neighbor graphs, a geometric data structure shown to encode local information on the data density. The second approach speeds up kernel k-means, a popular Hilbert space embedding and clustering method. This more efficient approach relies on a new interpretation – and alternative use – of kernel-sketching as a geometry-preserving random projection in Hilbert space.
    Finally, we will present recent experimental results combining the benefits of both approaches in the IoT application domain.
    The talk is based on various works with collaborators Sanjoy Dasgupta, Kamalika Chaudhuri, Ulrike von Luxburg, Heinrich Jiang, Bharath Sriperumbudur, Kun Yang, and Nick Feamster.

    4/29/2021
    12:00 – 1:00pm ET
    Jonas Martin PetersTitle: Causality and Distribution Generalization

    Abstract: Purely predictive methods do not perform well when the test distribution changes too much from the training distribution. Causal models are known to be stable with respect to distributional shifts such as arbitrarily strong interventions on the covariates, but do not perform well when the test distribution differs only mildly from the training distribution. We discuss anchor regression, a framework that provides a trade-off between causal and predictive models. The method poses different (convex and non-convex) optimization problems and relates to methods that are tailored for instrumental variable settings. We show how similar principles can be used for inferring metabolic networks. If time allows, we discuss extensions to nonlinear models and theoretical limitations of such methodology.

    4/29/2021
    1:00 – 2:00pm ET
    Laura GrigoriTitle: Randomization and communication avoiding techniques for large scale linear algebra

    Abstract: In this talk we will discuss recent developments of randomization and communication avoiding techniques for solving large scale linear algebra operations. We will focus in particular on solving linear systems of equations and we will discuss a randomized process for orthogonalizing a set of vectors and its usage in GMRES, while also exploiting mixed precision.  We will also discuss a robust multilevel preconditioner that allows to further accelerate solving large scale linear systems on parallel computers.

  • Math Science Literature Lecture Series
    10:00 am-11:30 am
    12/01/2024

    Zhengwei Liu (Tsinghua University)

    Title: Subfactors–in Memory of Vaughan Jones

    Abstract: Jones initiated modern subfactor theory in early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial, for which Jones won the Fields Metal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed.

    Talk chair: Arthur Jaffe

    Slides | Video 

  • Swampland Seminar
    10:00 am-11:30 am
    12/01/2024

    Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

  • Quantum Matter
    10:00 am
    12/01/2024
    CMSA QMMP 03.03.23

    Quantum Matter Seminar

    Speaker: Anna Hasenfratz (University of Colorado)

    Title: Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions
    Abstract: 4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the conformal phase is well established, very little is known about the nature of the phase transition or the strong coupling phase.
    Lattice QCD methods can predict the RG $\beta$ function, but the calculations are often limited by non-physical bulk phase transition that prevent exploring the strong coupling region of the phase diagram. Even the critical flavor number is controversial, estimates vary between $N_f=8$ and 14 for fundamental fermions.
    Using an improved lattice actions that include heavy Pauli-Villars (PV) type bosons to reduce ultraviolet fluctuations, I was able to simulate an SU(3) system with 8 fundamental flavors at much stronger renormalized coupling than previously possibly. The numerical results indicate a smooth phase transition from weak coupling to a strongly coupled phase.
    I investigate the critical behavior of the transition using finite size scaling. The result of the scaling analysis is not consistent with a first order phase transition, but it is well described by   Berezinsky-Kosterlitz-Thouless or BKT scaling. BKT scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that warrants further investigations.
    The strongly coupled phase appear to be chirally symmetric but gapped, suggesting symmetric mass generation (SMG). This could be the consequence of the lattice fermions used in this study. Staggered fermions in the massless limit are known to be anomaly free, allowing an SMG phase in the continuum limit.

     


    References:
    Phys.Rev.D 106 (2022) 1, 014513 • e-Print: 2204.04801
    Phys.Rev.D 104 (2021) 7, 074509 • e-Print: 2109.02790
    For anomalies and staggered fermion, see
    Phys.Rev.D 104 (2021) 9, 094504 • e-Print: 2101.01026
    https://www.youtube.com/watch?v=3jtNsFGszjE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=14
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Xiao-Gang Wen (MIT)

    Title: A 6-year journey: from gravitational anomaly to a unified theory of generalized symmetry

    Abstract: Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topological-order correspondence. I will also discuss some applications of emergent generalized symmetry.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/16/2020 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Swampland Seminar
    10:00 am-11:30 am
    12/01/2024
    Speakers: Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)
    Title4d strings at strong coupling
    As usual, the format will be 45 min talk + 30 min discussion, to encourage participation from the audience.
    Looking forward to seeing you there!
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    General Relativity Program Minicourses

    10:00 am-1:00 pm
    12/01/2024-05/17/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Minicourses

    General Relativity Program Minicourses

    During the Spring 2022 semester, the CMSA hosted a program on General Relativity.

    This semester-long program included four minicourses running in March, April, and May;  a conference April 4–8, 2022;  and a workshop from May 2–5, 2022.

     

    ScheduleSpeakerTitleAbstract
    March 1 – 3, 2022
    10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
    Dr. Stefan CzimekCharacteristic Gluing for the Einstein EquationsAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).
    March 22 – 25, 2022
    22nd & 23rd, 10:00 am – 11:30am ET
    24th & 25th, 11:00 am – 12:30pm ET
    Location: Hybrid. CMSA main seminar room, G-10.
    Prof. Lan-Hsuan HuangExistence of Static Metrics with Prescribed Bartnik Boundary DataAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is

    1. The conjecture and an overview of the results
    2. Static regular: a sufficient condition for existence and local uniqueness
    3. Convex boundary, isometric embedding, and static regular
    4. Perturbations of any hypersurface are static regular

    Video on Youtube: March 22, 2022

    March 29 – April 1, 2022 10:00am – 12:00pm ET, each day

    Location: Hybrid. CMSA main seminar room, G-10.

    Prof. Martin TaylorThe nonlinear stability of the Schwarzschild family of black holesAbstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.
    April 19 & 21, 2022
    10 am – 12 pm ET, each dayZoom only
    Prof. Håkan AndréassonTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.

    Video 4/19/2022

    Video 4/22/2022

    May 16 – 17, 2022
    10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
    Prof. Marcelo DisconziA brief overview of recent developments in relativistic fluidsAbstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.

    1. Set-up, review of standard results, physical motivation.
    2. The relativistic Euler equations: null structures and the problem of shocks.
    3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
    4. Relativistic viscous fluids.

    Video 5/16/2022

    Video 5/17/2022

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: John Baez (University of California, Riverside)

    Title: Two of my favorite numbers: 8 and 24

    Abstract: The numbers 8 and 24 play special roles in mathematics. The number 8 is special because of Bott periodicity, the octonions and the E8 lattice, while 24 is special for many reasons, including the binary tetrahedral group, the 3rd stable homotopy group of spheres, and the Leech lattice. The number 8 does for superstring theory what the number 24 does for bosonic string theory. In this talk, which is intended to be entertaining, I will overview these matters and also some connections between the numbers 8 and 24.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 05.12.23

    Quantum Matter Seminar

    Speaker: Carolyn Zhang (U Chicago)

    Title: Anomalies of (1+1)D categorical symmetries

    Abstract: We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $A$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the \emph{electric} Lagrangian algebra, that describes a phase with $A$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $A$. We observe that if there exists a different gapped boundary, given by a \emph{magnetic} Lagrangian algebra, then there exists a gapped phase where $A$ is not spontaneously broken at all, which means that $A$ is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $A$ being anomaly-free. As an application, we consider the Drinfeld centers of $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.

    https://www.youtube.com/watch?v=hSzBMYEY_q8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=4

  • Swampland Seminar
    10:00 am-11:00 am
    12/01/2024

    Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 06.30.23

    Quantum Matter Seminar

    Speaker: Marieke Van Beest (SCGP)

    Title: Monopoles, Scattering, and Generalized Symmetries

    Abstract: In this talk, we will discuss the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle, as they can carry fractional quantum numbers. We argue that such outgoing particles live in the twisted sector of a topological co-dimension 1 surface, which ends topologically on the monopole. This symmetry defect is often non-invertible, and as such the outgoing radiation not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory, which is a new prediction.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 06.26.23

    Quantum Matter Seminar

    Title: Chiral fermionic CFTs of central charge ≤ 16

    Abstract: We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac’s theorem and bosonization/fermionization. This talk will discuss the derivation of this result, its application to the classification of non-supersymmetric heterotic string theories, and along the way we’ll address some oft-overlooked subtleties of bosonization from the point of view of anomalies and topological phases.

  • Quantum Matter
    10:00 am-12:00 pm
    12/01/2024
    CMSA QMMP 06.13.23

    Quantum Matter Seminar

    Speaker: Brandon C. Rayhaun (C. N. Yang ITP, Stony Brook University)

    Title: Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality

    Abstract: Conformal field theories in (1+1)D are key actors in many dramas of physics and mathematics. Their classification has therefore been an important and long-standing problem. In this talk, I will explain the main ideas behind the classification of (most) “small” bosonic CFTs. Here, I use the adjective “small” informally to refer to theories with low central charge (less than 24) and few primary operators (less than 5). Time and attention permitting, I will highlight two applications of this result. First, I will describe how it can be used in tandem with bosonization and fermionization techniques to establish the classification of chiral fermionic CFTs with central charge less than 23. Second, I will showcase how it can be used to bootstrap generalized global symmetries using the concept of “symmetry/subalgebra duality.”

    Talk based on arXiv:2208.05486 [hep-th] (joint work with Sunil Mukhi) and arXiv:2303.16921 [hep-th].

    https://www.youtube.com/watch?v=NrOcsiUmSh0&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=1&t=2s

     

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 03.24.23

    Quantum Matter Seminar

    Speaker: Alexander Zlokapa, MIT

    Title: Traversable wormhole dynamics on a quantum processor

    Abstract: The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

     

    https://www.youtube.com/watch?v=iYkVuju_sP8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=11

  • CMSA EVENT: 2020 Big Data Conference (Virtual)
    10:00 am-2:05 pm
    12/01/2024-08/25/2020

    On August 24-25, 2020 the CMSA hosted our sixth annual Conference on Big Data. The Conference featured many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. The 2020 Big Data Conference took place virtually.

    Videos of the talks are available in this youtube playlist.

     

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Schedule:
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/1/2021 Math Physics

    10:00 am-11:00 am
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/22/2021 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Cheryne Jonay (Stanford)

    Title: A Physical Theory of Two-stage Thermalization

    Abstract: One indication of thermalization time is subsystem entanglement reaching thermal values. Recent studies on local quantum circuits reveal two exponential stages with decay rates $r_1$ and $r_2$ of the purity before and after thermalization. We provide an entanglement membrane theory interpretation, with $r_1$ corresponding to the domain wall free energy. Circuit geometry can lead to $r_1 < r_2$, producing a “phantom eigenvalue”. Competition between the domain wall and magnon leads to $r_2 < r_1$ when the magnon prevails. However, when the domain wall wins, this mechanism provides a practical approach for measuring entanglement growth through local correlation functions.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 04.28.23

    Quantum Matter Seminar

    Title: Fracton Self-Statistics

    Speaker: Hao Song (ITP-CAS)

    Abstract: Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating other excitations are called fractons. Here we address a fundamental open question — can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged, and show their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of abelian fracton orders. Finally, we show the existence of semionic or fermionic fracton self-statistics in some twisted variants of the checkerboard model and Haah’s code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.

    References: H Song, N Tantivasadakarn, W Shirley, M Hermele, arXiv:2304.00028.

    https://www.youtube.com/watch?v=TBAEif9XVww&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=6

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 04.21.23 (1)

    Quantum Matter Seminar

    Speaker: Prof. Subir Sachdev (Harvard)

    Title: A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order

    Abstract: Soon after the discovery of high-temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low-temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the “pseudogap metal” phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.
    As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.
    This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Mathias S. Scheurer, and S. S., arXiv:2302.07885

    https://www.youtube.com/watch?v=ueT28iMdjzE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=7

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/12/2021 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/5/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/5/2021 Interdisciplinary Science Seminar

    10:00 am-11:00 am
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Pre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am

    Pre-talk Title: Introduction to the singularities of the MMP


    Speaker: Dori Bejleri (Harvard Math & CMSA)

    Title: Moduli of boundary polarized Calabi-Yau pairs

    Abstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher, H. Blum, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang.

     

     

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 04.14.23

    Quantum Matter Seminar

    Speaker: Guanyu Zhu (IBM Quantum, T. J. Watson Research Center)

    Title: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries

    Abstract: Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects.

    References:
    1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua
    2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O&#39;Connor, Guanyu Zhu
    3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

     

    https://www.youtube.com/watch?v=APcDMMRI9VU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=8

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/8/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Mathematical Physics Seminar, Mondays

    10:00 am-11:00 am
    12/01/2024

    The seminar on mathematical physics will be held on Mondays from 10:00 – 11:00am ET on Zoom. Please email the seminar organizers to learn how toattend. This year’s Seminar will be organized by Yoosik Kim (yoosik@cmsa.fas.harvard.edu), Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu), and Yang Zhou (yangzhou@cmsa.fas.harvard.edu).

    Join the Math-Physics mailing list

    The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

    Spring 2021:

    DateSpeakerTitle/Abstract
    2/1/2021Choa Dongwook
    (KIAS)Video
    TitleFukaya category of Landau-Ginzburg orbifolds.

    Abstract: Landau-Ginzburg orbifold is just another name for a holomorphic function W with its abelian symmetry G. Its Fukaya category can be viewed as a categorification of a homology group of its Milnor fiber. In this introductory talk, we will start with some classical results on the topology of isolated singularities and its Fukaya-Seidel category. Then I will explain a new construction for such category to deal with a non-trivial symmetry group G. The main ingredients are classical variation map and the Reeb dynamics at the contact boundary. If time permits, I will show its application to mirror symmetry of LG orbifolds and its Milnor fiber. This is a joint work with C.-H. Cho and W. Jeong

    2/8/2021Jérémy Guéré (Fourier Institute)TitleCongruences on K-theoretic Gromov-Witten invariants

    Abstract: K-theoretic Gromov-Witten invariants of smooth projective varieties have been introduced by YP Lee, using the Euler characteristic of a virtual structure sheaf. In particular, they are integers. In this talk, I look at these invariants for the quintic threefold and I will explain how to compute them modulo 41, using the virtual localization formula under a finite group action, up to genus 19 and degree 40.

    2/15/2021Zhiwei Zheng (Max Planck Institute)

    Video

    Title: Some new results on automorphisms of hypersurfaces

    Abstract: It is natural to study automorphisms of hypersurfaces in projective spaces. In this talk, I will discuss a new approach to determine all possible orders of automorphisms of smooth hypersurfaces with fixed degree and dimension. Then we consider the specific case of cubic fourfolds, and discuss the relation with Hodge theory.

    2/22/2021Yu-Shen Lin (Boston University)

    Video

    TitleFull SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

    Abstract: Strominger–Yau–Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi–Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

    3/1/2021Carlos S. Shahbazi (Hamburg University)

    Video

    TitleMathematical supergravity and its applications to differential geometry.

    Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

    3/8/2021Miguel Moreira (ETH)

    Video

    TitleVirasoro constraints for stable pairs.

    Abstract: The theory of stable pairs (PT) with descendents, defined on a 3-fold X, is a sheaf theoretical curve counting theory. Conjecturally, it is equivalent to the Gromov-Witten (GW) theory of X via a universal (but intricate) transformation, so we can expect that the Virasoro conjecture on the GW side should have a parallel in the PT world. In joint work with A. Oblomkov, A. Okounkov, and R. Pandharipande, we formulated such a conjecture and proved it for toric 3-folds in the stationary case. The Hilbert scheme of points on a surface S might be regarded as a component of the moduli space of stable pairs on S x P1, and the Virasoro conjecture predicts a new set of relations satisfied by tautological classes on S[n] which can be proven by reduction to the toric case.

    3/15/2021Spring break
    3/22/2021Ying Xie (Shanghai Center for Mathematical Sciences)Title: Derived categories for Grassmannian flips

    Abstract: Flip is a fundamental surgery operation for constructing minimal models in higher-dimensional birational geometry. In this talk, I will introduce a series of flips from Lie theory and investigate their derived categories. This is a joint program with Conan Leung.

    3/29/2021Emanuel Scheidegger (Peking University)Title:  On the quantum K-theory of the quintic.

    Abstract: Quantum cohomology is a deformation of the cohomology of a projective variety governed by counts of stable maps from a curve into this variety. Quantum K-theory is in a similar way a deformation of K-theory but also of quantum cohomology, It has recently attracted attention in physics since a realization in a physical theory has been found. Currently, both the structure and examples in quantum K-theory are far less understood than in quantum cohomology.
    We will explain the properties of quantum K-theory in comparison with quantum cohomology, and we will discuss the examples of projective space and the quintic hypersurface in P^4.
    4/5/2021Gaëtan Borot (HU Berlin)

    Video

    TitleTopological recursion in 4d N = 2 supersymmetric gauge theories

    Abstract: According to the Alday-Gaiotto-Tachikawa conjecture (proved in this case by Schiffman and Vasserot), the instanton partition function in 4d N = 2 SU(r) supersymmetric gauge theory on P^2 with equivariant parameters \epsilon_1,\epsilon_2 is the norm of a Whittaker vector for W(gl_r) algebra. I will explain how these Whittaker vectors can be computed (at least perturbatively in the energy scale) by topological recursion for \epsilon_1 +\epsilon_2 = 0, and by a non-commutation version of the topological recursion in the Nekrasov-Shatashvili regime where \epsilon_1/\epsilon_2 is fixed. This is a joint work to appear with Bouchard, Chidambaram and Creutzig.

    4/12/2021Fei Yan (Rutgers)TitleNetworks and quantization

    Abstract: I will describe two quantization scenarios. The first scenario involves the construction of a quantum trace map computing a link “invariant” (with possible wall-crossing behavior) for links L in a 3-manifold M, where M is a Riemann surface C times a real line. This construction unifies the computation of familiar link invariant with the refined counting of framed BPS states for line defects in 4d N=2 theories of class S. Certain networks on C play an important role in the construction. The second scenario concerns the study of Schroedinger equations and their higher order analogues, which could arise in the quantization of Seiberg-Witten curves in 4d N=2 theories. Here similarly certain networks play an important part in the exact WKB analysis for these Schroedinger-like equations. At the end of my talk I will also try to sketch a possibility to bridge these two scenarios.

    4/19/2021Hazel Mak (Brown University)TitleBranching Rules and Young Tableaux Methods: 10D & 11D Supergravity

    Abstract: In this talk, I will review 4D, N = 1 off-shell supergravity. Then I present explorations to construct 10D and 11D supergravity theories in two steps. The first step is to decompose scalar superfield into Lorentz group representations which involves branching rules and related methods. Interpretations of component fields by Young tableaux methods will be presented. The second step is to implement an analogue of Breitenlohner’s approach for 4D supergravity to 10D and 11D theories.

    4/26/2021Owen Gwilliam (UMass. Amherst)

    Video

    TitleTopological-holomorphic field theories and their BV quantizations

    Abstract: Topological field theories and holomorphic field theories have each had a substantial impact in both physics and mathematics, so it is natural to consider theories that are hybrids of the two, which we call topological-holomorphic and denote as THFTs. Examples include Kapustin’s twist of N=2, D=4 supersymmetric Yang-Mills theory and Costello’s 4-dimensional Chern-Simons theory. In this talk about joint work with Rabinovich and Williams, I will define THFTs, describe several examples, and then explain how to quantize them rigorously and explicitly, by building on techniques of Si Li.  Time permitting, I will indicate how these results offer a novel perspective on the Gaudin model via 3-dimensional field theories.


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/14/2020Lino Amorim (Kansas State University)TitleNon-commutative Gromov-Witten invariants

    Abstract:  I will describe an analogue of Saito’s theory of primitive forms for Calabi-Yau A-infinity categories. Under some conditions on the Hochschild cohomology of the category, this construction recovers the (genus zero) Gromov-Witten invariants of a symplectic manifold from its Fukaya category. This includes many compact toric manifolds, in particular projective spaces.

    9/21/2020Yuhan Sun (Rutgers)Title: Displacement energy of Lagrangian 3-spheres

    Abstract:  We study local and global Hamiltonian dynamical behaviors of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that there is a one-parameter family of Lagrangian tori near S, which are nondisplaceable in X. When dim S = 3, we obtain a new estimate of the displacement energy of S, by estimating the displacement energy of a one-parameter family of Lagrangian tori near S.

    9/28/2020Shota Komatsu (CERN)Title: Wilson loops as matrix product states

    Abstract:  In this talk, I will discuss a reformulation of the Wilson loop in large N gauge theories in terms of matrix product states. The construction is motivated by the analysis of supersymmetric Wilson loops in the maximally super Yang–Mills theory in four dimensions, but can be applied to any other large N gauge theories and matrix models, although less effective. For the maximally super Yang–Mills theory, one can further perform the computation exactly as a function of ‘t Hooft coupling by combining our formulation with the relation to integrable spin chains.

    10/5/2020Ming Zhang (UBC)Title: Verlinde/Grassmannian correspondence and applications.

    Abstract: In the 90s’, Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten’s work by relating the $\text{GL}_{n}$ Verlinde numbers to the level $l$ quantum K-invariants of the Grassmannian $\text{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence.

    The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will discuss the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.  At the end of the talk, I will describe some applications of this correspondence.

    10/12/2020Cancelled -Columbus Day
    10/19/2020Ben Gammage (Harvard)Title3d mirror symmetry for abelian gauge groups

    Abstract: 3d mirror symmetry is a proposed duality relating a pair of 3-dimensional supersymmetric gauge theories. Various consequences of this duality have been heavily explored by representation theorists in recent years, under the name of “symplectic duality”. In joint work in progress with Justin Hilburn, for the case of abelian gauge groups, we provide a fully mathematical explanation of this duality in the form of an equivalence of 2-categories of boundary conditions for topological twists of these theories. We will also discuss some applications to homological mirror symmetry and geometric Langlands duality.

    10/26/2020Cancelled
    11/2/2020Haoyu Sun (Berkeley)TitleDouble-Janus linear sigma models and generalized quadratic reciprocity

    Abstract: We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d N=4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T^2 fibered over S^1) times a circle with an SL(2,Z) duality wall inserted on S^1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2,Z), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
    11/9/2020An Huang (Brandeis)Titlep-adic strings, Einstein equations, Green’s functions, and Tate’s thesis

    Abstract: I shall discuss a recent work on how p-adic strings can produce perturbative quantum gravity, and an adelic physics interpretation of Tate’s thesis.
    11/16/2020
    10:00am ET
    Matt Kerr (WUSTL)Title:  Differential equations and mixed Hodge structures

    Abstract: We report on a new development in asymptotic Hodge theory, arising from work of Golyshev–Zagier and Bloch–Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry.  The talk will focus exclusively on the Hodge/period-theoretic aspects through two main examples.
    Given a variation of Hodge structure M on a Zariski open in P^1, the periods of the limiting mixed Hodge structures at the punctures are interesting invariants of M.  More generally, one can try to compute these asymptotic invariants for iterated extensions of M by “Tate objects”, which may arise for example from normal functions associated to algebraic cycles. The main point of the talk will be that (with suitable assumptions on M) these invariants are encoded in an entire function called the motivic Gamma function, which is determined by the Picard-Fuchs operator L underlying M. In particular, when L is hypergeometric, this is easy to compute and we get a closed-form answer (and a limiting motive).  In the non-hypergeometric setting, it yields predictions for special values of normal functions; this part of the story is joint with V. Golyshev and T. Sasaki.

    11/23/2020

    11:30am ET

    Kyoung-Seog Lee (U of Miami)TitleDerived categories and motives of moduli spaces of vector bundles on curves

    Abstract: Derived categories and motives are important invariants of algebraic varieties invented by Grothendieck and his collaborators around 1960s. In 2005, Orlov conjectured that they will be closely related and now there are several evidences supporting his conjecture. On the other hand, moduli spaces of vector bundles on curves provide attractive and important examples of algebraic varieties and there have been intensive works studying them. In this talk, I will discuss derived categories and motives of moduli spaces of vector bundles on curves. This talk is based on joint works with I. Biswas and T. Gomez.

    11/30/2020Zijun Zhou (IPMU)Title: 3d N=2 toric mirror symmetry and quantum K-theory

    Abstract: In this talk, I will introduce a new construction for the K-theoretic mirror symmetry of toric varieties/stacks, based on the 3d N=2 mirror symmetry introduced by Dorey-Tong. Given the toric datum, i.e. a  short exact sequence 0 -> Z^k -> Z^n -> Z^{n-k} -> 0, we consider the toric Artin stack of the form [C^n / (C^*)^k]. Its mirror is constructed by taking the Gale dual of the defining short exact sequence. As an analogue of the 3d N=4 case, we consider the K-theoretic I-function, with a suitable level structure, defined by counting parameterized quasimaps from P^1. Under mirror symmetry, the I-functions of a mirror pair are related to each other under the mirror map, which exchanges the K\”ahler and equivariant parameters, and maps q to q^{-1}. This is joint work with Yongbin Ruan and Yaoxiong Wen.

    12/7/2020Thomas Grimm (Utrecht)TitleModuli Space Holography and the Finiteness of Flux Vacua

    Abstract: In this talk I describe a holographic perspective to study field spaces that arise in string compactifications. The constructions are motivated by a general description of the asymptotic, near-boundary regions in complex structure moduli spaces of Calabi-Yau manifolds using asymptotic Hodge theory. For real two-dimensional field spaces, I introduce an auxiliary bulk theory and describe aspects of an associated sl(2) boundary theory. The bulk reconstruction from the boundary data is provided by the sl(2)-orbit theorem of Schmid and Cattani, Kaplan, Schmid, which is a famous and general result in Hodge theory. I then apply this correspondence to the flux landscape of Calabi-Yau fourfold compactifications and discuss how this allows us, in work with C. Schnell, to prove that the number of self-dual flux vacua is finite

    For a listing of previous Mathematical Physics Seminars, please click here.

  • Seminars

    Seminars Colloquia & Seminar
    Social Science Applications Forum

    10:00 am-11:00 am
    12/01/2024

    During the Summer of 2020, the CMSA will be hosting a periodic Social Science Applications Seminar.

    The list of speakers is below and will be updated as details are confirmed.

    For a list of past Social Science Applications talks, please click here.
    DateSpeakerTitle/Abstract
    7/13/2020 10:00-11:00am ETLudovic Tangpi (Princeton)Please note, this seminar will take place online using Zoom.

    Title: Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls

    Abstract: This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in non-cooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space.
    For security reasons, you will have to show your full name to join the meeting.

    7/27/2020
    10:00pm
    Michael Ewens (Caltech)Please note, this seminar will take place online using Zoom.

    Title: Measuring Intangible Capital with Market Prices

    Abstract: Despite the importance of intangibles in today’s economy, current standards prohibit the capitalization of internally created knowledge and organizational capital, resulting in a downward bias of reported assets. As a result, researchers estimate this value by capitalizing prior flows of R&D and SG&A. In doing so, a set of capitalization parameters, i.e. the R&D depreciation rate and the fraction of SG&A that represents a long-lived asset, must be assumed. Parameters now in use are derived from models with strong assumptions or are ad hoc. We develop a capitalization model that motivates the use of market prices of intangibles to estimate these parameters. Two settings provide intangible asset values: (1) publicly traded equity prices and (2) acquisition prices. We use these parameters to estimate intangible capital stocks and subject them to an extensive set of diagnostic analyses that compare them with stocks estimated using existing parameters. Intangible stocks developed from exit price parameters outperform both stocks developed by publicly traded parameters and those stocks developed with existing estimates. (Joint work with Ryan Peters and Sean Wang.)

  • Mathematical Physics Seminar
    10:00 am-11:00 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

     

    Speaker: Carlos S. Shahbazi (Hamburg University)

    Title: Mathematical supergravity and its applications to differential geometry

    Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA QMMP 04.07.23

    Quantum Matter Seminar

    Speaker: Nishad Maskara (Harvard)

    Title: Enhancing Detection of Topological Order by Local Error Correction

    Abstract: The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator.  Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.

     

    https://www.youtube.com/watch?v=oWIelx6_taU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=9

  • Algebraic Geometry in String Theory Seminar
    10:00 am-11:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA AGST Seminar 04.03.2023

    Algebraic Geometry in String Theory Seminar

    Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse

    Title: Kähler-Einstein metrics on families of Fano varieties

    Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Nat Tantivasadakarn (Caltech)

    Title: From wave-function collapse and Galois solvability to the realization of non-Abelian topological order on a quantum device

    Abstract: I will review our recent set of theoretical works on efficiently preparing long range quantum entanglement with adaptive quantum circuits: the combination of measurements with unitary gates whose choice can depend on previous measurement outcomes. I will show that this additional ingredient can be leveraged to prepare the long sought-after non-Abelian topological phases with a circuit depth that is independent of system size. Using this framework, we uncover a complexity hierarchy of long-range entangled states based on the minimal number of measurement layers required to create the state. Moreover, we find that certain non-Abelian states that cannot be efficiently prepared with adaptive circuits have a surprising connection to the unsolvability of the quintic polynomial.

    Finally, I will describe our recent collaboration with Quantinuum where we present the first unambiguous realization of non-Abelian D4 topological order and demonstrate control of its anyons. In particular, we are able to detect a non-trivial braiding where three non-Abelian anyons trace out the Borromean rings in spacetime, a signature unique to non-Abelian topological order.

  • Mathematical Physics Seminar
    10:00 am-11:00 am
    12/01/2024

    Speaker: Yu-Shen Lin (Boston University)

    Title: Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

    Abstract: Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi-Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/15/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Quantum Matter Seminar

    Speaker: Abijith Krishnan (MIT)

    Title: A Plane Defect in the 3d O(N) Model

    Abstract: It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

     

    https://www.youtube.com/watch?v=6cDK3TJ_H8w&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=10

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    2/10/2021 Strongly Correlated Quantum Materials

    10:00 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 06.09.23

    Quantum Matter Seminar

    Speakers: Gerald Höhn (Kansas State University) & Sven Möller (University of Hamburg)

    Title: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24

    Abstract: We discuss the classfication of self-dual vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely chiral 2-dimensional fermionic conformal field theories with just one primary field.

    There are exactly 969 such SVOAs under suitable regularity assumptions and the assumption that the shorter moonshine module VB^# is the unique self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1 spaces vanish.

    We construct and classify the self-dual SVOAs by determining the 2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central charge 24 and also by realising them as simple-current extensions of a dual pair containing a certain maximal lattice VOA. We show that all SVOAs besides VB^# x F and potential fake copies thereof stem from elements of the Conway group Co_0, the automorphism group of the Leech lattice.

    By splitting off free fermions F, if possible, we obtain the classification for all central charges less than or equal to 24.
    Reference: G. Höhn, S. Möller, arXiv:2303.17190.

    https://www.youtube.com/watch?v=U0alYxX05xU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=2

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Previous Random Matrix & Probability Theory Seminars

    10:26 am-10:27 am
    12/01/2024

    Spring 2020:

    DateSpeakerTitle/Abstract
    2/26/2020Louigi Addario-Berry (McGill University)Title: Hipster random walks and their ilk 

    Abstract: I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.

    4/1/2020Ian Jauslin (Princeton)This meeting will be taking place virtually on Zoom.

    Title: A simplified approach to interacting Bose gases
    Abstract: I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.

    4/22/2020Martin Gebert (UC Davis)This meeting will be taking place virtually on Zoom.

    TitleLieb-Robinson bounds for a class of continuum many-body fermion systems

    Abstract: We introduce a class of UV-regularized two-body interactions for
    fermions in $\R^d$ and prove a Lieb-Robinson estimate for the dynamics
    of this class of many-body systems. As a step towards this result, we
    also prove a propagation bound of Lieb-Robinson type for continuum
    one-particle Schr\“odinger operators. We apply the propagation bound to
    prove the existence of a strongly continuous infinite-volume dynamics on
    the CAR algebra.

    4/29/2020Marcin Napiórkowski (University of Warsaw)This meeting will be taking place virtually on Zoom.

    TitleFree energy asymptotics of the quantum Heisenberg spin chain

    Abstract: Spin wave theory suggests that low temperature properties of the Heisenberg model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction. Based on joint work with Robert Seiringer.

    5/6/2020Antti Knowles (University of Geneva)TitleField theory as a limit of interacting quantum Bose gases

    Abstract: We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the mean-field limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions d = 1,2,3. For d > 1 the Gibbs measure is supported on distributions of negative regularity and we have to renormalize the interaction. The proof is based on a functional integral representation of the grand canonical Gibbs state, in which convergence to the mean-field limit follows formally from an infinite-dimensional stationary phase argument for ill-defined non-Gaussian measures. We make this argument rigorous by introducing a white-noise-type auxiliary field, through which the functional integral is expressed in terms of propagators of heat equations driven by time-dependent periodic random potentials. Joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.
    5/13/2020Sven Bachmann (University of British Columbia)TitleQuantized quantum transport and Abelian anyons

    Abstract: I’ll discuss recent developments in the study of quantized quantum transport, focussing on the quantum Hall effect. Beyond presenting an index taking rational values, and which is the Hall conductance in the adapted setting, I will explain how the index is intimately paired with the existence of quasi-particle excitations having non-trivial braiding properties.

    5/20/2020Kristina Schubert (TU Dortmund)TitleFluctuation Results for General Ising Models — Block Spin Ising Models and Random Interactions

    Abstract: Starting from the classical Curie-Weiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins in which the vertices are divided into a finite number of blocks and where pair interactions are given according to their blocks. The magnetization is then the vector of magnetizations within each block, and we are interested in its behaviour and in particular in its fluctuations. On the other hand, we consider Ising models on Erdős-Rényi random graphs. Here, I will also present results on the fluctuations of the magnetization.

     

    Fall 2019:

    DateSpeakerTitle/Abstract
    9/11/2019Subhabrata SenTitle: Sampling convergence for random graphs: graphexes and multigraphexes

    Abstract: We will look at structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs, Chayes, Cohn and Veitch ’17). Sam- pling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We will introduce this framework and motivate the components of a graphex. Subsequently, we will discuss the graphex limit for several well-known sparse random (multi)graph models. This is based on joint work with Christian Borgs, Jennifer Chayes, and Souvik Dhara.

    9/25/2019Jeff Schenker (Michigan State)Title: An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states  

    Abstract: Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one — “entanglement breaking’’ – channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh)

    10/3/2019

     

    Thursday

    4:30pm

    Jian Ding (UPenn)Title: Distances associated with Liouville quantum gravity

    Abstract: I will review some recent progresses on distances associated with Liouville quantum gravity, which is a random measure obtained from exponentiating a planar Gaussian free field.

    The talk is based on works with Julien Dubédat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne, Ofer Zeitouni and Fuxi Zhang in various combinations.

    10/9/2019Ruth Williams (UCSD)Title: Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

    Abstract: Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy. It has been a standing problem to prove stability of this general model when the average load on the system is less than the network’s capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and indicate how to prove stability of the fluid model under mild conditions.

    This talk is based on joint work with Yingjia Fu.

    10/11/2019Cancelled
    10/16/2019Wei-Kuo Chen (University of Minnesota)Title: The generalized TAP free energy

    Abstract: Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag.

    10/23/2019Souvik Dhara (MIT)Title: A new universality class for critical percolation on networks with heavy-tailed degrees

    Abstract: The talk concerns critical behavior of percolation on finite random networks with heavy-tailed degree distribution. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdős-Rényi random graph. Subsequently, there has been a surge in the literature identifying two universality classes for the critical behavior depending on whether the asymptotic degree distribution has a finite or infinite third moment.

    In this talk, we will present a completely new universality class that arises in the context of degrees having infinite second moment. Specifically, the scaling limit of the rescaled component sizes is different from the general description of multiplicative coalescent given by Aldous and Limic (1998). Moreover, the study of critical behavior in this regime exhibits several surprising features that have never been observed in any other universality classes so far.

    This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden.

    10/30/2019Aram Harrow (MIT)Title: Random quantum circuits, phase transitions and complexity

    Abstract: Random unitary dynamics are a toy model for chaotic quantum dynamics and also have applications to quantum information theory and computing. Recently, random quantum circuits were the basis of Google’s announcement of “quantum computational supremacy,” meaning performing a task on a programmable quantum computer that would difficult or infeasible for any classical computer. Google’s approach is based on the conjecture that random circuits are as hard to classical computers to simulate as a worst-case quantum computation would be. I will describe evidence in favor of this conjecture for deep random circuits and against this conjecture for shallow random circuits. (Deep/shallow refers to the number of time steps of the quantum circuit.) For deep random circuits in Euclidean geometries, we show that quantum dynamics match the first few moments of the Haar measure after roughly the amount of time needed for a signal to propagate from one side of the system to the other. In non-Euclidean geometries, such as the Schwarzschild metric in the vicinity of a black hole, this turns out not to be always true. I will also explain how shallow quantum circuits are easier to simulate when the gates are randomly chosen than in the worst case. This uses a simulation algorithm based on tensor contraction which is analyzed in terms of an associated stat mech model.

    This is based on joint work with Saeed Mehraban (1809.06957) and with John Napp, Rolando La Placa, Alex Dalzell and Fernando Brandao (to appear).

    11/6/2019Bruno Nachtergaele (UC Davis)TitleThe transmission time and local integrals of motion for disordered spin chains

    Abstract:  We investigate the relationship between zero-velocity Lieb-Robinson bounds and the existence of local integrals of motion (LIOMs) for disordered quantum spin chains. We also study the effect of dilute random perturbations on the dynamics of many-body localized spin chains. Using a notion of transmission time for propagation in quantum lattice systems we demonstrate slow propagation by proving a lower bound for the transmission time. This result can be interpreted as a robustness property of slow transport in one dimension. (Joint work with Jake Reschke)

    11/13/2019Gourab Ray (University of Victoria)Title: Logarithmic variance of height function of square-iceAbstract: A homomorphism height function on a finite graph is a integer-valued function on the set of vertices constrained to have adjacent vertices take adjacent integer values. We consider the uniform distribution over all such functions defined on a finite subgraph of Z^2 with predetermined values at some fixed boundary vertices. This model is equivalent to the height function of the six-vertex model with a = b = c = 1, i.e. to the height function of square-ice. Our main result is that in a subgraph of Z^2 with zero boundary conditions, the variance grows logarithmically in the distance to the boundary. This establishes a strong form of roughness of the planar uniform homomorphisms.

     

    Joint work with: Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran Raoufi.

    11/20/2019Vishesh Jain (MIT)Title: A combinatorial approach to the quantitative invertibility of random matrices.

     

    Abstract: Abstract: Let $s_n(M_n)$ denote the smallest singular value of an $n\times n$ random matrix $M_n$. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood–Offord theory or net arguments) for obtaining upper bounds on the probability that $s_n(M_n)$ is smaller than $\eta \geq 0$ for quite general random matrix models. Such estimates are a fundamental part of the non-asymptotic theory of random matrices and have applications to the strong circular law, numerical linear algebra etc. In several cases of interest, our approach provides stronger bounds than those obtained by Tao and Vu using inverse Littlewood–Offord theory.

     

     

     

    2018-2019

    DateSpeakerTitle/Abstract
    9/28/2018

    *Friday, 10:00am*

    Yash Deshpande (MIT)Title: Estimating low-rank matrices in noise: phase transitions from spin glass theory

    Abstract: Estimating low-rank matrices from noisy observations is a common task in statistical and engineering applications. Following the seminal work of Johnstone, Baik, Ben-Arous and Peche, versions of this problem have been extensively studied using random matrix theory. In this talk, we will consider an alternative viewpoint based on tools from mean field spin glasses. We will present two examples that illustrate how these tools yield information beyond those from classical random matrix theory. The first example is the two-groups stochastic block model (SBM), where we will obtain a full information-theoretic understanding of the estimation phase transition. In the second example, we will augment the SBM with covariate information at nodes, and obtain results on the altered phase transition.

    This is based on joint works with Emmanuel Abbe, Andrea Montanari, Elchanan Mossel and Subhabrata Sen.

    10/3/2018Ian Jauslin (IAS)Title: Liquid Crystals and the Heilmann-Lieb model

    Abstract: In 1979, O.Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb.

    10/10/2018Afonso Bandeira (NYUTitle: Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment

    Abstract: Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions and orientations; Cryo-Electron Microscopy (Cryo-EM) imaging where projections of a molecule density are taken from unknown rotations, and several others.

    One fundamental example of this type of problems is Multi-Reference Alignment: Given a group acting in a space, the goal is to estimate an orbit of the group action from noisy samples. For example, in one of its simplest forms, one is tasked with estimating a signal from noisy cyclically shifted copies. We will show that the number of observations needed by any method has a surprising dependency on the signal-to-noise ratio (SNR), and algebraic properties of the underlying group action. Remarkably, in some important cases, this sample complexity is achieved with computationally efficient methods based on computing invariants under the group of transformations.

    10/17/2018

    3:30pm

    Thomas Chen (UT Austin)Title: Dynamics of a heavy quantum tracer particle in a Bose gas

    Abstract: We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R^3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit where N tends to infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. This is joint work with Avy Soffer (Rutgers University).

    10/24/2018

    *Room G02*

    Tselil Schramm (Harvard/MIT)Title: (Nearly) Efficient Algorithms for the Graph Matching Problem in Correlated Random Graphs

    Abstract: The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known.

    Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng.

    10/30/2018

    *Tuesday

    10:30am

    SC 507*

    Lauren Williams (Harvard)Title: Introduction to the asymmetric simple exclusion process (from a combinatorialist’s point of view)

    Abstract: The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, subject to the condition that there is at most one particle per site. This model was introduced in 1970 by biologists (as a model for translation in protein synthesis) but has since been shown to display a rich mathematical structure. There are many variants of the model — e.g. the lattice could be a ring, or a line with open boundaries. One can also allow multiple species of particles with different “weights.” I will explain how one can give combinatorial formulas for the stationary distribution using various kinds of tableaux. I will also explain how the ASEP is related to interesting families of orthogonal polynomials, including Askey-Wilson polynomials, Koornwinder polynomials, and Macdonald polynomials.

    11/7/2018Willhelm Schlag (Yale)Title: on the Bourgain-Dyatlov fractal uncertainty principle

    Abstract: We will present the Bourgain-Dyatlov theorem on the line, it’s connection with other uncertainty principles in harmonic analysis, and my recent partial progress with Rui Han on the problem of higher dimensions.

    11/14/2018David Gamarnik (MIT)Title: Two Algorithmic Hardness Results in Spin Glasses and Compressive Sensing.

    Abstract: I will discuss two computational problems in the area of random combinatorial structures. The first one is the problem of computing the partition function of a Sherrington-Kirkpatrick spin glass model. While the the problem of computing the partition functions associated with arbitrary instances is known to belong to the #P complexity class, the complexity of the problem for random instances is open. We show that the problem of computing the partition function exactly (in an appropriate sense) for the case of instances involving Gaussian couplings is #P-hard on average. The proof uses Lipton’s trick of computation modulo large prime number, reduction of the average case to the worst case instances, and the near uniformity of the ”stretched” log-normal distribution.

    In the second part we will discuss the problem of explicit construction of matrices satisfying the Restricted Isometry Property (RIP). This challenge arises in the field of compressive sensing. While random matrices are known to satisfy the RIP with high probability, the problem of explicit (deterministic) construction of RIP matrices eluded efforts and hits the so-called ”square root” barrier which I will discuss in the talk. Overcoming this barrier is an open problem explored widely in the literature. We essentially resolve this problem by showing that an explicit construction of RIP matrices implies an explicit construction of graphs satisfying a very strong form of Ramsey property, which has been open since the seminal work of Erdos in 1947.

    11/28/2018Sean O’ Rourke (UC Boulder)Title: Universality and least singular values of random matrix products

    Abstract: We consider the product of m independent iid random matrices as m is fixed and the sizes of the matrices tend to infinity.  In the case when the factor matrices are drawn from the complex Ginibre ensemble, Akemann and Burda computed the limiting microscopic correlation functions.  In particular, away from the origin, they showed that the limiting correlation functions do not depend on m, the number of factor matrices. We show that this behavior is universal for products of iid random matrices under a moment matching hypothesis.  In addition, we establish universality results for the linear statistics for these product models, which show that the limiting variance does not depend on the number of factor matrices either. The proofs of these universality results require a near-optimal lower bound on the least singular value for these product ensembles.

    12/5/2018

    *Room G02*

    Omer Angel (UBC)Title: balanced excited random walks

    Abstract: I will present results on the scaling limit and asymptotics of the balanced excited random walk and related processes. This is a walk the that moves vertically on the first visit to a vertex, and horizontally on every subsequent visit. We also analyze certain versions of “clairvoyant scheduling” of random walks.

    Joint work with Mark Holmes and Alejandro Ramirez.

    2/7/2019

    Science Center 530

    Ramis Movassagh (IMB Research)Title: Generic Gaplessness, and Hamiltonian density of states from free probability theory

    Abstract: Quantum many-body systems usually reside in their lowest energy states. This among other things, motives understanding the gap, which is generally an undecidable problem. Nevertheless, we prove that generically local quantum Hamiltonians are gapless in any dimension and on any graph with bounded maximum degree.

    We then provide an applied and approximate answer to an old problem in pure mathematics. Suppose the eigenvalue distributions of two matrices M_1 and M_2 are known. What is the eigenvalue distribution of the sum M_1+M_2? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions. We will describe FPT and show examples of its powers for approximating physical quantities such as the density of states of the Anderson model, quantum spin chains, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly (provably NP-hard). Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in fresh new contexts.

    2/14/2019Nike Sun (MIT)Title: Capacity lower bound for the Ising perceptron

    Abstract: The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results.

    2/21/2019Michael Loss (Georgia Tech)Title: Some results for functionals of Aharonov-Bohm type

    Abstract: In this talk I present some variational problems of Aharonov-Bohm type, i.e., they include a  magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a  variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.

    3/6/2019

    4:15pm

    Science Center 411

    Ilya Kachkovskiy (Michigan State University)Title: Localization and delocalization for interacting 1D quasiperiodic particles.

    Abstract: We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large coupling localization depends on symmetries of the single-particle potential. If the potential has no cosine-type symmetries, then we are able to show large coupling localization at all energies, even if the interaction is not small (with some assumptions on its complexity). If symmetries are present, we can show localization away from finitely many energies, thus removing a fraction of spectrum from consideration. We also demonstrate that, in the symmetric case, delocalization can indeed happen if the interaction is strong, at the energies away from the bulk spectrum. The result is based on joint works with Jean Bourgain and Svetlana Jitomirskaya.

    3/14/2019

    5:45pm

    Science Center 232

    Anna Vershynina (University of Houston)Title: How fast can entanglement be generated in quantum systems?

    Abstract: We investigate the maximal rate at which entanglement can be generated in bipartite quantum systems. The goal is to upper bound this rate. All previous results in closed systems considered entanglement entropy as a measure of entanglement. I will present recent results, where entanglement measure can be chosen from a large class of measures. The result is derived from a general bound on the trace-norm of a commutator, and can, for example, be applied to bound the entanglement rate for Renyi and Tsallis entanglement entropies.

    3/28/2019

    Room G02

    Xuwen Chen (University of Rochester)Title: The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics

    Abstract: We derive the 3D energy-critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. We develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false sharp trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new HUFL (hierarchical uniform frequency localization) property for the GP hierarchy and use it to prove a new type of uniqueness theorem.

    4/4/2019Paul Bourgade (NYU)Title: Log-correlations and branching structures in analytic number theory

    Abstract: Fyodorov, Hiary and Keating have predicted the size of local maxima of L-function along the critical axis, based on analogous random matrix statistics. I will explain this prediction in the context of the log-correlated universality class and branching structures. In particular I will explain why the Riemann zeta function exhibits log-correlations, and outline the proof for the leading order of the maximum in the Fyodorov, Hiary and Keating prediction. Joint work with Arguin, Belius, Radziwill and Soundararajan.

    4/9/2019

    Tuesday

    12:00pm

    Room G02

    Giulio Biroli (ENS Paris)Title: Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices

    Abstract: I consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. I will show how to obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $\theta>1$, in large deviations characterized by a small value of $u$, i.e. $u<1-1/\theta$, the second-largest eigenvalue pops out from the Wigner semi-circle and the associated eigenvector orients in the direction corresponding to the rank-one perturbation. These results can be generalized to the Wishart Ensemble, and extended to the first $n$ eigenvalues and the associated eigenvectors.

    Finally, I will discuss motivations and applications of these results to the study of the geometric properties of random high-dimensional functions—a topic that is currently attracting a lot of attention in physics and computer science.

    4/11/2019Rui Han (Georgia Tech)Title: Spectral gaps in graphene structures

    Abstract: We present a full analysis of the spectrum of graphene in magnetic fields with constant flux through every hexagonal comb. In particular, we provide a rigorous foundation for self-similarity by showing that for irrational flux, the spectrum of graphene is a zero measure Cantor set. We also show that for vanishing flux, the spectral bands have nontrivial overlap, which proves the discrete Bethe-Sommerfeld conjecture for the graphene structure. This is based on joint works with S. Becker, J. Fillman and S. Jitomirskaya.

    4/25/2019Benjamin Fehrman (Oxford)Title:  Pathwise well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

    Abstract:  We present a pathwise well-posedness theory for stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise.  Such equations arise in the theory of mean field games, approximate the Dean-Kawasaki equation in fluctuating fluid dynamics, describe the fluctuating hydrodynamics of the zero range process, and model the evolution of a thin film in the regime of negligible surface tension.  Motivated by the theory of stochastic viscosity solutions, we pass to the equation’s kinetic formulation, where the noise enters linearly and can be inverted using the theory of rough paths. The talk is based on joint work with Benjamin Gess.

    4/30/2019TBATBA
    5/2/2019Jian Ding (UPenn)TBA

    2017-2018

    Date…………Name…………….Title/Abstract
    2-16-20183:30pm

    G02

    Reza Gheissari (NYU)Dynamics of Critical 2D Potts ModelsAbstract: The Potts model is a generalization of the Ising model to $q\geq 3$ states with inverse temperature $\beta$. The Gibbs measure on $\mathbb Z^2$ has a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the phase transition is continuous while when $q>4$, the phase transition is discontinuous and the disordered and ordered phases coexist.

    We will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat bath/Metropolis) for the 2D Potts model, where the mixing time on an $n \times n$ torus should transition from $O(\log n)$ at high temperatures to $\exp(c_\beta n)$ at low temperatures, via a critical slowdown at $\beta_c(q)$ that is polynomial in $n$ when $q \leq 4$ and exponential in $n$ when $q>4$.

    2-23-20183:30pm

    G02

    Mustazee Rahman (MIT)On shocks in the TASEPAbstract: The TASEP particle system runs into traffic jams when the particle density to the left is smaller than the density to the right. Macroscopically, the particle density solves Burgers’ equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP shock whereby we identify the microscopic fluctuations around the shock by using exact formulas for the correlation functions of TASEP and its KPZ scaling limit. The resulting laws are related to universal laws of random matrix theory.

    For the curious, here is a video of the shock forming in Burgers’ equation:

    4-20-20182:00-3:00pmCarlo Lucibello(Microsoft Research NE)The Random Perceptron Problem: thresholds, phase transitions, and geometryAbstract: The perceptron is the simplest feedforward neural network model, the building block of the deep architectures used in modern machine learning practice. In this talk, I will review some old and new results, mostly focusing on the case of binary weights and random examples. Despite its simplicity, this model provides an extremely rich phenomenology: as the number of examples per synapses is increased, the system undergoes different phase transitions, which can be directly linked to solvers’ performances and to information theoretic bounds. A geometrical analysis of the solution space shows how two different types of solutions, akin to wide and sharp minima, have different generalization capabilities when presented with new examples.  Solutions in dense clusters generalize remarkably better,  partially closing the gap with Bayesian optimal estimators.  Most of the results I will present were first obtained using non rigorous techniques from spin glass theory and many of them haven’t been rigorously established yet,  although some big steps forward have been taken in recent years.
    4-20-20183:00-4:00pmYash Despande(MIT)Phase transitions in estimating low-rank matricesAbstract: Low-rank perturbations of Wigner matrices have been extensively studied in random matrix theory; much information about the corresponding spectral phase transition can be gleaned using these tools. In this talk, I will consider an alternative viewpoint based on tools from spin glass theory, and two examples that illustrate how these they yield information beyond traditional spectral tools. The first example is the stochastic block model,where we obtain a full information-theoretic picture of estimation. The second example demonstrates how side information alters the spectral threshold. It involves a new phase transition that interpolates between the Wigner and Wishart ensembles.
    DateNameTitle/Abstract
    9-27-17Herbert Spohn, Technische Universität MünchenHydrodynamics of integrable classical and quantum systems

    Abstract:  In the cold atoms community there is great interest in developing Euler-type hydrodynamics for one-dimensional integrable quantum systems, in particular with application to domain wall initial states.  I provide some mathematical physics background and also compare with integrable classical systems.

    10-23-17

    *12:00-1:00pm, Science Center 232*

     Madhu Sudan, Harvard SEASGeneral Strong Polarization

    A recent discovery (circa 2008) in information theory called Polar Coding has led to a remarkable construction of error-correcting codes and decoding algorithms, resolving one of the fundamental algorithmic challenges in the field. The underlying phenomenon studies the “polarization” of a “bounded” martingale. A bounded martingale, X_0,…,X_t,…  is one where X_t in [0,1]. This martingale is said to polarize if Pr[lim_{t\to infty} X_t \in {0,1}] = 1. The questions of interest to the results in coding are the rate of convergence and proximity: Specifically, given epsilon and tau > 0 what is the smallest t after which it is the case that Pr[X_t in (tau,1-tau)] < epsilon? For the main theorem, it was crucial that t <= min{O(log(1/epsilon)), o(log(1/tau))}. We say that a martingale polarizes strongly if it satisfies this requirement. We give a simple local criterion on the evolution of the martingale that suffices for strong polarization. A consequence to coding theory is that a broad class of constructions of polar codes can be used to resolve the afore-mentioned algorithmic challenge.

    In this talk I will introduce the concepts of polarization and strong polarization.  Depending on the audience interest I can explain why this concept is useful to construct codes and decoding algorithms, or explain the local criteria that help establish strong polarization (and the proof of why it does so).

    Based on joint work with Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, and Atri Rudra.

    10-25-17

    *2:00-4:00pm*

    Subhabrata Sen (Microsoft and MIT)

    Noga Alon,(Tel Aviv University)

    Subhabrata Sen, “Partitioning sparse random graphs: connections with mean-field spin glasses”

    Abstract: The study of graph-partition problems such as Maxcut, max-bisection and min-bisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cut-sizes on sparse Erd\ ̋{o}s-R\'{e}nyi and random regular graphs.

    Based on joint work with Aukosh Jagannath.

    Noga Alon, “Random Cayley Graphs”

    Abstract: The study of random Cayley graphs of finite groups is related to the  investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given  group with a prescribed number of generators.  Several intriguing questions that remain open will be mentioned as well.

    11-1-17

    *2:00-4:00pm*

    Kay Kirkpatrick (Illinois)

    and

    Wei-Ming Wang (CNRS)

    Kay Kirkpatrick, Quantum groups, Free Araki-Woods Factors, and a Calculus for Moments

     Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to free Araki-Woods factors, and cases where we have surprisingly good rates of convergence. This is joint work with Michael Brannan. Time permitting, we’ll mention another quantum central limit theorem for Bose-Einstein condensation and work in progress.

    Wei-Min Wang, Quasi-periodic solutions to nonlinear PDE’s

    Abstract: We present a new approach to the existence of time quasi-periodic solutions to nonlinear PDE’s. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a Lagrangian approach to KAM theory, as suggested by J. Moser.

    11-8-17Elchanan MosselOptimal Gaussian Partitions.

    Abstract: How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution.

    The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory.

    I will survey the little we know about this problem and the major open problems in the area.

    11-10-17

    *12pm SC 232*

    Zhe Wang (NYU)A Driven Tagged Particle in One-dimensional Simple Exclusion Process

    Abstract: We study the long-time behavior of a driven tagged particle in a one-dimensional non-nearest- neighbor simple exclusion process.  We will discuss two scenarios when the tagged particle has a speed. Particularly, for the ASEP, the tagged particle can have a positive speed even when it has a drift with negative mean; for the SSEP with removals, we can compute the speed explicitly. We will characterize some nontrivial invariant measures of the environment process by using coupling arguments and color schemes.

    11-15-17

    *4:00-5:00pm*

    *G02*

    Daniel Sussman (BU)Multiple Network Inference: From Joint Embeddings to Graph Matching

    Abstract: Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiple-network framework remains a relatively under-explored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, face-to-face interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, we’ll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching.

    11-20-17

    *Monday

    12:00-1:00pm*

     Yue M. Lu

    (Harvard)

    Asymptotic Methods for High-Dimensional Inference: Precise Analysis, Fundamental Limits, and Optimal Designs
    Abstract: Extracting meaningful information from the large datasets being compiled by our society presents challenges and opportunities to signal and information processing research. On the one hand, many classical methods, and the assumptions they are based on, are simply not designed to handle the explosive growth of the dimensionality of the modern datasets. On the other hand, the increasing dimensionality offers many benefits: in particular, the very high-dimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will mention recent work on exploiting such blessings of dimensionality via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widely-used spectral method for nonconvex signal recoveries; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and mean-field limits to analyze nonconvex optimization algorithms for high-dimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with high-dimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices.
    11-29-17David Gamarink (MIT)(Arguably) Hard on Average Constraint Satisfaction Problems

    Abstract: Many combinatorial optimization problems defined on random instances such as random graphs, exhibit an apparent gap between the optimal value, which can be estimated by non-constructive means, and the best values achievable by fast (polynomial time) algorithms. Through a combined effort of mathematicians, computer scientists and statistical physicists, it became apparent that a potential and in some cases a provable obstruction for designing algorithms bridging this gap is an intricate geometry of nearly optimal solutions, in particular the presence of chaos and a certain Overlap Gap Property (OGP), which we will introduce in this talk. We will demonstrate how for many such problems, the onset of the OGP phase transition indeed nearly coincides with algorithmically hard regimes. Our examples will include the problem of finding a largest independent set of a graph, finding a largest cut in a random hypergrah, random NAE-K-SAT problem, the problem of finding a largest submatrix of a random matrix, and a high-dimensional sparse linear regression problem in statistics.

    Joint work with Wei-Kuo Chen, Quan Li, Dmitry Panchenko,  Mustazee Rahman, Madhu Sudan and Ilias Zadik.

    12-6-17

    *2:00-4:00pm*

    Philippe Rigollet (MIT)

    2-3 pm

    &

    Ankur Moitra (MIT)

    3-4 pm

    Philippe Rigollet (MIT), Exact Recovery in the Ising Block Model 

    Abstract: Over the past fifteen years, the problem of learning Ising models from independent samples has been of significant interest in the statistics, machine learning, and statistical physics communities. Much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models, primarily in the case where the interaction graph is sparse. In parallel, stochastic blockmodels have played a more and more preponderant role in community detection and clustering as an average case model for the minimum bisection model. In this talk, we introduce a new model, called Ising blockmodel for the community structure in an Ising model. It imposes a block structure on the interactions of a dense Ising model and can be viewed as a structured perturbation of the celebrated Curie-Weiss model. We show that interesting phase transitions arise in this model and leverage this probabilistic analysis to develop an algorithm based on semidefinite programming that recovers exactly the community structure when the sample size is large enough. We also prove that exact recovery of the block structure is actually impossible with fewer samples.

    This is joint work with Quentin Berthet (University of Cambridge) and Piyush Srivastava (Tata Institute).

    Ankur Moitra (MIT), A New Approach to Approximate Counting and Sampling 

    Abstract: Over the past sixty years, many remarkable connections have been made between statistical physics, probability, analysis and theoretical computer science through the study of approximate counting. While tight phase transitions are known for many problems with pairwise constraints, much less is known about problems with higher-order constraints.
    Here we introduce a new approach for approximately counting and sampling in bounded degree systems. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random. In our setting, the solution space is not even connected and we introduce alternatives to the usual Markov chain paradigm.

    12-14-17TBD
    DateNameTitle
    09-16-2015Scott Aaronson, MITBosonSampling and the Permanents of Gaussian Matrices
    09-23-2015Xin Sun, MITAlmost sure multi fractal spectrum of SLE
    09-28-2015Li-Cheng Tsai, StanfordKPZ equation limit of interacting particle systems
    09-30-2015Kyle Luh, YaleRandom Matrices: l1 Concentration and Dictionary Learning with Few Samples
    10-07-2015Martin Zirnbauer, Cologne/Simons CenterBott periodicity and the “Periodic Table” of topological insulators and superconductors
    10-14-2015Benjamin Schweinhart, Harvard CMSAUniversality Conjectures for Curvature Flow on Graphs
    10-21-2015Nicholas Cook, UCLA
    10-28-2015Vu-Lan Nguyen, Université Paris DiderotVariants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer
    11-04-2015Vadim Gorin, MITLargest eigenvalues in random matrix beta-ensembles: structures of the limit.
    11-18-2015Louis-Pierre Arguin, CUNYThe maximum of the characteristic polynomial of random unitary matrices 
    11-19-2015Nicholas Zygouras, Univ. of WarwickFrom disorder relevance to the 2d Stochastic Heat Equation
    11-25-2015ThanksgivingNo seminar
    12-02-2015Eero Saksman (Helsinki)The uniqueness of Gaussian multiplicative chaos revisited
    12-04-2015Guillaume Barraquand, ColumbiaRandom walks in Beta random environment
    01-27-2016Louigi Addario-Berry, McGillSlowdown of the front for branching Brownian motion with decay of mass
    02-03-2016Antti Knowles, ETH ZurichAn optimal rotational invariant estimator for general covariance matrices
    02-10-2016No Seminar this week
    02-17-2016Florent Bekerman, MITTransport Methods and Universality for beta-matrix models
    02-24-2016Aukosh Jagannath, Courant InstituteThe Parisi variational problem
    03-02-2016No Seminar this weekTwo next week
    03-09-2016Adam Marcus, PrincetonPolynomials and (finite) free probability
    03-11-2016Hao Shen, ColumbiaThe Sine-Gordon stochastic PDE and regularity structures
    03-16-2016Spring Recess
    03-23-2016Zeev Rudnick, Tel-Aviv and IASQuantum chaos, eigenvalue statistics and the Fibonacci sequence
    03-30-2016Nikolai Makarov, CaltechRandom normal matrices with hard edge spectrum
    04-06-2016Timo Seppalainen, WisconsinVariational formulas and Busemann functions for random paths in a random medium
    04-11-2016 (Science Center 530)Milton D. Jara, IMPAAround the strong KPZ universality conjecture
    04-20-2016Mark Rudelson, MichiganDelocalization of eigenvectors of random matrices
    04-27-2016Marek Biskup, UCLALocal limit theory for extreme values of 2D Discrete Gaussian Free Field
    05-04-2016No Talk
    05-11-2016 (2:30-3:30pm, Room G10)Laure Saint-Raymond, École Normale SupérieureFluctuating dynamics for a 2D rarified gas of hard disks
    06-01-2016Jun Yin, University of WisconsinGeneralized Circular Law
    06-08-2016Paul Bourgade, NYUExtremes of random matrices and log-correlated fields
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Aghil Alaee, Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form.

    The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    2/10/2022Tin Yau Tsang (UC Irvine)Title: Dihedral ridigity and mass

    Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

    2/17/2022Shiraz Minwalla
    (Tata Institute of Fundamental Research, Mumbai)
    Title: Black Hole dynamics at Large D

    Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

    2/24/2022Achilleas Porfyriadis
    (Harvard Black Hole Initiative)
    Title: Extreme Black Holes: Anabasis and Accidental Symmetry

    Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2) transformation properties of the spherically symmetric linear perturbations of
    AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of  AdS_2.

    3/10/2022David Fajman (University of Vienna)Title: The Einstein-flow on manifolds of negative curvature

    Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.
    3/21/2022Prof. Arick Shao (Queen Mary University of London)Title: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

    Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

    In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

    This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

    3/24/2022Qian Wang, University of OxfordTitle: Rough solutions of the $3$-D compressible Euler equations

    Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

    3/28/2022Emanuele Berti, Johns Hopkins UniversityTitle: Black Hole Spectroscopy

    Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

    4/7/2022CMSA General Relativity Conference
    4/14/2022Chao Liu, Huazhong University of Science and TechnologyTitle: Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4

    Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

    4/21/2022Jinhua Wang,
    Xiamen University
    Title: Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system

    Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

    4/28/2022Allen Fang, Sorbonne UniversityTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

    Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/10/2021

    (10:30am – 11:30am (Boston time)

    Philippe G. LeFloch, Sorbonne University and CNRSTitle: Asymptotic localization, massive fields, and gravitational singularities

    Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

    9/17/2021

    (10:30am – 11:30am (Boston time)

    Igor Rodnianski, Princeton UniversityTitle: Stable Big Bang formation for the Einstein equations

    Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

    9/24/2021

    (10:30am – 11:30am (Boston time)

    Alex LupsascaTitle: On the Observable Shape of Black Hole Photon Rings

    Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

    10/1/2021

    (10:30am – 11:30am (Boston time)

    Zhongshan An, University of ConnecticutTitle: Static vacuum extensions of Bartnik boundary data near flat domains

    Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

    10/8/2021

    (10:30am – 11:30am (Boston time)

    Xiaoning Wu, Chinese Academy of SciencesTitleCausality Comparison and Postive Mass

    Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

    10/15/2021

    (10:30am – 11:30am (Boston time)

    Jiong-Yue Li, Sun Yat-Sen UniversityTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations

    Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

    10/22/2021

    (11:00am – 12:30pm (Boston time)

    Roberto Emparan, University of BarcelonaTitleThe Large D Limit of Einstein’s Equations

    Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

    10/28/2021Jorge Santos, University of CambridgeTitle: The classical interior of charged black holes with AdS asymptotics

    Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

    11/4/2021
    at 10 am ET
    Elena Giorgi, Columbia UniversityTitle: The stability of charged black holes

    Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

    11/11/2021
    *9:30 am ET*
    Siyuan Ma, Sorbonne UniversityTitle: Sharp decay for Teukolsky equation in Kerr spacetimes

    Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

    11/19/2021

    (10:30–11:30 am ET)

    Nishanth Gudapati, Clark UniversityTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes

    Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

    12/2/2021Professor Geoffrey Comp
    ére, Université Libre de Bruxelles
    Title: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger

    Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

    12/16/2021Xinliang An, University of SingaporeTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation

    Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker: Yifan Wang (NYU)

    Title: Fusion Category Symmetries in Quantum Field Theory

    Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti

    ble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

  • Swampland Seminar
    10:30 am-12:00 pm
    12/01/2024

    During the 2021-22 academic year, the CMSA will be co-hosting a seminar on Swampland, with the Harvard Physics Department, organized by Miguel Montero, Cumrun Vafa, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend, please subscribe here.

    Talks will be posted on the Swampland Seminars YouTube channel. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/31/2022Rafael Álvarez-García (DESY Hamburg)Title: Membrane Limits in Quantum Gravity
    2/7/2022Du Pei (Harvard CMSA)Title: Holomorphic CFTs and topological modular forms

    Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

    2/28/2022 Tom Rudelius (UC, Berkeley)Title: Generalized Global Symmetries and the Weak Gravity Conjecture
    3/7/2022Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)Title: 4d strings at strong coupling
    3/21/2022Patrick Draper (Univ. of Illinois) and Alvaro Herraez (IPhT Saclay).Open Mic Discussion
    Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)
    3/28/2022Fernando Quevedo (Cambridge)Title: On renormalisation group induced moduli stabilisation and brane-antibrane inflation

    Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

    4/5/2022Simon Caron-Huot (McGill University) and Julio Parra (Caltech)Title: Causality constraints on corrections to Einstein gravity

    Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

    4/11/2022Timm Wrase and Eduardo Gonzalo (Lehigh)Title: Type IIB flux compactifications with $h^{1,1}=0$

    Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

    4/18/2022José Calderón (IFT Madrid)Open mic Swampland Discussion

    Topic: Cobordism

    5/9/2022Georges Obie (Harvard)Title: Inflation and light Dark Matter constraints from the Swampland

    Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/13/2021John Stout (Harvard)Title: Decoding Divergent Distances

    Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

    9/20/2021Manki Kim (MIT)Title: Small Cosmological Constants in String Theory

    Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

    9/27/2021Eran Palti (Ben Gurion)Title: Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

    Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

    10/18/2021Thomas Van Riet (KU Leuven)Title: The Festina Lente Bound

    Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for  phenomenology, both top-down and bottom-up.

    10/25/2021Joe Conlon (Oxford)Title: Exploring the Holographic Swampland

    Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

    11/01/2021Pieter Bomans (Princeton)Title: Bubble instability of mIIA on AdS_4 x S^6

    Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

    11/15/2021Nima Arkani-Hamed (IAS), and Gary Shiu (UW-Madison) This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be Swampland constraints, Unitarity and Causality. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.
    11/22/2021Thomas Grimm (Utrecht University)Title: Taming the Landscape

    Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

    11/29/2021Timm Wrase (Lehigh University)Title: Scale separated AdS vacua?

    Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

    12/6/2021Lars Aalsma (University of Wisconsin-Madison)Title: Extremal Black Hole Corrections from Iyer-Wald

    Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024

    Speaker: Michail Savvas, UT Austin

    Title: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds

    Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
    In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

    Organizer: Seminars
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    peaker: Ady Stern & David Mross (Weizmann)

    Speaker: Ady Stern & David Mross (Weizmann

    Title: The nu=5/2 enigma: Recent insights from theory and experiment

    Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:30 pm
    12/01/2024

     

    Nathanan Tantivasadakarn (Harvard)

    Video

    TitleHybrid Fracton Orders

    Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

    Based on 2102.09555 and 2106.03842

     

     

     

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024
    CMSA-QMMP-12.01.21-1544x2048

    Speaker: Daniel Harlow (MIT)

    Title: Symmetry in quantum field theory and quantum gravity 1

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

  • Quantum Matter
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-11.24.21-1583x2048

    Speaker: Shinsei Ryu (Princeton University)

    Title: Multipartitioning topological phases and quantum entanglement

    Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024

    Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
    In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    2/3/2021 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    4/23/2020 Condensed Matter Seminar

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    12/01/2024
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    10:30 am-11:30 am
    12/01/2024
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    12/01/2024
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    12/01/2024
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    12/01/2024
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    12/01/2024
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    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    3/25/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
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    3/27/2020 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    4/3/2020 General Relativity Seminar

    10:30 am-12:00 pm
    12/01/2024
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    12/01/2024
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    4/16/2020 Condensed Matter Seminar

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    10:30 am-12:00 pm
    12/01/2024
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    4/29/2020 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    4/29/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    12/01/2024
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    10:30 am-12:00 pm
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    10:30 am-12:00 pm
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    10:30 am-12:00 pm
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    12/01/2024
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    5/28/2020 Condensed Matter Seminar

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    10:30 am-12:00 pm
    12/01/2024
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    2/20/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • General Relativity Seminar
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    12/01/2024
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    10/9/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    9/10/18 Topology Seminar

    10:30 am-12:00 am
    12/01/2024-09/11/2018
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    4/1/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
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    4/24/2019 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    4/25/2019 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    4/26/2019 Topology

    10:30 am-12:40 pm
    12/01/2024
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    12/01/2024
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    9/13/2019 General Relativity

    10:30 am-11:30 am
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-11:30 am
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    10/2/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    10/11/2019 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    2/13/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    10/16/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    10/18/2019 General Relativity

    10:30 am-11:30 am
    12/01/2024
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    General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    10/30/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    11/1/2019 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    11/6/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    11/8/2019 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    11/13/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    11/27/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    12/11/2019 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/06/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • General Relativity Seminar
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    6/18/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    7/9/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/16/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/17/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 am
    12/01/2024-12/23/2020
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 am
    12/01/2024-01/29/2021
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker:  Jaume Gomis (Perimeter PI)

    Title: Global Anomalies on the Hilbert Space

    Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers” that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker:  Xiao-Gang Wen (MIT)

    Title: A solution to the chiral fermion problem

    Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

  • Quantum Matter
    10:30 am-12:00 am
    12/01/2024-02/25/2021
  • Quantum Matter
    10:30 am-12:00 am
    12/01/2024-02/26/2021
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/7/2020 Math Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 am
    12/01/2024-03/18/2021

    Speaker: Silviu Pufu (Princeton University)

    Title: Exact symmetries and threshold states in two-dimensional models for QCD

    Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of confinement in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    5/12/2021 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/9/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/15/2020 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    4/15/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    7/16/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    unnamed-3-600x338

    In the 2020-2021 academic year, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom.

    Cuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator, several fascinating phases emerge, including a d-wave superconductor, a pseudo-gap metal, and strange metal. After intensive studies from experimental, theoretical, and numerical communities for more than three decades, remarkable progress has been made, but basic questions remain:

    1. What is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling, spin fluctuations, or resonating-valence-bonds?
    2. How do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters, or do we need an unconventional picture involving fractionalization?
    3. Is the strange metal at optimal doping associated with a quantum critical point? And if so, what is the driving force of this phase transition?

    The cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics, such as quantum spin liquids, topological order, and non-Fermi liquids. In the coming years, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series, we hope to accelerate this process by bringing together deeper conversations between experimental, theoretical, and numerical experts with different backgrounds and perspectives.

    The Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar.

    Seminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard).

    Scientific program advisors: Professor Subir Sachdev (Harvard), Professor Patrick Lee (MIT).

    In order to learn how to attend this series, please fill out this form.

    For more information, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu)

    Spring 2022

    April 20, 2022 | 11:30 – 1:00 pm ET

    Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)

    Title: Superconductivity in infinite-layer nickelates

    Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.


    February 3, 2022 | 11:30 – 1:00 pm ET

    Lu Li (U Michigan)

    Title: Quantum Oscillations of Electrical Resistivity in an Insulator

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    2020 – 2021

    September 2, 2020 | 10:30am ET

    Sachdev
    Subir Sachdev (Harvard)

    TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

    Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
    describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

    Video

    September 23, 2020 | 10:30am ET

    Sachdev
    Subir Sachdev (Harvard)

    Title: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II

    Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

    Video

    September 24, 2020 | 12:00pm ET

    hqdefault
    Inna Vishik (University of California, Davis)

    Title: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video

    October 15, 2020 | 10:30am ET

    unnamed
    Louis Taillefer (Université de Sherbrooke)

    TitleNew signatures of the pseudogap phase of cuprate superconductors

    Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

    Video

    October 28, 2020 | 10:30am ET

    lee_patrick
    Patrick Lee (MIT)

    Title: The not-so-normal normal state of underdoped Cuprate

    Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

    Video

    November 6, 2020 |12:30pm ET

    Shen
    Zhi-Xun Shen (Stanford University)

    Title: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors

    Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
    Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
    magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
    (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
    experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

    [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
    [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
    [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
    [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
    [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
    [6] A. Lanzara et al., Nature 412, 510 (2001)
    [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
    [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
    [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
    [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
    [11] A.G. Loeser et al., Science 273, 325 (1996)
    [12] S. Chen et al., Science, 366, 6469 (2019)
    [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
    [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
    [15] Yu He et al., Science, 362, 62 (Oct. 2018)
    [16] Z. Chen, Y. Wang et al., preprint, 2020

    Video

    November 12, 2020 |10:30am ET

    Chandra-Varma
    Chandra Varma (Visting Professor, University of California, Berkeley.
    Emeritus Distinguished Professor, University of California, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:
    1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
    2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
    3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
    4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting,
    (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
    (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
    (iii) Problems.Video

    November 18, 2020 |10:30am ET

    download
    Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

    Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

    Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

    Video

    November 19, 2020 |10:30am ET

    Fradkin
    Eduardo Fradkin (University of Illinois at Urbana-Champaign)

    Title: Pair Density Waves and Intertwined Orders in High Tc Superconductors

    Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

    Video

    November 25, 2020 |10:30am ET

    Si-1coborc
    Qimiao Si (Rice University)

    Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

    Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

    December 2, 2020 |10:30am ET

    Chubukov
    Andrey Chubukov (University of Minnesota)

    Title: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

    Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

    December 9, 2020 |10:30am ET

    Hsieh
    David Hsieh (Caltech)

    Title:  Signatures of anomalous symmetry breaking in the cuprates  

    Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
    [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

    [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516

    December 16, 2020 |10:30am ET

    weng
    Zheng-Yu Weng (Tsinghua University)

    TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

    Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

    December 17, 2020 |10:30am ET

    60cf9077a3c10b1135231e866012bda8
    Steven Kivelson (Stanford University)

    Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

    Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.

    January 20, 2021 |10:30am ET

    Devereaux
    Thomas Peter Devereaux (Stanford University)

    Title:  Numerical investigations of models of the cuprates

    Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

    I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

    February 3, 2021 |10:30am ET

    viewphoto
    Philip Phillips (University of Illinois Urbana-Champaign)

    Title: Beyond BCS: An Exact Model for Superconductivity and Mottness

    Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
    [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

    February 10, 2021 |10:30am ET

    todadri_senthil
    Senthil Todadri (MIT)

    Title: Strange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

    Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
    [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.07896
    [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

    April 1, 2021 |9:00am ET

    weng
    Naoto Nagaosa (University of Tokyo)

    TitleApplied physics of high-Tc theories

    Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

    April 22, 2021 |10:30am ET

    lee
    Dung-Hai Lee (UC Berkeley)

    Title: “Non-abelian bosonization in two and three spatial dimensions and some applications”

    Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.

    May 12, 2021 |10:30am ET

    weng
    André-Marie Tremblay (Université de Sherbrooke)

    Title: A unified theoretical perspective on the cuprate phase diagram

    Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

    August 11, 2021 |10:30am ET

    image
    Piers Coleman (Rutgers)

    Title: Order Fractionalization*

    Abstract: I will discuss the interplay of spin fractionalization with broken
    symmetry. When a spin fractionalizes into a fermion, the resulting particle
    can hybridize or pair with the mobile electrons to develop a new kind of
    fractional order parameter. The concept of “order fractionalization” enables
    us to extend the concept of off-diagonal order to encompass the formation of
    such order parameters with fractional quantum numbers, such as spinorial
    order[1].
    A beautiful illustration of this phenomenon is provided by a model
    which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This
    model explicitly exhibits order fractionalization and is expected to undergo a
    discrete Ising phase transition at finite temperature into an
    order-fractionalized phase with gapless Majorana excitations.
    The broader implications of these considerations for Quantum
    Materials and Quantum Field Theory will be discussed.
    Work done in collaboration with Yashar Komijani, Anna Toth and Alexei
    Tsvelik.
    [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018).
    [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

    September 15, 2021 |10:30am ET

    0049_7858_headshot-scaled-aspect-ratio-420-334-2-scaled-840x668-c-default
    Liang Fu (MIT)

    Title: Three-particle mechanism for pairing and superconductivity

    Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

    [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
    [2] V. Crepel and L. Fu, arXiv:2103.12060
    [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

    September 29, 2021 |11:30am ET (special time)

    Ong
    Nai Phuan Ong (Princeton University)

    Title:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al., Nature Physics 17, 915 (2021).Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

    Date TBA |10:30am ET

    image_normal
    Suchitra Sebastian (University of Cambridge)

    Title: TBA

    Date TBA |10:30am ET

    hoffman
    Jenny Hoffman (Harvard University)

    Title: TBA

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/14/2020 Mathematical Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/21/2020 Math-Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    9/23/2020 Strongly Correlated Quantum Materials Series

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/1/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/05/2020 Math Physics Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/25/2020 Strongly Correlated Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/19/2020 Math Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    10/28/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/9/2020 Math-Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/12/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/18/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/19/20 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-12.02.21-1544x2048-1

    Speaker: Daniel Harlow (MIT)

    Title: Symmetry in quantum field theory and quantum gravity 2

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/2/2020 Math-Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Xueyang Song (MIT)

    Title: Phase transitions out of quantum Hall states in moire TMD bilayers

    Abstract: Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\’e Transition Metal Dichalcogenide (TMD) bilayers, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth.  At filling -2/3, we describe a direct transition between the FQAH state and a Charge Density Wave (CDW) insulator. The critical theory resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by  Barkeshli and McGreevy.   Crucially we show that translation symmetry alone is enough to enable a second order CFL-FL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order.  A striking signature is a universal jump of resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFL-FL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist.  We also present a critical theory for the CFL to FL transition at filling -3/4.  Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-04.06.2022-1583x2048-1

    Youtube Video

     

    Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024
    CMSA QMMP 02.17.23

    Quantum Matter Seminar

    Speaker: Rahul Sahay (Harvard)

    Title: Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics

    Abstract: While many-body quantum systems can in principle host exotic quantum spin liquid (QSL) states, realizing them as ground states in experiments can be prohibitively difficult. In this talk, we show how non-equilibrium dynamics can provide a streamlined route toward creating QSLs. In particular, we show how a simple Hamiltonian parameter sweep can dynamically project out condensed anyons from a family of initial product states (e.g. dynamically “un-Higgs”), yielding a QSL-like state. We christen such states “quantum spin lakes” which, while not thermodynamically large QSLs, enable their study in NISQ-era quantum simulators. Indeed, we show that this mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. Time permitting, we will discuss how our theory motivates a tree tensor network-based numerical tool—reliant on our theory—that quantitatively reproduces the experimental data two orders of magnitude faster than conventional brute-force simulation methods. Finally, we will highlight that even spin liquid states that are unstable in equilibrium—namely, 2 + 1D U(1) spin liquid states—can be robustly prepared by non-equilibrium dynamics.

     

    https://www.youtube.com/watch?v=ECT9nozk2SY&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=15

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Professor Harvey Reall (University of Cambridge) 

    Title: The second law of black hole mechanics in effective field theory

    Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs.

    Video
  • Quantum Matter
    10:30 am-12:30 pm
    12/01/2024

    Speaker: Kenichi Konishi (UNIPI.IT)

    Title: Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: Recent developments

    Abstract: After many years of efforts, still very little is known today about the physics of strongly-coupled chiral gauge theories in four dimensions, in spite of an important role they might play in the physics of fundamental interactions beyond the standard SU(3)xSU(2)xU(1) model. This is in stark contrast with the vectorlike gauge theories for which we have many solid results, thanks to some exact theorems, to the lattice simulation studies, to the Seiberg-Witten exact solution of N=2 supersymmetric gauge theories, and last, but not the least, to the real-world strong-interaction phenomenology and experimental tests of Quantum Chromodynamics.

    The purpose of this seminar is to discuss the results of our recent efforts to improve the understanding of the strongly-coupled chiral gauge theories. Among the main tools of analysis are the consideration of anomalies. We use both the conventional ’t Hooft anomaly-matching ideas, and new, more stringent constraints coming from the generalized anomalies involving some higher-form symmetries. Also, the so-called strong anomalies, little considered in the context of chiral gage theories, are found to carry significant implications.

    As the playground we study several classes of SU(N) gauge theories, the so-called Bars-Yankielowicz models, the generalized Georgi-Glashow models, as well as a few other simple theories with the fermions in complex, anomaly-free representations of the color SU(N).

    Color-flavor-locked dynamical Higgs phase and dynamical Abelianization, emerge, among others, as two particularly interesting possible phases the system can flow into in the infrared, depending on the matter fermion content of the model.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Sheldon Katz, UIUC

    Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants

    Abstract:  A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3.  These X are nodal CY threefolds which do not admit a projective small resolution.  B-model techniques can be applied to compute GV invariants up to g \le 32.  This raises the question: what is the geometric meaning of these invariants?

    Evidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by Kuznetsov.  One of these moduli stacks is a stacky small resolution X’ of X itself.  This leads to another geometric interpretation of the invariants as being associated with moduli of sheaves on X’ twisted by a Brauer class.  Geometric computations based on these working definitions always agree with the B-model computations.

    This talk is based on joint work with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe.

     

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Speaker: Seth Koren (University of Chicago)

    Title: Baryon Minus Lepton Number BF Theory for the Cosmological Lithium Problem

    Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+  3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
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    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024

    Topological Quantum Matter Seminar

    Speaker: Amanda Young, UIUC

    Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential

    Abstract: Haldane pseudopotentials were first introduced as Hamiltonian models for the fractional quantum Hall effect, and it has been long expected that they should exhibit the characteristic properties of this exotic phase of matter, including a spectral gap above the ground state energy. We will discuss recent work that verified this gap conjecture for a truncated version of the 1/3-filled Haldane pseudopotential in the cylinder geometry. Numerical evidence suggested that for open boundary conditions the gap of the truncated model closes as the cylinder radius converges to zero and that this closure is due to the presence of edge modes; in contrast, for periodic boundary conditions, the gap remains robustly order one in the same radius limit. The standard scheme for applying spectral gap estimating techniques to the model with periodic boundary conditions, though, produces a lower bound on the bulk gap that still reflects the energy of the edge modes. To obtain an estimate on the bulk gap that reflects its true behavior, a new gap estimating strategy was developed. By customizing the spectral gap method to key invariant subspaces of the Hamiltonian, we are able to successfully avoid the edge states and produce a more accurate lower bound on the bulk gap. In this talk, we discuss this invariant subspace strategy for proving bulk gaps in the presence of edge states. This is based off joint work with S. Warzel.

     

     

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-04.28.22-1583x2048

    Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    Superconductivity in infinite-layer nickelates

    10:30 am-1:00 pm
    12/01/2024
    CMSA-Strongly-Correlated-Quantum-Materials-and-High-Temperature-Superconductors-04.20.21-1583x2048

    Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Thorsten Schimannek (Utrecht University)

    Title: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants

    Abstract: The physics of M-theory and Type IIA strings on a projective nodal CY 3-folds is determined by the geometry of a small resolution, even if the latter is not Kähler. We will demonstrate this explicitly in the context of a family of Calabi-Yau double covers of P^3. Using conifold transitions, we prove that the exceptional curves in any small resolution are torsion while M-theory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary Gopakumar-Vafa invariants, that is associated to the singular Calabi-Yau and captures the enumerative geometry of the non-Kähler resolutions. We further argue that twisted circle compactifications of the 5d theory are dual to IIA compactifications on the nodal CY 3-fold with a flat but topologically non-trivial B-field. As a result, the torsion refined invariants are encoded in the topological string partition functions with different choices for the global topology of a flat B-field.

    The talk is based on 2108.09311, 2212.08655 (with S. Katz, A. Klemm, and E. Sharpe) and 2307.00047 (with S. Katz).

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: An Huang (Brandeis)

    Pre-talk Speaker: TBA: 10:00-10:30 am

    Title: A p-adic Laplacian on the Tate curve

    Abstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.30.2022-1583x2048-1

    Youtube Video

     

    Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy.  This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport.  We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation.  Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem.  The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories.  Our techniques generalize to other RG flow equations beyond Polchinski’s.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 09.15.22

    General Relativity Seminar
    Title: The Gregory-Laflamme instability of black strings revisited
     
    Abstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string.
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA GR Seminar 04.27.23

    General Relativity Seminar

    Speaker: Philippe G. LeFloch, Sorbonne University and CNRS

    Title: The localized seed-to-solution method for the Einstein constraints

    Abstract: I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set, we define a “localized seed-to-solution” map, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly, as we prove it, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis, we discover the notion of ‘asymptotic modulators’, as we call them, or “correctors” to the standard ADM invariants.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.23.2022-1583x2048

    Youtube Video

     

    Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.16.2022-1544x2048-1

    Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv  2201.00903.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker: Petr Hořava (UC Berkeley)

    Title: Topological Quantum Gravity and the Ricci Flow – Part I

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-02.16.2022-1544x2048

    Speaker: Petr Hořava (UC Berkeley)

    Title: Topological Quantum Gravity and the Ricci Flow – Part I

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Jonah Herzog-Arbeitman, Princeton University

    Title: Exact Results in Flat Band Hubbard Models

    Abstract: Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multi-orbital case: the mean-field theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and low-energy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution reveals the importance of quantum geometry in escaping (some of) BCS phenomenology within a tractable and nontrivial strong coupling theory.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.09.2022-1544x2048-1

    Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Pre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am

    Speaker: Kai Xu (CMSA)

    Title: Motivic decomposition of moduli space from brane dynamics

    Abstract: Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.02.2022-1544x2048

    Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Ho Tat Lam, MIT

    Title: Dipolar and modulated symmetry protected topological phases

    Abstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-02.24.2022-1544x2048-1

    Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Maksym Fedorchuk (Boston College)

    Title: CM-minimizers and standard models of Fano fibrations over curves

    Abstract: A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of K-stable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CM-minimizers without base change. In answering this question, we arrive at a theory of Koll\’ar stability for fibrations over one-dimensional bases, and standard models of Fano fibrations. I will explain the joint work with Hamid Abban and Igor Krylov in which we show that the CM-minimizers for del Pezzo fibrations are Corti’s standard models and related work in progress on quartic threefold hypersurfaces.

     

  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Ho Tat Lam (MIT)

    Title: Non-invertible Symmetry Enforced Gaplessness

    Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

     

    https://www.youtube.com/watch?v=A-47aZ4HS1k&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=16

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: David Favero, University of Minnesota

    Title: Gauged Linear Sigma Models and Cohomological Field Theories

    Abstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker.  Gauged Linear Sigma Models (GLSMs)  serve as a means of interpolating between Kahler geometry and singularity theory.  In enumerative geometry, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.   In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs.  Furthermore, we proved that these invariants form a Cohomological Field Theory.   In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss the construction of these general invariants.  Briefly, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”.  This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Professor Oscar Dias (University of Southampton)

    Title: Strong Cosmic Censorship

    Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally, I will discuss some possibilities (quantum effects, non-smooth initial data,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024

    Topological Quantum Matter Seminar

    Speaker: Shenghan Jiang, Kavli Institute for Theoretical Sciences UCAS

    Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States

    Abstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has been established that topological insulator phases persist as stable phases. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wavefunctions for numerical simulations is highly desirable.
    In this talk, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions, we write down tensor equations, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems.

     

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Naqing Xie (Fudan University)

    Title: Gravitational Wave, Angular Momentum, and Supertranslation Ambiguity
    Abstract: The supertranslation ambiguity of angular momentum is a long-standing and conceptually important issue in general relativity. Recently, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However, in the compact binary coalescence community, supertranslation ambiguity is often ignored. We have shown that, in the linearised theory of gravitational wave, the new angular momentum coincides with the classical definition at the quadrupole level. This talk is based on a recent joint work with Xiaokai He and Xiaoning Wu.
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar

    General Relativity Seminar

    Speaker: Nikolaos Athanasiou
    Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
    Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Sergei Dubovsky (New York University)
    Title: Love Symmetry of Black Holes
    Abstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2,ℝ) symmetry in the suitably defined near zone approximation. We show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2,ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2,ℝ) representations. It is this highest-weight property that forces the static Love numbers to vanish. We show that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. The Love symmetry also exhibits a peculiar UV/IR mixing.
  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024
    CMSA QMMP 02.03.23

    Quantum Matter Seminar

    Speaker: Han Yan (Rice U)

    Title: Fracton orders in hyperbolic space and its excitations with fractal mobility

    Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.

    Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

     

    https://www.youtube.com/watch?v=ekfKNCKzZyE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=17

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA GR Seminar 09.29.22

    General Relativity Seminar

    Speaker: Marcelo Disconzi, Vanderbilt University

    Title: Generalrelativistic viscous fluids
    Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.
  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Andrew Harder, Lehigh University

    Pre-talk Speaker: TBA: 10:00-10:30 am

    Title: Deformations of Landau-Ginzburg models and their fibers

    Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-12.08.21-1544x2048

    Speaker: Fei Yan (Rutgers)

    Title: Defects, link invariants and exact WKB

    Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Pengyu Le (BIMSA)

    Title: Asymptotic geometry of null hypersurface in Schwarzschild spacetime and null Penrose inequality

    Abstract: Null Penrose inequality is an important case of the well-known Penrose inequality on a null hypersurface. It conjectures the relation between the area of the outmost marginally trapped surface and the Bondi mass at null infinity. Following the proposal of Christodoulou and Sauter, we employ the perturbation method to study the asymptotic geometry of null hypersurfaces at null infinity in a perturbed vacuum Schwarzshild spacetime. We explain how to apply this perturbation theory to prove null Penrose inequality on a nearly spherically symmetric null hypersurface in a perturbed vacuum Schwarzschild spacetime.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Uri Kol, CMSA

    Title: Duality in Einstein’s Gravity

    Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-02-2016 Random Matrix & Probability Theory Seminar

    10:32 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    10:36 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-07-16 Mathematical Physics Seminar

    10:38 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar

    Special Seminar
    11-04-16 Special Seminar

    10:42 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    10:43 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-09-2016 Random Matrix & Probability Theory Seminar

    10:44 am
    12/01/2024

    No additional detail for this event.

  • Program
    10:44 am-11:04 am
    12/01/2024-06/12/2021
    CMSA-2-600x338

    The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

    Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

    In this course, we will start with an introduction to computer programming, algorithm, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

    The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

    This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard related perks (such as a place to live if you are in Boston over the summer.)

    However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

    If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited to 10 people, so don’t wait too long to apply.

  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Quantum Matter Seminar

    10:45 am-12:45 pm
    12/01/2024
  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Birational geometry

    10:45 am-12:15 pm
    12/01/2024
    Lecture_Shokurov-pdf

    Vyacheslav V. Shokurov (Johns Hopkins University)

    Title: Birational geometry

    Abstract: About main achievements in birational geometry during the last fifty years.

    Talk chair: Caucher Birkar

    Video

  • Seminars
    10:46 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    10:56 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    10:57 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-14-16 Mathematical Physics Seminar

    10:58 am
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Rodrigo Silva, University of Maryland

    Title: Quantization of causal diamonds in 2+1 dimensional gravity

    Abstract: We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with a fixed boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that has the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required — in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham’s group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

     

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Black Hole Formation

    11:00 am-12:00 pm
    12/01/2024
    Lecture_Bieri-pdf

    Lydia Bieri (University of Michigan)

    Title: Black Hole Formation

    Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the dynamical mathematical structures of the Einstein equations. Black holes are related to the presence of trapped surfaces in the spacetime manifold. Christodoulou proved that in the regime of pure general relativity and for arbitrarily dispersed initial data, trapped surfaces form through the focusing of gravitational waves provided the incoming energy is large enough in a precisely defined way. The proof combines new ideas from geometric analysis and nonlinear partial differential equations as well as it introduces new methods to solve large data problems. These methods have many applications beyond general relativity. D. Christodoulou’s result was generalized in various directions by many authors. It launched mathematical activities going into multiple fields in mathematics and physics. In this talk, we will discuss the mathematical framework of the above question. Then we will outline the main ideas of Christodoulou’s result and its generalizations, show relations to other questions and give an overview of implications in other fields.

    Video

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Michael Freedman

    11:00 am-12:30 pm
    12/01/2024
    20bottfeatureplain-1

    20bottfeatureplain
    On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.

    This will be the third annual lecture series held in honor of Raoul Bott.

    Lecture 1
    October 4th, 11:00am (Boston time)
    Title: The Universe from a single Particle

    Abstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.

    Video

    Lecture 2
    October 5th, 11:00am (Boston time)
    Title: Controlled Mather Thurston Theorems.

    Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374  

    Video

     

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Shuaijie Qian (Harvard CMSA)

    Title: Some non-concave dynamic optimization problems in finance

    Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present our recent work on some non-concave dynamic optimization problems, where the concavification principle may not hold and the resulting value function is indeed non-concave.

    The first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation, where the average tax basis and the average mining cost serves as an approximation, respectively. This approximation results in a non-concave value function, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover, the penalty method still works and converges to the value function.

    The second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints, which makes the concavification principle invalid, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous, we introduce a new definition of viscosity solution, prove the corresponding comparison principle, and show that a monotone, stable, and consistent finite difference scheme converges to the solution of the utility maximization problem.

     

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Mauricio Romo

    Title: Quantum trace and length conjecture for hyperbolic knot

    Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Diandian Wang(Harvard University)

    Title: Pole skipping, quasinormal modes, shockwaves and their connection to chaos

    Abstract: A chaotic quantum system can be studied using the out-of-time-order correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function — that seems to also know things: things like the Lyapunov exponent and the butterfly velocity, which are important quantifiers of the OTOC. Then I will talk about a systematic way of deriving pole-skipping conditions for general holographic CFTs dual to classical bulk theories and how to use this framework to derive a few interesting statements including: (1) theories with higher spins generally violate the chaos bound; (2) the butterfly velocity calculated using pole skipping agrees with that calculated using shockwaves for arbitrary higher-derivative gravity coupled to ordinary matter; (3) shockwaves are related to a special type of quasinormal modes. As we will see, the techniques are entirely classically gravitational, which I will go through with a certain level of details.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Maria Rodriguez (Utah)

    Title: Tidal Squeezing of Black Holes

    Abstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Chethan Krishnan (IISc Bangalore)

    Title: A Smooth Horizon without a Smooth Horizon

    Abstract: I will talk about some work that is about to appear, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls, fuzzballs, Type I algebras,…)

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Alejandro Poveda

    Title: Compactness and Anticompactness Principles in Set Theory

    Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.

  • Seminars

    Seminars Colloquia & Seminar
    3/30/2020 Math Physics Seminar

    11:00 am-12:00 pm
    12/01/2024
  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    17 Oxford St, Cambridge, MA 02138

    Swampland Seminar

    Location: Jefferson Physical Laboratory, Seminar room J356

    Speaker: Markus Dierigl (LMU Munich)

    Title: IIB Explored – Dualities, Bordisms, and the Swampland

    Abstract: In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries, we discuss which defects need to be included to break them completely. Interestingly, we find many backgrounds that are well-known in the F-theory literature, such as [p,q]-7-branes, non-Higgsable clusters, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications, which I will discuss in more detail.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Damian van de Heisteeg

    Title: Light states in the interior of CY moduli spaces

    Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Lionel Mason (Oxford)

    Title: Geometry at Strong coupling for amplitudes/Wilson loops

    Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024

    General Relativity Seminar

    Speaker: Andras Vasy (Stanford)

    Title: The Feynman propagator and self-adjointness

    Abstract: In this talk I will discuss the Feynman and anti-Feynman inverses for wave operators on certain Lorentzian manifolds; these are two inverses which from a microlocal analysis perspective are more natural than the standard causal (advanced/retarded) ones. For instance, for the spectral family of the wave operator, these are the natural inverses when the spectral parameter is non-real. Indeed, I will explain that these connect to the self-adjointness of the wave operator, and the positivity properties that follow.

     

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Fernando Marchesano (IFT Madrid)

    Title: EFT strings and emergence

    Abstract: We revisit the Emergence Proposal in 4d N=2 vector multiplet sectors that arise from  type II string Calabi-Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA compactifications, where EFT strings arise from NS5-branes wrapping internal four-cycles, and consider a set of infinite-distance moduli-space limits that can be classified in terms of a scaling weight w=1,2,3. It has been shown before how one-loop threshold effects of an infinite tower of BPS particles made up of D2/D0-branes generate the asymptotic behaviour of  the gauge kinetic functions along limits with $w=3$. We extend this result to w=2 limits, by taking into account D2-brane multi-wrapping numbers. In w=1 limits the leading tower involves EFT string oscillations, and one can reproduce the behaviour of both weakly and strongly-coupled U(1)’s independently on whether the EFT string is critical or not, by assuming that charged modes dominate the light spectrum.

  • Seminars

    Seminars Colloquia & Seminar
    5/8/2020 General Relativity Seminar

    11:00 am
    12/01/2024
  • Active Matter Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter

    Active Matter Seminar
    Speaker: Shenshen Wang, UCLA
    Title:  Limit and potential of adaptive immunity
    Abstract: The adaptive immune system is able to learn from past experiences to better fit an
    unforeseen future. This is made possible by a diverse and dynamic repertoire of cells
    expressing unique antigen receptors and capable of rapid Darwinian evolution within an
    individual. However, naturally occurring immune responses exhibit limits in efficacy,
    speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical
    frameworks we developed to (1) explore functional impacts of non-equilibrium antigen
    recognition, and (2) identify conditions under which natural selection acting local in time
    can find adaptable solutions favorable in the long run, through exploiting environmental
    variations and functional constraints.
  • Seminars

    Seminars Colloquia & Seminar
    5/15/2020 General Relativity Seminar

    11:00 am
    12/01/2024
  • Probability Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA Probability Seminar 03.09.23

    Probability Seminar

    Speaker: Jean-Christophe Mourrat (ENS Lyon)

    Title: On the free energy of spin glasses with multiple types

    Abstract: In the simplest spin-glass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups, which we can visualize as forming two layers, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there, and some partial progress.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Member Seminar
    Speaker: Shai Chester
    Title: Derivation of AdS/CFT for Vector Models

    Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories, and at finite temperature.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Ben McKenna

    Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance

    Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Jake McNamara (Caltech)
    Title: Parity and Cobordism
    Abstract: The swampland cobordism conjecture provides a convenient way to discuss conserved charges associated with the topology of spacetime. However, much of the power of the cobordism conjecture comes from a mathematical black box: the Adams spectral sequence. In this talk, I will give physical meaning to this black box through a concrete example: domain walls arising from the spontaneously breaking of parity symmetry, which arise in particle physics in Nelson-Barr models. I will argue that parity domain walls are exactly stable, and interpret this stability as the result of an unusual type of gauge symmetry that can only occur in gravitational theories.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-16-2016 Random Matrix & Probability Theory Seminar

    11:00 am
    12/01/2024

    No additional detail for this event.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Jie Wang

    Title: Kahler geometry in twisted materials

    Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making many-body states less stable in flatbands.

    In this talk, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform, but still exhibit exact properties such as model wavefunctions, density algebra, exact parent Hamiltonians. I will discuss both the theory of ideal flatband, its experimental realization in Dirac materials as well as implications.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar 

    Speaker: Zhigang Yao

    Title: Principal flow, sub-manifold and boundary

    Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold, a manifold passing through the center of the data, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find, use and interpret the principal sub-manifold, by which a principal boundary can be further defined for data sets on manifolds.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Swampland Seminar
    Speaker: Aasmund Folkestad (MIT)
    Title: The Penrose Inequality as a Constraint on Low Energy Quantum Gravity
    Abstract: In this talk, I argue that the Penrose inequality (PI) can be used to constrain low energy theories compatible AdS/CFT, and possibly also quantum gravity in flat space. Focusing on AdS/CFT, it is shown that the PI can be violated for minimally coupled scalar fields, and I produce exclusion plots on couplings that respect the PI. I also present numerical evidence that top-down scalar theories and supersymmetric theories respect the PI. Finally, similar to the Breitenlohner-Freedman bound, I give a necessary condition for the stability AdS that constrains coupling constants (beyond the scalar mass).
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/28/2020 Mathematical Physics Seminar

    11:00 am-12:00 pm
    12/01/2024
  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: David Andriot (Annecy, LAPTH)

    Title: String theory scalar potentials and their critical points

    Abstract: Positive scalar potentials in string effective theories could provide an origin to Dark Energy, responsible for the accelerated expansion of our universe today or during inflation. It is thus crucial to characterize these scalar potentials, namely their slope, their critical points (de Sitter solutions) and the associated stability, as also advocated by the Swampland Program. We will present such characterizations. Going further, we will also discuss negative scalar potentials, and make related observations on anti-de Sitter solutions, in particular on a new mass bound, as well as comments on scale separation.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Paul-Konstantin Oehlmann(Northeastern)

    Title: Anomalies of Discrete Gauge Symmetries and their Cancellation in 6D F-theory

    Abstract: We consider 6D SUGRAs with a discrete gauge group G, engineered via F-theory compactifications on genus-one fibered threefolds. We argue that group G suffers from Dai-Freed anomalies that can be canceled via a discrete Green-Schwarz mechanism. We comment on the ambiguity to assign this GS term in the 7D Anomaly theory which leads to choices that are not all compatible with F-theory.

    In F-theory we then deduce this Anomaly coefficient explicitly by computing the elliptic genera of the non-critical strings that couple to the 6D two-form fields: Their 2D worldsheet theories inherits a G Flavor symmetries whose t’Hooft anomaly cancels the 6D Dai-Freed anomaly in the bulk via inflow. This talk is based on work in preparation together with Markus Dierigl and Thorsten Schimmanek.

  • CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
    11:00 am-8:45 pm
    12/01/2024-05/09/2021
    Summer,Warm,Sun,Light,Forest,Aerial,View

    This workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom

    The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data.

    This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

    The first half of the workshop will feature talks aimed at graduate students, newcomers, and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications.

    For the discussions, we are soliciting open problems in mathematical theory and applications of shape analysis. You are encouraged to post problems by sending an email to geometricproblemsfrg@gmail.com.

    We invite junior researchers to present a short talk in the workshop. The session will be held on Friday, May 7th or Saturday, May 8th at 4pm and are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks, the organizers will review the submissions and let you know if you have been selected. If you are interested please send your title and abstract to tianqi@cmsa.fas.harvard.edu by the end of May 2nd.

     

    Organizers:

    • David Glickenstein, University of Arizona
    • Joel Hass, University of California, Davis
    • Patrice Koehl, University of California, Davis
    • Feng Luo, Rutgers University, New Brunswick
    • Tianqi Wu, Harvard University
    • Shing-Tung Yau, Harvard University

    Featured lectures:

    • Christopher Bishop, Stony Brook
    • Keenan Crane, Carnegie Mellon

    Speakers include:

    • Miri Ben-Chen, Technion – Israel Institute of Technology
    • Alexander Bobenko, Technische Universität Berlin, Germany
    • Ulrike Buecking, Free University, Germany
    • Nadav Dym, Duke University
    • Ivan Izmestiev, Vienna University of Technology
    • Yanwen Luo, Rutgers
    • Stephan Tillmann, The University of Sydney
    • Max Wardetzky, University of Goettingen
    • Xu Xu, Wuhan University
  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics

    Title: Quantum magnet chains and Kashiwara crystals

    Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva, Joel Kamnitzer, and Alex Weekes.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Swampland Seminar
    Speaker: Samir Mathur (Ohio State)
    Title: The story of the information paradox
    Abstract:  In 1975 Hawking argued that black hole evaporation would lead to a loss of unitarity in quantum theory.  The small corrections theorem made Hawking’s argument into a precise statement: if semiclassical physics hold to leading order in any gently curved region of spacetime, then there can be no resolution to the paradox. In string theory, whenever people have been able to construct microstates explicutly, the states turned out to be horizon sized objects (fuzzballs) with no horizon; such a structure of microstates resolves the information paradox since their is no pair creation at a vacuum horizon. There have been a set of parallel attempts to resolve the paradox (with ideas involving wormholes, islands etc) where the horizon is smooth in some leading approximation. An analysis of such models however indicated that in each case the exact quantum gravity theory would either have to be nonunitary or to have dynamics at infinity that is conflict with usual low energy physics in the lab.
  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Swampland Seminar 01.30.23

    Swampland Seminar

    Speaker: Ignatios Antoniadis (LPTHE Paris)
    Title: Swampland program, extra dimensions and supersymmetry breaking
    Abstract: I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalisation of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.
  • Colloquium
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 04.03.2023

    Colloquium

    Speaker: Luca Iliesiu, Stanford

    Title: Black hole microstate counting from the gravitational path integral

    Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Swampland Seminar 04.10.23

    Swampland Seminar

    Speaker: Seung-Joo Lee (IBS Daejeon)

    Title: Swampland bounds on the abelian gauge sectors

    Abstract: In this talk we will derive various bounds on the 0-form and the 1-form abelian gauge sectors of gravitational effective theories in 6 dimensions with minimal supersymmetry. We will start by considering 6-dimensional F-theory vacua with at least one tensor multiplets, to bound for them the number of the (0-form) U(1) gauge factors as well as the cyclic orders of the 1-form discrete gauge factors. While the two abelian gauge sectors may look rather independent, we will observe that both are heavily constrained by the solitonic heterotic strings present in the spectrum, which provide a common intuition for the derived bounds. Building upon the heterotic intuition, we will also try extending the arena to address analogous bounds for all F-theory vacua in 6 dimensions and even beyond. If time permits, several applications and future directions of research will be discussed at the end of the talk.

  • Math Science Literature Lecture Series
    11:00 am-12:30 pm
    12/01/2024

    Sergiu Klainerman (Princeton University)

    Title: Nonlinear stability of Kerr black holes for small angular momentum

    Abstract: According to a well-known conjecture,  initial data sets,  for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon)   which approaches  (globally)  a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $|a|/m $ sufficiently small. The work, ArXiv:2104.11857v1,  also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr,  with Szeftel and Elena Giorgi,  which I will also describe.

    Talk chair: Lydia Bieri 

    Video

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin

    Title: Explicit Ramsey Graphs and Two Source Extractors

    Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    Jefferson Hall Room 368, 17 Oxford St, Cambridge, MA 02138

    Swampland Seminar

    Speaker: Thomas Grimm (Utrecht U.)

    Title: The Tameness of Quantum Field Theories

    Abstract: Tameness is a generalized notion of finiteness that is restricting the geometric complexity of sets and functions. The underlying mathematical foundation lies in tame geometry, which is built from o-minimal structures introduced in mathematical logic. In this talk I formalize the connection between quantum field theories and logical structures and argue that the tameness of a quantum field theory relies on its UV definition. I quantify our expectations on the tameness of effective theories that can be coupled to quantum gravity and on CFTs. In particular, I present tameness conjectures about CFT observables and propose universal constraints that render spaces of CFTs to be tame sets. I then highlight the relation of these conjectures to other swampland conjectures, e.g., by arguing that the tameness of CFT observables restricts having parametrical gaps in the operator spectrum.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Swampland Seminar 03.27.23

    Swampland Seminar

    Speaker: Valerio De Luca (UPenn)

    Title: Recent developments on the tidal Love numbers of black holes

    Abstract: Tidal Love numbers describe the deformability of compact objects under the presence of external tidal perturbations, and are found to be exactly zero for black holes in pure General Relativity. This property is however fragile, since they receive corrections from higher-order derivative terms in the theory. We show that the tidal deformability of neutral black holes is constrained by the Weak Gravity Conjecture.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Alvaro Herraez (Saclay)

    Title: The Emergence Proposal in Quantum Gravity and the Species Scale

    Abstract: The Emergence Proposal claims that in Quantum Gravity the kinetic terms of the fields in the IR emerge from integrating out (infinite) towers of particles up to the QG cutoff. After introducing this proposal in the context of the Swampland Program, I will explain why it is natural to identify this QG cutoff with the Species Scale, motivating it by direct computation in the presence of the relevant towers. Then, I will present evidence for this proposal by directly studying how it is realized in different string theory setups, where the kinetic terms of scalars, p-forms and even scalar potentials can be shown to emerge after integrating out such towers.

     

     

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024

    General Relativity Seminar

    Speaker: Daniel Kolb (Max Planck Institute)

    Title: Quasi-Local Mass in a Binary Black Hole Merger

    Abstract: One of the major open problems in classical general relativity is how one should define the mass of a finite region of space. In this talk, we will investigate a promising definition proposed by Wang and Yau in 2009. A closed 2-surface bounding the region of interest is embedded isometrically into Minkowski space. The mass is then calculated by comparing the extrinsic geometries. The Wang-Yau mass has many desirable properties, but it has previously not been calculated for surfaces in dynamical spacetimes. To remedy this, we will discuss how the Wang-Yau mass can be computed in practice and extend the definition to surfaces important in black hole dynamics: their quasi-local horizons. Finally, we look at how this mass behaves in a merger of black holes.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: David Kubiznak (Charles University)

    Title: Remarkable symmetries of rotating black holes

    Abstract: It is well known that the Kerr geometry admits a non-trivial Killing tensor and its ‘square root’ known as the Killing-Yano tensor. These two objects stand behind Carter’s constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object — the principal Killing-Yano tensor — generates a tower of explicit and hidden symmetries responsible for integrability of geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes described by the `magic square’ version of the Lense-Thirring solution, giving rise to a geometrically preferred spacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.

  • General Relativity Seminar
  • General Relativity Seminar
  • General Relativity Seminar
  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Leo Stein (Mississippi)

    Title: Resolving memory in numerical relativity, and fixing BMS frames for modeling

    Abstract: Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE), and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames, we can extract well-defined remnant quantities, perform precision ringdown modeling, and build complete surrogate waveform models that capture memory effects.

  • Seminars

    Seminars Colloquia & Seminar
    3-2-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    12/01/2024-03/03/2018
  • Seminars

    Seminars Colloquia & Seminar
    2-16-2018 Mirror Symmetry Seminar

    11:00 am
    12/01/2024
  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge MA 02138

    General Relativity Seminar

    Speaker: David Fajman (Vienna)

    Title: Fluid stabilization in slowly expanding cosmological spacetime

    Abstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.

     

    Talk via Zoom, broadcast in G10

     

  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    4-13-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    12/01/2024-04/14/2018
  • Seminars

    Seminars Colloquia & Seminar
    10/19/2018 Mirror Symmetry Seminar

    11:00 am-11:00 pm
    12/01/2024
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    02-09-2018 Mirror Symmetry Seminar

    11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2-23-2018 Mirror Symmetry Seminar

    11:00 am
    12/01/2024
  • Member Seminar
    11:01 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-21-16 Mathematical Physics Seminar

    11:02 am
    12/01/2024

    No additional detail for this event.

  • Algebraic Geometry in String Theory Seminar
    11:02 am-12:02 pm
    12/01/2024

    Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    11:03 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:03 am-11:04 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:04 am
    12/01/2024

    The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

    Spring 2020

    DateSpeakerTitle/Abstract
    1/29/2020David Yang (Harvard)

    Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

    2/5/2020Scott Aaronson (UT Austin)

    Video

    Title: Gentle Measurement of Quantum States and Differential Privacy

    Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
    of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

    Based on joint work with Guy Rothblum (arXiv:1904.08747)

    2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

    Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

    2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

    Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

    2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

    Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
    3/4/2020

    4:45 – 5:45pm

    Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

    Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

    In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

    3/11/2020

    Postponed

    Jose Scheinkman

    (Columbia)

    This colloquium will be rescheduled at a later date. 

    Title: Menu Costs and the Volatility of Inflation

    Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

    3/12/2020

    4:00 – 5:00pm

    Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

    Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

    Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

    Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

    3/25/2020Cancelled
    4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

    Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

    Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

    4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

    Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

    Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
    explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
    fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

    4/15/2020
    Lars Andersson (Max-Planck Institute for Gravitational Physics)
    This meeting will be taking place virtually on Zoom.

    Title: Stability of spacetimes with supersymmetric compactifications

    Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

    4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow in high codimension

    Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

    4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

    Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

    5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

    Title: Energy, Mass and Radiation in General Spacetimes

    Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

    5/13/2020Mikhail Lukin (Harvard)

    Video

    This meeting will be taking place virtually on Zoom.

    Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

    Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

    5/20/2020This meeting will be taking place virtually on Zoom.

    Fall 2019

    DateSpeakerTitle/Abstract
    9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

    Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

    ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

    ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

    ◦ The natural Nullstellensatz are falling into place.

    The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

    9/25/2019Pavel Etingof (MIT)

     

    Title: Double affine Hecke algebras

    Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

    10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

    Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

    10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

     

    Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

     

    Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

    John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

    Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

    Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

    Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

    10/16/2019Aram Harrow (MIT)

    Video

    Title: Monogamy of entanglement and convex geometry

    Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

    10/23/2019No talk
    10/30/2019Nima Arkani-Hamed (IAS)

    Video

    Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
    11/6/2019Kevin Costello (Perimeter Institute)

    Video

    Title: A unified perspective on integrability

     

    Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

    11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

    Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

    11/20/2019Xi Yin (Harvard)

    Video

    Title: An Introduction to the Non-Perturbative Bootstrap

    Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

    11/25/2019

    Monday

    Madhu Sudan (Harvard)
    Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

    In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

    Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

    12/4/2019Xiao-Gang Wen (MIT)
    Video
    Title: Emergence of graviton-like excitations from a lattice model

    Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

    2018-2019

    DateSpeakerTitle/Abstract
    9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

    Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

    10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

    Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

    10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

    Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

    10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

    Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

    In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

    10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

    Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

    11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

    Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

    11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

    Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

    11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

    Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

    12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

    Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

    Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

    12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

    Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

    1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

    Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

    2/7/2019

    *Thursday*

    Ulrich Mueller (Princeton)Title: Inference for the Mean

    Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

    2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

    Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

    2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

    Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

    [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

    2/27/2019

    2:30pm

    Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

    Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

    3/6/2019

    2:30pm

    Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

    Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

    3/13/2019

    5:15pm

    Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

    Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

    3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

    Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

    3/27/2019

    5:15pm

    Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    4/3/2019

    2:30pm

    Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

    Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

    4/10/2019

    2:30pm

    Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

    Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

    Paper

    Online Appendix

    4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

    Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

    .

    [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

    [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

    [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

    4/24/2019Shengwu Li (Harvard)
    Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
    Date…………SpeakerTitle
    02-09-2018 *Friday       Fan Chung

    (UCSD)

    Sequences: random, structured or something in between

    There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

    testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

    02-14-2018Zhengwei Liu

    (Harvard Physics)

    A new program on quantum subgroups

    Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

    02-21-2018Don Rubin

    (Harvard)

    Essential concepts of causal inference — a remarkable history

    Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

    02-26-2018 *MondayTom Hou

    (Caltech)

    Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

    Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

    03-07-2018Richard Kenyon

    (Brown)

    Harmonic functions and the chromatic polynomial

    Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

    03-14-2018
    03-21-2018
    03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

    Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

    We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
    [Based on joint work with Song Mei and Phan-Minh Nguyen]

    03-30-2018
    04-04-2018Ramesh Narayan 

    (Harvard)

    Black Holes and Naked Singularities

    Abstract: Black Hole solutions in General Relativity contain Event Horizons and
    Singularities. Astrophysicists have discovered two populations of
    black hole candidates in the Universe: stellar-mass objects with
    masses in the range 5 to 30 solar masses, and supermassive objects
    with masses in the range million to several billion solar
    masses. There is considerable evidence that these objects have Event
    Horizons. It thus appears that astronomical black hole candidates are
    true Black Holes. Direct evidence for Singularities is much harder to
    obtain since, at least in the case of Black Holes, the Singularities
    are hidden inside the Event Horizon. However, General Relativity also
    permits Naked Singularities which are visible to external
    observers. Toy Naked Singularity models have been constructed, and
    some observational features of accretion flows in these spacetimes
    have been worked out.

    04-11-2018Pablo Parrilo

    (MIT)

    Graph Structure in Polynomial Systems: Chordal Networks

    Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

    04-18-2018Washington Taylor

    (MIT)

    On the fibration structure of known Calabi-Yau threefolds

    Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

    04-25-2018 Xi Yin

    (Harvard)

    How we can learn what we need to know about M-theory

    Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

    05-02-2018
    05-09-2018

    2016-2017

    DateNameTitle/Abstract
    01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

    Title: Spectral graph theory of cognitive maps

    Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

    02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

    Sean_Eddy

    Title: Biological sequence homology searches: the future of deciphering the past 

    Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

    02-08-17Matthew Headrick, Brandeis University

    matthew_headrick

    Title: Quantum entanglement, classical gravity, and convex programming: New connections

    Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

    02-15-17Masahito Yamazaki, IMPU

    Masahito Yamazaki

     Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

    Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

    Video

    02-22-17Steven Rayan, University of Saskatchewan

    Title: Higgs bundles and the Hitchin system

    Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

    Video

    03-01-17Jun Liu, Harvard University

    Jun liu

    Title: Expansion of biological pathways by integrative Genomics

    Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

    Based on the joint work with Yang Li and the Vamsi Mootha lab.

    Video

    03-08-17Gabor Lippner, Northeastern University

    ---

    Title: Evolution of cooperation in structured populations

    Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

    In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
    03-15-17 Spring Break: No session
    03-22-17Gunther Uhlmann, University of Washington

    guntherUhlman

    Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
    waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
    The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
    We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
    03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

    Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

    NOTE: This talk will begin at 4:00pm

    04-05-17Gongjie Li, Harvard University

    GongjieLi

    Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

    Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

    Video

    04-12-17Shlomo Razamat, Israel Institute of Technology

    ShlomoRazamat

    Title: Complicated four-dimensional physics and simple mathematics

    Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

    Video

    04-19-17Cumrun Vafa, Harvard University

    CumrunVafa

    Title: String Swampland

    Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

    04-27-17Mehran Kardar, MIT

    MehranKardar

    Title: Levitation by Casimir forces in and out of equilibrium

    Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

    Note: This talk will begin at 3:00pm

    05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

    Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
    similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
    have led to substantial progress in protein structural and functional
    predictions.

    Note:  This talk will begin at 4:00pm

    05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

    Abstract: A deterministic or random system with a conservation law is often used to
    approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

    Note: This talk will be held in the Science Center, Room 507

    05-10-17
    05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

    Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

    05-24-17 NO COLLOQUIUM
    05-31-17Peter Michor, University of Vienna

     Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

    Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

    DateNameTitle
    09-09-16

    Bong Lian, Brandeis

    portrait

    Title: Riemann-Hilbert Problem and Period Integrals

    Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

    09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

    Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

    09-21-16Prof. L. Mahadevan, Harvard SEAS

    Mahadevan_200x300

    Title: “Morphogenesis: Biology, Physics and Mathematics”

    Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

    09-28-16Hong Liu, MIT

    liu_hong

    Title: A new theory of fluctuating hydrodynamics

    Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

    We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

    Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

    10-05-16

    Alexander LogunovTel-Aviv University

    alex

    Title: Zeroes of harmonic functions and Laplace eigenfunctions

     Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

    10-12-16 Conan Nai Chung Leung, CUHK

    conan_profile

    Title:  Coisotropic A-branes and their SYZ transform

    Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

    10-19-16Vaughan Jones, UC Berkeley

    vj6

    Title: Are the Thompson groups any good as a model for Diff(S^1)?

    Abstract. The Thompson groups are by definition groups of piecewise linear
    diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
    be conjugated to a group of smooth diffeomorphisms. That’s the good news.
    The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
    procedure analogous to the constructions of the central extension of Diff(S^1)?
    I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

     10-26-16

    Henry Cohn, Microsoft

    ????????????????????????????????????

    Sums of squares, correlation functions, and exceptional geometric structures

    Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

    11-02-16

    Christian Borgs, Microsoft

    Borgs

    Title:  Graphon processes and limits of   sparse graph sequences

    Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

    In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

    11-09-16

    TIME CHANGE: 4PM

    Norden E. HuangNational Central University, (Taiwan)

    member1_clip_image003

    Title: On Holo-Hilbert Spectral Analysis

    Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

    11-16-16Tristan Collins, Harvard University

    image

    TIME CHANGE: 3:30PM

    Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

    Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

    11-22-16 TUESDAY

    TIME CHANGE: 4-5PM

    Xiangfeng Gu, Stonybrook

    Title: Differential Geometric Methods for Engineering Applications

    Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

    11-30-16

    TIME CHANGE: 4:20PM

    Sharad Ramanathan, Harvard MCB & SEAS

    Ramanathan.Sharad_200x300

    Title: Finding co-ordinate systems to monitor the development of mammalian embryos
     12-07-16

    Valentino Tosatti, Northwestern

    Title: Metric limits of hyperkahler manifolds

    Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

     12-14-16

    2015-2016

    DateNameTitle
    09-02-2015Madhu SudanRobust low-degree testing
    09-09-2015Mithat Unsal
    What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
    09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
    09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
    09-30-2015Leslie ValiantHolographic Algorithms
    10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
    10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
    10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
    10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
    11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
    11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
    11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
    11-25-2015ThanksgivingNo seminar
    12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
    12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
    01-27-2016Conan LeungSome modern aspects of Morse theory 
    02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
    02-10-2016Chun Peng Wang
    02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
    02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
    03-02-2016Lydia BieriMathematical General Relativity
    03-09-2016Piotr ChruscielThe mathematics of gravitation
    03-16-2016Spring BreakNo Talk
    03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
    03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
    04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
    04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
    04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
    04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
    04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
    05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
    05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
  • Colloquium
    11:05 am-11:06 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:07 am-11:08 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:08 am-11:09 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-22-2016 Random Matrix & Probability Theory Seminar

    11:12 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-07-2016 Random Matrix & Probability Theory Seminar

    11:16 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-05-16 Mathematical Physics Seminar

    11:17 am
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
    11:19 am
    12/01/2024-11/14/2019
    Dynamics-12-x-18-683x1024

    On November 12-14, 2019 the CMSA will be hosting a workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Biological cells are the fundamental units of life, and predictive modeling of cellular dynamics is essential for understanding a myriad of biological processes and functions. Rapid advances in technologies have made it possible for biologists to measure many variables and outputs from complex molecular and cellular networks with various inputs and environmental conditions. However, such advances are far ahead of the development of mathematical theory, models and methods needed to secure a deep understanding of how high-level robust behaviors emerge from the interactions in complex structures, especially in dynamic and stochastic environments. This workshop will bring together mathematicians and biological scientists involved in developing mathematical theories and methods for understanding, predicting and controlling dynamic behavior of molecular and cellular networks. Particular emphasis will be placed on efforts directed towards discovering underlying biological principles that govern function, adaptation and evolution, and on the development of associated mathematical theories.

    Organizers: Jeremy Gunawardena (Harvard) and Ruth Williams (University of California, San Diego)

    A limited amount of funding is available to help in defraying the travel costs of early career researchers, women, and underrepresented minorities, participating the workshop. Early career researchers are researchers who received their Ph.D. in 2014 or later, or who are Ph.D. students expecting to complete their Ph.D. by the end of 2020.

    To apply, please send a CV, a statement of why you wish to attend, and, if you are a grad student, a letter of support from your advisor to Sarah LaBauve at slabauve@math.harvard.edu

    All applications received by 5pm, EDT, October 28, 2019 will receive full consideration.

    Speakers: 

    Videos from the workshop can be found in the Youtube playlist.

  • Seminars
    11:21 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:21 am-11:22 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-14-2016 Random Matrix & Probability Theory Seminar

    11:22 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    11:24 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    11:25 am
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Learning from health data in the million genome era
    11:26 am
    12/01/2024

    On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

    Speakers: 

    • Heidi Rehm, Ph.D.
      Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
    • Saiju Pyarajan, Ph.D.
      Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
    • Tianxi Cai, Sci.D
      John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
    • Susan Redline, M.D., M.P.H
      Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
    • Avinash Sahu, Ph.D.
      Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
    • Peter J. Park, Ph.D.
      Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
    • David Roberson
      Community Engagement Manager, Seven Bridges

    Registration & Schedule

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    9/29/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    4/20/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    12/15/2020 Computer Science for Math

    11:30 am-12:30 pm
    12/01/2024
  • Quantum Matter
    11:30 am-1:00 pm
    12/01/2024

    Quantum Matter Seminar

    Speaker: Daniel S. Freed (U Texas)

    Title: Topological symmetry in field theory

    Abstract: Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries,” “higher symmetries,” “noninvertible symmetries,” etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory. This is joint work with Constantin Teleman and Greg Moore.

     

    https://www.youtube.com/watch?v=y5uHfqVGunA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=26

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Quantum Field Theory Seminar

    11:30 am-12:00 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/24/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    Quantum Oscillations of Electrical Resistivity in an Insulator

    11:30 am-1:00 pm
    12/01/2024
    CMSA-QMMP-02.03.2022

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    9/22/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    9/15/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    10/6/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    Rank-Based Independence Testing in Near Linear Time

    11:30 am-12:30 pm
    12/01/2024

    Speaker: Chaim Even-Zohar (Alan Turing Institute, London)

    Title: Rank-Based Independence Testing in Near Linear Time

    Abstract: In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.
    We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.

    Joint work with Calvin Leng.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    10/20/2020 Computer Science for Math

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    5/11/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/3/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    4/6/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    10/27/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    01-30-2017 Mathematical Physics Seminar

    11:30 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/23/2020 Mathematical Physics Seminar

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/17/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/2/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/23/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    3/2/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Quantum Matter
    11:30 am-1:00 pm
    12/01/2024

    Speaker: Lu Li (U Michigan)

    Title: Quantum Oscillations of Electrical Resistivity in an Insulator

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/10/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    3/9/2021 Computer Science for Mathematicians

    11:30 am-12:30 am
    12/01/2024-03/10/2021
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    3/23/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/9/2021 Computer Science for Math

    11:30 am-12:30 pm
    12/01/2024
  • Seminars
    11:32 am
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    11:33 am-1:33 pm
    12/01/2024

    Title: Symmetry types in QFT and the CRT theorem

    Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-06-2017 Mathematical Physics Seminar

    11:33 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-13-2017, Mathematical Physics Seminar

    11:34 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    11:35 am
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
    11:36 am
    12/01/2024-10/30/2019
    Space-Time-poster-5

    As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

    Everyone is welcome to attend the lectures.

    The master class workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Photos of the event

    Organizers:

  • Member Seminar
    11:37 am
    12/01/2024

    Hansol Hong, Harvard

    Title: Homological Mirror Functors

    Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

  • Colloquium
    11:39 am-11:40 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:40 am-11:41 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    11:42 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:43 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:45 am
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    11:47 am-1:47 pm
    12/01/2024

    Title: Applications of instantons, sphalerons and instanton-dyons in QCD

    Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

    Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

  • Quantum Matter
    11:48 am-1:48 pm
    12/01/2024

    Title: Oscillations in the thermal conductivity of a spin liquid*

    Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

    *Czajka et al., Nature Physics 17, 915 (2021).

    Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

  • Quantum Matter
    11:49 am-1:49 pm
    12/01/2024

    Title: Line defects in CFTs: Renormalization group flows and semiclassical limits

    Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

  • Seminars

    Seminars Colloquia & Seminar
    10/24/2019 Quantum Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/21/2019 Condensed Matter seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/5/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/12/2019 Quantum Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/7/2019 Quantum Matter Seminar

    11:50 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/31/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • CMSA EVENT: Quantum Information Workshop
    11:52 am-11:53 am
    12/01/2024
    Asset-6-600x338

    Please note, this workshop has been postponed to a later date. Details will be posted to this page when they are available.

    The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

    The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

    More information to follow.

  • Quantum Matter
    11:54 am-1:54 pm
    12/01/2024

    Title: A tour of categorical symmetry

    Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-12-2017 Random Matrix & Probability Theory Seminar

    11:56 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:56 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-22-2017 Random Matrix & Probability Theory Seminar

    11:58 am
    12/01/2024

    No additional detail for this event.

  • Algebraic Geometry in String Theory Seminar
    11:58 am-12:58 pm
    12/01/2024

    Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.

  • Colloquium
    11:58 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    11:59 am
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4/1/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Chuck Doran

    Title: Modularity of Landau-Ginzburg Models

    Abstract:  Fano varieties are the basic building blocks of algebraic varieties.  Smooth Fano varieties have been classified in dimensions one (the projective line), two (del Pezzo surfaces), and three (Mori-Mukai classification).  What does Mirror Symmetry have to say about such classifications?  By studying the Landau-Ginzburg models mirror to smooth Fano threefolds we can transform the Mori-Mukai classification into an effective uniruledness result for moduli spaces of certain K3 and abelian surfaces.  This is joint work with Andrew Harder, Ludmil Katzarkov, Mikhail Ovcharenko, and Victor Przjalkowski (arXiv:2307.15607).

     

     

  • Seminars

    Seminars Colloquia & Seminar
    3/02/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/19/2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/9/2020 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Samy Jelassi

    Title: An introduction to mixture of experts in deep learning

    Abstract: Scale has opened new frontiers in natural language processing – but at a high cost. Mixture-of-Experts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By doing so, the parameter count is decoupled from the compute per example leading to very large, but efficient models. In this talk, I will review the concept of mixture of experts, provide a basic description of the Switch Transformers model, characterize some of their behaviors and conclude by highlighting some open problems in the field. This talk is mainly based on the following papers: https://arxiv.org/pdf/2101.03961.pdfhttps://arxiv.org/pdf/2209.01667.pdf .

  • Seminars

    Seminars Colloquia & Seminar
    1/28/2018 Mathematical Physics Seminar

    12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/24/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/22/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Mike Douglas

    Title: AI and Theorem Proving

    Abstract: We survey interactive theorem proving and the Lean theorem prover, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.

  • Seminars

    Seminars Colloquia & Seminar
    3/23/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/4/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Zi Yang Kang

    Title: Deformations of Landau-Ginzburg models and their fibers

    Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

  • Seminars

    Seminars Colloquia & Seminar
    4/25/2019 Fluid Dynamics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/25/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Kai Xu (CMSA)

    Title: Moduli of vector bundles on curve and semiorthogonal decomposition

    Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived Θ-stratification.

     

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    9/24/2020 Strongly Correlated Quantum Materials

    12:00 pm-1:30 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Juven Wang

    Title: Categorical Symmetry of the Standard Model from Gravitational Anomaly

    Abstract: In the Standard Model, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.147652204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ16 respectively. For this construction, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, or the 3d boundary topological order of 4d ℤTF4-time-reversal symmetric topological superconductor [2302.14862].

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Benjamin McKenna

    Title: Random matrices and large deviations

    Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson.

     

  • Seminars

    Seminars Colloquia & Seminar
    3/4/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Daniel Kapec (CMSA)

    Title: Black Holes as Quantum Systems

    Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles.

     

  • Seminars

    Seminars Colloquia & Seminar
    12/18/2019 Quantum Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/25/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/8/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/11/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Max Wiesner

    Title: Quantum Gravity constraints beyond asymptotic regimes

    Abstract: Not every effective field theory that is consistent in the absence of gravity can be completed to a consistent theory of quantum gravity. The goal of the Swampland program is to find general criteria that distinguish effective field theories, that can be obtained as a low-energy approximation of quantum gravity, from those that are inconsistent in the presence of gravity. These criteria are oftentimes motivated by patterns observed in explicit compactifications of perturbative string theory and have passed many non-trivial tests in asymptotic regions of the field space such as, e.g., weak coupling limits. Still, the Swampland criteria should equally apply to effective theories that do not arise in asymptotic regions of the field space of string theory compactifications. In this talk I will summarize some of my recent works that studies the interior of regions of the field space of string theory in the context of the Swampland program.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/3/2020 Math-Physics

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/2/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/3/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/4/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/13/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024-04/22/2020
  • Seminars

    Seminars Colloquia & Seminar
    4/15/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/10/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/29/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Sunghyuk Park

    Title: Quantum UV-IR map and curve counts in skeins

    Abstract: Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong.

    In this talk, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules, using skein-valued curve counts of Ekholm and Shende.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/29/2018 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Farzan Vafa

    Title: Dynamics of active nematic defects on cones

    Abstract: In the first part of the talk, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge, which in analogy to electrostatics, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle, which is determined by charged defects screening the effective apex charge: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk, we investigate the dynamics of an active nematic on a cone, and via simulations find long-time circular orbits of either one or two flank defects, with transitions between these states mediated by the apex via defect absorption, emission, or defect pair creation.

  • Probability Seminar
    12:00 pm-1:00 pm
    12/01/2024

    Probability Seminar

    Speaker: Jun Yin (UCLA)

    Title: A random matrix model towards the quantum chaos transition conjecture

    Abstract: The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE.

    This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of the same phenomenon, shedding light on the intricacies of this long-standing conjecture.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/5/2018 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Dan Kapec

    Title: Hints of Flat Space Holography

    Abstract: Despite our detailed understanding of holography in Anti-de Sitter space, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space, bulk gravitons produce a boundary stress tensor, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Changji Xu

    Title: Spectral gap and two-point functions in spin glasses

    Abstract: Many have worked on spin glass models over the past 50 years, including physicists, mathematicians, and computers. A question that arises is whether computers yield dependable simulation results. In this talk, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.

  • Algebraic Geometry in String Theory Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Oliver Schlotterer (Uppsala University)

    Title: Modular graph forms and iterated integrals in string amplitudes

    Abstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful cross-talk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress in clarifying their connection with modular graph forms.

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Faidra Monachou

    Title: Optimal Dynamic Allocation: Simplicity through Information Design

    Abstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that, when the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the information disclosed about each object is an interval containing the object quality, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases, these intervals become coarser, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality, in terms of the Lorenz order.

  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Freid Tong

    Title: On complete Calabi-Yau metrics and some related Monge-Ampere equations

    Abstract: We will give a basic introduction to constructions for complete Calabi-Yau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of Tian-Yau in the 90s and have attracted a lot of attention in recent years. I will discuss some joint work with B. Guo and T. Collins on a singular version of such a construction, as well as some ongoing work with Prof. Yau on some related boundary value problems.

     

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Jue Liu

    Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds

    Abstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass, we define a new quasilocal mass using the Hamilton method. With this definition, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture, that is under what conditions there will be a static extension to the given Bartnik data.

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Barak Weiss  

    Title: New bounds on lattice covering volumes, and nearly uniform covers

    Abstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK, such that L+rK = R^n, normalized by the covolume of L. Pairs (L,K) with small covering volume correspond to efficient coverings of space by translates of K, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE, Hebrew University) and Oded Regev (CS, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.

  • Math Science Literature Lecture Series
    12:00 pm-1:30 pm
    12/01/2024

    Ralph Cohen (Stanford University)

    Title: Immersions of manifolds and homotopy theory

    Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest dimension Euclidean space into which every n-manifold embeds or immerses. The embedding question is still very much unsolved, and the immersion question was solved in the 1980’s. I will discuss the homotopy theoretic techniques involved in the solution of this problem, and contributions in the 60’s, 70’s and 80’s of Massey, Brown, Peterson, and myself. I will also discuss questions regarding the best embedding and immersion dimensions of specific manifolds, such has projective spaces. Finally, I will end by discussing more modern approaches to studying spaces of embeddings due to Goodwillie, Weiss, and others. This talk will be geared toward a general mathematical audience.

    Talk chair: Michael Hopkins

    Video

  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Quantum Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/30/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars
    12:00 pm-1:30 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Puskar Mondal

    Title: Recent progress on coupled Einstein-Yang-Mills dynamics

    Abstract: I will discuss my recent work with prof. S.T. Yau on Einstein-Yang-Mills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gauge-gravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a double-null framework play an important role. I’ll sketch how the special structure of the Einstein and Yang-Mills nonlinearities play a crucial role in obtaining the stability result of non-expanding spacetimes in particular AF spacetimes.

  • Seminars

    Seminars Colloquia & Seminar
    9/16/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/20/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/6/2019 Math Physics

    12:00 pm-1:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/2/2020 Strongly Correlated Quantum Materials

    12:00 pm-1:30 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-5-2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/27/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Puskar Mondal (CMSA)

    Title: On the Breakdown of Einstein’s Gravity

    Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-26-2018 Math Physics Seminar

    12:00 pm-1:30 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/3/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Aghil Alaee

    Title: A quasi-local mass in general relativity

    Abstract: One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime, which can include a star, black hole, or galaxy. We define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition.  Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau.

     

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Chuck Doran

    Title: Motivic Geometry of Two-Loop Feynman Integrals

    Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/19/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Gabriel Wong

    Title: Quantum information and extended topological quantum field theory

    Abstract: Recently, ideas from quantum information theory have played an important role in condensed matter and quantum gravity research. Most of these applications focus on the entanglement structure of quantum states, and the computation of entanglement measures such as entanglement entropy has been an essential part of the story. In this talk, we will address some subtleties that arise when trying to define entanglement entropy in quantum field theory and quantum gravity. In particular, we will explain why extended topological field theory provides a useful framework to define and compute entanglement entropy in a continuous system. Time permitting, we will explain some recent applications of these ideas in low dimensional quantum gravity and to topological string theory.

     

     

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-2-2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/28/2019 Math Physics

    12:00 pm-1:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/26/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Aghil Alaee

    Title: Toroidal Positive Mass Theorem

    Abstract: In this talk, we review the positive mass conjecture in general relativity and prove a toroidal version of this conjecture in an asymptotically hyperbolic setting.

  • Seminars

    Seminars Colloquia & Seminar
    10/7/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Iacopo Brivio (CMSA)

    Title: Extension of pluricanonical forms in positive and mixed characteristics

    Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{times m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring.

     

  • Seminars

    Seminars Colloquia & Seminar
    9/9/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Michael Simkin

    Title: Randomized algorithms in combinatorics

    Abstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples:

    1. Enumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other?
    2. Constructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In 1973 Erdos conjectured that there exist STSs with arbitrary large girth (informally, no small set of vertices spans many triples). I will discuss the use of randomized algorithms to prove this conjecture. Joint work with Kwan, Sah, and Sawhney.
    3. Thresholds in random graphs and hypergraphs: I will discuss how randomized algorithms can be combined with the recent resolution of the Kahn–Kalai conjecture to determine thresholds in random (hyper) graph theory. Joint work with Pham, Sah, and Sawhney.
  • Seminars

    Seminars Colloquia & Seminar
    3/25/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Quantum Matter
    12:00 pm-1:30 pm
    12/01/2024
  • Seminars
    12:00 pm-1:00 pm
    12/01/2024
    Raymarching and the Thurston Geometries

    On Wednesday, December 16 at 12:00 p.m. EST, WAM and CMSA will host a holiday seminar featuring Sabetta Matsumoto, Georgia Institute of Technology who will present The Inside View: Raymarching and the Thurston Geometries.

    The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon, Henry Segerman and Steve Trettel.

    Visit the event page

    Register to access this event here

     

  • Quantum Matter
    12:00 pm-1:00 pm
    12/01/2024

    Speaker: Eric Sharpe (Virginia Tech)

    Title: Anomaly resolution via decomposition

    Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

  • Quantum Matter
    12:00 pm-1:00 pm
    12/01/2024

    Speaker: Biao Lian (Princeton)

    Title: Integrability and chaos of 1+1d chiral edge states

    Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

  • General Relativity Seminar
    12:00 pm-1:00 pm
    12/01/2024

    The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
    04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
    04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
    04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
    05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
    05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
    05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
    05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Juven Wang

    Title: Open Problems in Physics and Novel Solutions from Math

     

    Abstract: (1) How do neutrinos obtain tiny mass and oscillate between e, \mu, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis?

    (2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions?

    (3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry?

    (4) Family/Generation problem: Why are there three families/generations of quarks and leptons?

    In my talk, I will sketch and propose novel solutions to these challenging open problems in physics based on my own work (available on arXiv, some jointly with my collaborators).

    I will show that the eclectic cross-disciplinary fertilization of ideas between the Math-Physics geometry and topology, Quantum Condensed Matter, and High-Energy Physics (theory, pheno, lattice) can help solving these big problems.

    The (1) answer relates to Ultra Unification: a Z_{16} class Atiyah-Patodi-Singer eta invariant (Baryon – Lepton)-protected topological superconductor and a symmetry-extended anomalous topological quantum field theory.

    The (2) and (3) answers relate to a trivial cobordism class and Symmetric Mass Generation, and disordering and removing the Pecci-Quinn axions.

    The (4) answer has to do with the Hirzebruch signature and Atiyah-Singer index theorem, gravitational Chern-Simons theory, and 3 E8 quantum Hall states.

     

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Title: Duality in Einstein’s Gravity

    Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/8/2021 Interdisciplinary Science Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Alejandro Poveda

    Title: On compactness phenomena

    Abstract: In this presentation I shall be preoccupied with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behavior. This phenomenon is intrinsic to the very architecture of the mathematical universe and manifests to us in a cornucopia of forms. Over the past fifty years, the study of compactness phenomena has been a cornerstone of research in set theory. This talk will present recent discoveries regarding compactness principles, spanning classical themes like the tree property and stationary reflection, while also forging novel connections with other topics, such as Woodin’s HOD Conjecture.

  • Active Matter Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 10.20.22

    Active Matter Seminar
    Speaker: Sharad Ramanathan, Harvard
    Title: Attempts at understanding human axial elongation and patterning
    Abstract: Some of the most dramatic events during human development is the axial elongation of the embryo with concomitant changes in the geometry and composition of the underlying tissues. The posterior part of the embryo gives rise to the spinal cord, vertebral column, ribcage, back muscles, and dermis.  In this talk, I will present our attempts at coaxing human embryonic stem cells to form these structures of the early human embryo that closely recapitulate the geometry, relative arrangements, composition, and dynamics of development of the early spinal cord flanked progenitors of the musculoskeletal system. Our goal was to do so, such that we could build hundreds of these organoids at a time. I will also present preliminary results for the use of this system to understand key events during early human development through imaging and genetic perturbations.
  • Colloquium
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    colloquium

    Colloquium

    Speaker: Yannai Gonczarowski (Harvard)

    Title: Strategyproof-Exposing Mechanisms Descriptions

    Abstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.

    By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.

    Joint work with Ori Heffetz and Clayton Thomas.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-22-2017 Random Matrix & Probability Theory Seminar

    12:01 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:03 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Cosmic Road to New Physics
    12:04 pm
    12/01/2024
    The colourful star cluster NGC 3532

    The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

    The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

    Organizers:

    Scientific Advisory:

    Speakers: 

    CosmicRoad_Poster

  • Colloquium
    12:05 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:06 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:08 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:09 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar
    12:10 pm-1:10 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

     

    Speaker: Man-Wai Cheung

    Title: Compactification for cluster varieties without frozen variables of finite type

    Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

  • CMSA EVENT: 2019 Ding Shum Lecture
    12:11 pm
    12/01/2024
    DingShum-2019

    DSC_0468-e1568985499370

    On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

    Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

    Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

    Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

    This event is made possible by the generous funding of Ding Lei and Harry Shum.

    DingShum-2019

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-1-2017 Random Matrix & Probability Seminar

    12:11 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
    12:11 pm
    12/01/2024-04/19/2017

    From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

  • Colloquium
    12:12 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:13 pm-12:14 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-27-2017 Mathematical Physics Seminar

    12:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-7-2017 Social Science Applications Forum

    12:15 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:15 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/13/2019 Special Seminar

    12:15 pm-1:05 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3-8-2017 CMSA Special Lecture Series

    12:16 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
    12:19 pm
    12/01/2024-10/18/2019
    Noncommutative-Analysis-Poster-3

    On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

    This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

    Please register here

    Speakers:

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-8-2017 Random Matrix & Probability Theory Seminar

    12:21 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-6-2017 Mathematical Physics Seminar

    12:24 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    12:25 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-10-2017 Special Lecture Series

    12:27 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-21-2017 Social Science Applications Forum

    12:28 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
    12:28 pm
    12/01/2024-05/05/2019
    1 Oxford Street, Cambridge MA 02138
    Differential Geometry, Calabi-Yau theory and General Relativity

    Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

    On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

    Organizers:

    • Horng-Tzer Yau (Harvard)
    • Wilfried Schmid (Harvard)
    • Clifford Taubes (Harvard)
    • Cumrun Vafa (Harvard)

    Speakers:

    • Lydia Bieri, University of Michigan
    • Tristan Collins, MIT
    • Simon Donaldson, Imperial College
    • Fan Chung Graham, UC San Diego
    • Nigel Hitchin, Oxford University
    • Jun Li, Stanford University
    • Kefeng Liu, UCLA
    • Chiu-Chu Melissa Liu, Columbia University
    • Alina Marian, Northeastern University
    • Xenia de la Ossa, Oxford University
    • Duong H. Phong, Columbia University
    • Richard Schoen, UC Irvine
    • Andrew Strominger, Harvard University
    • Nike Sun, MIT
    • Clifford Taubes, Harvard University
    • Chuu-Lian Terng, UC Irvine
    • Valentino Tosatti, Northwestern University
    • Karen Uhlenbeck, University of Texas
    • Cumrun Vafa, Harvard University
    • Mu Tao Wang, Columbia University
    • Edward Witten, IAS
    • Stephen Yau, Tsinghua University, P.R. China
  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 03.22.2023

    Speaker: Mete Soner (Princeton University)

    Title: Synchronization in a Kuramoto Mean Field Game

    Abstract:  Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a  key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  We explore this system in the mean field formalism.  We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium.  The mean field game also exhibits a bifurcation from incoherence to self-organization.  This approach has found interesting applications including circadian rhythms and jet-lag recovery.  This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Tim Adamo, University of Edinburgh

    Title: An invitation to strong-field scattering

    Abstract: Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to all-multiplicity twistor and string methods.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Xi Yin (Harvard Physics) and Peter Kronheimer (Harvard Math)
    Topics:
    Xi Yin: What is string field theory?
    Peter Kronheimer: What is Seiberg-Witten theory?
  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Four-dimensional topology

    12:30 pm-1:30 pm
    12/01/2024
    Lecture_Manolescu-pdf

    Ciprian Manolescu (Stanford)

    Title: Four-dimensional topology

    Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to four-manifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience.

    Video

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 05.03.2023

    Speaker: Xin Guo, UC Berkeley

    Title: Generative Adversarial Networks (GANs): An Analytical Perspective

    Abstract: Generative models have attracted intense interests recently. In this talk, I will discuss one class of generative models, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis.

     

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)
    Topics:
    Dan Freed: What is framing anomaly? How is it different from other anomalies?
    Dan Berwick-Evans: What is Atiyah-Singer index theorem?
  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Speakers: Dan Freed (Harvard Math and CMSA), Denis Auroux (Harvard Math)

  • Math Science Literature Lecture Series
    12:30 pm-2:00 pm
    12/01/2024
    Lecture_Freedman-1-pdf

    Michael Freedman (Microsoft – Station Q)

    Title: A personal story of the 4D Poincare conjecture

    Abstract:  The proof of PC4 involved the convergence of several historical streams.  To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.

    Talk Chair: Peter Kronheimer

    Video

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 03.08.2023

    Speaker: Ning Su, University of Pisa

    Title: Conformal symmetry, Optimization algorithms and the Critical Phenomena

    Abstract: In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid phase transition and Heisenberg magnet to very high precision.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 03.29.2023

    Speaker: Ruth Britto (Trinity College Dublin)

    Title: Scattering amplitudes in quantum field theory

    Abstract: Particle collider experiments require a detailed description of scattering events, traditionally computed through sums of Feynman diagrams. However, it is not practical to evaluate Feynman diagrams directly for all significant scattering processes. Moreover, adding all diagrams reveals many cancellations: scattering amplitudes in theories such as QCD take remarkably simple forms. This simplicity is a clue that the perturbative theory is perhaps best understood without reference to Feynman diagrams. In fact, it has recently become possible to explain some of this simplicity. I will show how to derive many amplitudes efficiently and elegantly, and propose taming the remaining complexity with ideas drawn from combinatorics and geometry.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 04.26.2023.rev2

    Speaker: Max Metlitski (MIT)

    Title: Boundary behavior at classical and quantum phase transitions

    Abstract: There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter, where exotic protected boundary states are ubiquitous. In this talk, I’ll ask: what happens at a boundary of a system, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field, as well as some extensions to quantum phase transitions.

     

  • Colloquium
    12:30 pm
    12/01/2024

    No additional detail for this event.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University)

    Topics:

    Michael Douglas: “What is non-commutative field theory?”
    Mayuko Yamashita: “What is differential cohomology?”
  • Topological Quantum Matter Seminar
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Hart Goldman, University of Chicago

    Title: Composite fermions and the fractional quantum anomalous Hall effect

    Abstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk, I will argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new zero-field context. In particular, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end, I will present exact diagonalization evidence for such composite Fermi liquid states at zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs), I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 04.12.2023

    Speaker: James Halverson (Northeastern University)
     
    Title: Unexpected Uses of Neural Networks: Field Theory and Metric Flows

    Abstract:  We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics, sometimes leading to rigorous results. In this talk, however, I will argue that breakthroughs in deep learning theory are also useful for making progress, focusing on applications to field theory and metric flows. Specifically, I will introduce a neural network approach to field theory with a different statistical origin, that exhibits generalized free field behavior at infinite width and interactions at finite width, and that allows for the study of symmetries via the study of correlation functions in a different duality frame. Then, I will review recent progress in approximating Calabi-Yau metrics as neural networks and cast that story into the language of neural tangent kernel theory, yielding a theoretical understanding of neural network metric flows induced by gradient descent and recovering famous metric flows, such as Perelman’s formulation of Ricci flow, in particular limits.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 11.16.22 - 2

    Colloquium

    Speaker: Hidenori Tanaka (NTT Research at Harvard)

    Title: Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks

    Abstract: In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle, but the role of symmetry breaking is not well understood. Here, we develop a Lagrangian formulation to study the geometry of learning dynamics in neural networks and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. Then, we generalize Noether’s theorem known in physics to describe a unique symmetry breaking mechanism in learning and derive the resulting motion of the Noether charge: Noether’s Learning Dynamics (NLD). Finally, we apply NLD to neural networks with normalization layers and discuss practical insights. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    A tale of two balloons

    12:30 pm-1:30 pm
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-11.16.21

    Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
    Joint work with Omer Angel and Gourab Ray.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-20-2017 Mathematical Physics Seminar

    12:30 pm
    12/01/2024

    No additional detail for this event.

  • Math Science Literature Lecture Series
    12:30 pm-1:30 pm
    12/01/2024
    Lecture_Lian-pdf

    Bong Lian (Brandeis)

    Title: From string theory and Moonshine to vertex algebras

    Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed at a general audience.

    Slides | Video

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium

    Colloquium
    Speaker: Melody Chan
    Title: Moduli spaces of graphs
    Abstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.
  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.13.2023

    Title: Complete Calabi-Yau metrics: Recent progress and open problems

    Abstract: Complete Calabi-Yau metrics are fundamental objects in Kahler geometry arising as singularity models or “bubbles” in degenerations of compact Calabi-Yau manifolds.  The existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to Yau and Tian-Yau. I will describe some recent progress towards the question of existence, and explain some future directions, highlighting connections with notions of algebro-geometric stability.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Mike Douglas (Harvard CMSA) and Anurag Anshu (Harvard Computer Science)

    Topics:

    Mike Douglas: What are scaling laws in deep learning?

    Anurag Anshu: What’s the difference between classical information theory and quantum information theory (or classical computation vs quantum computation)?

     

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.02.2023

    Speaker: Max Reppen (Boston University)

    Title: Neural Optimal Stopping Boundary

    Abstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.12.22 (1)

    Colloquium

    Title: Complete disorder is impossible: Some topics in Ramsey theory

    Speaker: James Cummings, Carnegie Mellon University

    Abstract: The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory, which touches on many areas of mathematics including graph theory, set theory and dynamics. I will give an overview of Ramsey theory, emphasizing the diverse ideas which are at play in this area.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA)

    Topics:

    Dan Freed: What is Dijkgraaf-Witten theory?

    Sunghyuk Park: What happened at the Clay Math Institute Workshop?

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.19.22

    Colloquium

    Speaker: Patrick Lopatto (Brown)

    Title: The Mobility Edge of Lévy Matrices

    Abstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness, these models have been broadly applied in physics, finance, and statistics. When the entries have infinite mean, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/6/2020 Strongly Correlated Quantum Materials Lecture

    12:30 pm-3:00 pm
    12/01/2024
  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.08.2023

    Speaker: David Gamarnik (MIT)

    Title: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property

    Abstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph, the problem of finding a near ground state in a spin glass model, the problem of finding a satisfying assignment in a random constraint satisfaction problem, and many many more. Unfortunately, at the same time no formal computational hardness results exist which  explains this persistent algorithmic gap.

    In the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms which exhibit a form of stability/noise insensitivity.

    We will specifically show how to use this property to obtain stronger (stretched exponential) than the state of the art (quasi-polynomial) lower bounds on the size of constant depth Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph, and the problem of finding a near ground state of a p-spin model.

    Joint work with Aukosh Jagannath and Alex Wein

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math)

    Topics:

    Mike Hopkins: What are topological modular forms?

    Mihnea Popa: What is the abundance conjecture and why should it to be true?

     

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 09.28.22

    Colloquium

    Speaker: Dima Sinapova (Rutgers University)

    Title: The Tree Property and uncountable cardinals

    Abstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes.

    We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.

     

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.26.22

    Speaker: Virginia Vassilevska Williams (MIT)

    Title: Clique listing algorithms

    Abstract: A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history.

    A fundamental question, with many applications, is “How fast can one list all k-cliques in a given graph?”.

    Even just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant, such as 3 or 4 (independent of n), even the brute-force algorithm runs in polynomial time, O(n^k), and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k), the brute-force algorithm is in some sense optimal, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques, with running times depending on the number of vertices n, the number of edges m, the number of k-cliques T and more. We will focus on the case when k=3, but we will note some extensions.

    (Based on joint work with Andreas Bjorklund, Rasmus Pagh, Uri Zwick, Mina Dalirrooyfard, Surya Mathialagan and Yinzhan Xu)

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.22.2023

    Speaker: Netta Engelhardt (MIT)

    Title: The Black Hole Information Paradox: A Resolution on the Horizon?

    Abstract: The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary, and in particular its application to entanglement and complexity, however, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-5-2017 Random Matrix & Probability Theory Seminar

    12:31 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:32 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
    12:33 pm
    12/01/2024-05/01/2019

    From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Videos

    Speakers: 

     

    Monday, April 29

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

    Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

    10:00 – 10:30amBreak
    10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

    Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

    11:30 – 1:30pmLunch
    1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

    Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

    2:30 – 3:00pmBreak
    3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

    Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

    4:00 – 4:30pmBreak
    4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

    Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

     

    Tuesday, April 30

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

    Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

    10:00 – 10:30amBreak
    10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

    Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

    11:30 – 1:00pmLunch
    1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

    Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

    2:00 – 2:15pmBreak
    2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

    Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

    Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

    We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

    This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

    3:15 – 3:30pmBreak
    3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

    Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

    4:30 – 4:45pmBreak
    4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

    Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

     

    Wednesday, May 1

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

    Abstract: PDF

    This is joint work with Eric Rains and Douglas Stryker.

    10:00 – 10:30amBreak
    10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

    Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
    and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
    to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

    11:30 – 11:45amBreak
    11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

    Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

    In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

    This is a joint work with Felix Janda and Yongbin Ruan.

    12:45 – 2:30pmLunch
    2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

    Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

    3:30 – 4:00pmBreak
    4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

    Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-29-2017 Random Matrix & Probability Theory Seminar

    12:35 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-24-2017 Random Matrix & Probability Theory Seminar

    12:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-30-2017 CMSA Special Seminar

    12:38 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-27-2017 Mathematical Physics Seminar

    12:40 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:41 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-5-2017 Special Lecture Series

    12:42 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-7-2017 Special Lecture Series

    12:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Special Lecture Series

    12:44 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:45 pm-1:45 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 11.02.22

    Speaker: Liang Fu (MIT)

    Title: Doping and inverting Mott insulators on semiconductor moire superlattices

    Abstract: Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First, in an intermediate range of magnetic fields, doping this Mott insulator gives rise to a dilute gas of spin polarons, which form a pseudogap metal. Second, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.

  • Colloquium
    12:45 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-14-2017 Special Lecture Series

    12:46 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-3-2017 Mathematical Physics Seminar

    12:50 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    12:51 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Social Science Applications Forum

    12:53 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Mirror Symmetry and Stability
    12:55 pm
    12/01/2024-03/20/2019
    HMS-2019-1

    This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

    Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

    Speakers:

    Dylan Allegretti (Sheffield)
    Tristan Collins (MIT)
    Naoki Koseki (Tokyo)
    Chunyi Li (Warwick)
    Jason Lo (CSU Northridge)
    Emanuele Macrì (NEU & IHES)
    Genki Ouchi (Riken iTHEMS)
    Pranav Pandit (ICTS)
    Laura Pertusi (Edinburgh)
    Jacopo Stoppa (SISSA)
    Alex Takeda (UC Berkeley)
    Xiaolei Zhao (UC Santa Barbara)

    More details will be added later.

    Visit the event page for more information. 

     

    HMS-2019-1

  • Colloquium
    12:55 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:57 pm
    12/01/2024

    No additional detail for this event.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Active crystals are highly ordered structures that emerge from the nonequilibrium self-organization of motile objects, and have been widely studied in synthetic and bacterial active matter. In this talk, I will describe how swimming sea star embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiment, hydrodynamic theory, and simulations, we demonstrate that the formation, dynamics, and dissolution of these living crystals are controlled by the natural development of the embryos. Remarkably, due to nonreciprocal force and torque exchange between the embryos, the living chiral crystals exhibit self-sustained oscillations with dynamic signatures recently predicted to emerge in materials with odd elasticity.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character \theta of G, and a G-invariant function w on V.  This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient.  GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM, very few computations of these invariants have been carried out.  In this talk I will describe a new method for computing generating functions of GLSM invariants.  I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.

  • Math Science Literature Lecture Series
    1:00 pm-2:00 pm
    12/01/2024
    Lecture_Harris_updated-pdf

    Joe Harris (Harvard)

    Title: Rationality questions in algebraic geometry

    Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension two) and Hodge theory (dimension 3). But there remained much we didn’t understand about the condition of rationality, such as how it behaves in families. However, there has been recent progress: work of Hassett, Tschinkel, Pirutka and others, working with examples in dimension 4, showed that it is in general neither an open condition nor a closed one, but does behave well with respect to specialization. In this talk I’ll try to give an overview of the history of rationality and the current state of our knowledge.

    Video

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack), there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk, we first show that these three definitions are equivalent. Second, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third, we apply these results to various moduli situations, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    No additional detail for this event.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-01.27.2022

    Abstract: Fluids pervade complex systems, ranging from fish schools, to bacterial colonies and nanoparticles in drug delivery. Despite its importance, little is known about the role of fluid mechanics in such applications. Is schooling the result of vortex dynamics synthesized by individual fish wakes or the result of behavioral traits? Is fish schooling energetically favorable?  I will present multifidelity computational studies of collective swimming in 2D and 3D flows. Our studies demonstrate that classical models of collective swimming (like the Reynolds model) fail to maintain coherence in the presence of long-range hydrodynamic interactions. We demonstrate in turn that collective swimming can be achieved through reinforcement learning. We extend these studies to 2D and 3D viscous flows governed by the Navier Stokes equations. We examine various hydrodynamic benefits with a progressive increase of the school size and demonstrate the importance of controlling the vorticity field generated by up to 300 synchronized swimmers.

  • Seminars

    Seminars Colloquia & Seminar
    11/13/2019 General Relativity Seminar

    1:00 pm-2:00 pm
    12/01/2024
  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar
    Speaker: Herbert Levine (Northeastern)
    Title: Frustration-free states of cell fate networks: the case of the epithelial-mesenchymal transition

    Abstract: Cell fate decisions are made by allowing external signals to govern the steady-state pattern adopted by networks of interacting regulatory factors governing transcription and translation. One of these decisions, of importance for both developmental processes and for cancer metastasis, is the epithelial-mesenchymal transition (EMT). In this talk, we will argue that these biological networks have highly non-generic interaction structures such that they allow for phenotypic states with very low frustration, i.e. where most interactions are satisfied. This property has important consequences for the allowed dynamics of these systems.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA-GR-Seminar-03.10.22

    Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Gromov-Witten invariants count pseudo-holomorphic curves on a symplectic manifold passing through some fixed points and submanifolds. Similarly, open Gromov-Witten invariants are supposed to count disks with boundary on a Lagrangian, but in most cases such counts are not independent of some choices as we would wish. Motivated by Fukaya’11, J. Solomon and S. Tukachinsky constructed open Gromov-Witten invariants in their 2016 papers from an algebraic perspective of $A_{\infty}$-algebras of differential forms, utilizing the idea of bounding chains in Fukaya-Oh-Ohta-Ono’06. On the other hand, Welschinger defined open invariants on sixfolds in 2012 that count multi-disks weighted by the linking numbers between their boundaries. We present a geometric translation of Solomon-Tukachinsky’s construction. From this geometric perspective, their invariants readily reduce to Welschinger’s.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Max Lavrentovich, Worcester State University

    Title: Strongly driven mixtures and membranes: Out of equilibrium surprises

    Abstract: The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phase-separating colloidal mixture and a lipid membrane, which demonstrate counterintuitive properties when driven out of equilibrium. We will see that the phase separating mixture, when driven by a uniform force, develops (in simulations) an intriguing pattern with a characteristic length scale set by the magnitude of the drive. We will look at some theoretical approaches to understanding the pattern formation and possible experimental realizations. The membrane, when driven by an oscillatory electric field, develops (in experiments) a long-lived metastable state with a decreased capacitance and increased dissipation. This state may have implications for neuronal processing and memory formation.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.

    1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.

    2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-02.24.22

    Abstract: The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological
    disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes: (i) to explain the tortoise & hare story in bacterial competition: how motility of Pseudomonas aeruginosa bacteria leads to a slower invasion of bacteria colonies, which are individually faster, and
    (ii) how self-propelled defects lead to finding an unanticipated mechanism for cell death.

    I will then discuss various strategies to tame, otherwise chaotic, active flows, showing how hydrodynamic screening of active flows can act as a robust way of controlling and guiding active particles into dynamically ordered coherent structures. I will also explain how combining hydrodynamics with topological constraints can lead to further control of exotic morphologies of active shells.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    No additional detail for this event.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

  • Seminars

    Seminars Colloquia & Seminar
    12/6/2019 Special Seminar

    1:00 pm-2:00 pm
    12/01/2024
  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I will present a four-term exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations, the Hodge, weight, and perverse Leray filtrations, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the Clemens-Schmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    9/28/2021 Combinatorics, Physics and Probability Seminar

    1:00 pm
    12/01/2024

    Title: The hypersimplex and the m=2 amplituhedron

    Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.

  • Math Science Literature Lecture Series
    1:00 pm-2:00 pm
    12/01/2024

    Robert Griess (University of Michigan)

    Title: My life and times with the sporadic simple groups

    Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad school at University of Chicago,  I became fascinated with the unfolding story of sporadic simple groups. It involved theory, detective work and experiments. During this lecture, I will describe some of the people, important ideas and evolution of thinking about sporadic simple groups. Most should be accessible to a general mathematical audience.

    Video | Slides

  • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
    1:00 pm-6:00 pm
    12/01/2024-04/07/2018
    banner-image-1

    The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

    Confirmed Speakers:

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 11.17.22

    Active Matter Seminar

    Speaker: Max Prigozhin (Harvard)

    Title: Dynamic and multicolor electron microscopy

    Abstract: My lab is developing biophysical methods to achieve multicolor and dynamic biological imaging at the molecular scale. Our approach to capturing the dynamics of cellular processes involves cryo-vitrifying samples after known time delays following stimulation using custom cryo- plunging and high-pressure freezing instruments. To achieve multicolor electron imaging, we are exploring the property of cathodoluminescence—optical emission induced by the electron beam. We are developing nanoprobes (“cathodophores”) that will be used as luminescent protein tags in electron microscopy. We are applying these new methods to study G-protein- coupled receptor signaling and to visualize the formation of biomolecular condensates.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem, and new results in this direction, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-02.10.22

    Abstract: My lab is interested in the active and adaptive materials that underlie control of cell shape.  This has centered around understanding force transmission and sensing within the actin cytoskeleton.  I will first review our current understanding of the types of active matter that can be constructed by actin polymers.  I will then turn to our recent experiments to understand how Cell shape changes in epithelial tissue.  I will describe the two sources of active stresses within these tissues, one driven by the cell cycle and controlling cell-cell stresses and the other controlled by cell-matrix signaling controlling motility.  I will then briefly describe how we are using optogenetics to locally control active stresses to reveal adaptive and force-sensitive mechanics of the cytoskeletal machinery. Hopefully, I will convince you that recent experimental and theoretical advances make this a very promising time to study this quite complicated form of active matter.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: During development, organisms interact with their natural habitats while undergoing morphological changes, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria, a basal animal lineage that includes sea anemones, corals, hydras, and jellyfish, offers unique insight into the development and evolution of morphological complexity.  In my talk, I will introduce our research on “ethology of morphogenesis,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels, opening new perspectives about the design principle of soft-bodied animals. In addition, I will discuss a fascinating feature of cnidarian biology. For humans, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule.

    References
    Anniek Stokkermans, Aditi Chakrabarti, Ling Wang, Prachiti Moghe, Kaushikaram Subramanian, Petrus Steenbergen, Gregor Mönke, Takashi Hiiragi, Robert Prevedel, L. Mahadevan, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976

    Ikmi A, Steenbergen P, Anzo M, McMullen M, Stokkermans M, Ellington L, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensisNature communications, Sept 02; 11:4399

    He S, Del Viso F, Chen C, Ikmi A, Kroesen A, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensisScience, Vol. 361, Issue 6409, pp. 1377-1380.
    Ikmi A, McKinney SA, Delventhal KM, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensisNature communications. Nov 24; 5:5486.

  • Seminars

    Seminars Colloquia & Seminar
    Combinatorics & Complexity Seminar, Fridays

    1:00 pm-4:00 pm
    12/01/2024

    The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

    Additional information on CMSA’s Combinatorics and Complexity program can be found here.

     

    DateNameTitle/Abstract
    09-08-17TBA
    09-15-2017TBA
    09-22-17TBA
    09-29-17TBA
    10-06-17 TBA
    10-13-2017TBA
    10-20-2017TBA
    10-27-2017TBA
    11-03-2017TBA
    11-10-2017TBA
    11-17-2017TBA
    11-24-2017TBA
    12-01-2017TBA
    12-08-2017 TBA
  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 11.03.22

    Active Matter Seminar

    Speaker: Siavash Monfared, Niels Bohr Institute, Copenhagen

    Title: Force transmission informs the collective behavior of active cell layers

    Abstract: Collective cell migration drives numerous physiological processes such as tissue morphogenesis, wound healing, tumor progression and cancer invasion. However, how the interplay of mechanical interactions and the modes of collective self-organization among cells informs such processes is yet to be established. In this talk, I will focus on the role of three-dimensional force transmission, from a theoretical and computational perspective, on two phenomena: (1) cell extrusion from a cellular monolayer and (2) density-independent solid-like to fluid-like transition of active cell layers. For the first topic, I will focus on how increasing cell-cell adhesion relative to cell-substrate adhesion enables cells to collectively exploit distinct mechanical pathways – leveraging defects in nematic and hexatic phases associated with cellular arrangement – to eliminate an unwanted cell. For the second topic, I will show how solid-like to fluid-like transition in active cell layers is linked to the percolation of isotropic stresses. This is achieved via two distinct and independent paths to model this transition by increasing (a) cell-cell adhesion and (b) active traction forces. Additionally, using finite-size scaling analyses, the phase transition associated with each path is mapped onto the 2D site percolation universality class. Our results highlight the importance of force transmission in informing the collective behavior of living cells and opens the door to new sets of questions for those interested in connecting the physics of cellular self-organization to the dynamics of biological systems.

     

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will illustrate how this challenge can be overcome by elucidating the probabilistic connections between models of different levels of detail. These connections explain how stochastic partial differential equations (SPDE) arise naturally from particle models.

    I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.

  • Colloquium
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane. The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

     

     

    Speaker: Achilleas Porfyriadis, Harvard Black Hole Initiative

    Title: Extreme Black Holes: Anabasis and Accidental Symmetry

    Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of  AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Fred MacKintosh (Rice University)

    Title: Contractility, structure formation and fluctuations in active gels, with and without molecular motors

    Abstract: Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence, however, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified, reconstituted systems also point to contractility and structure formation in disordered, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this, as well as possible evidence for non-motor force generation.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Michael Shelley (Flatiron)

    Title: Active structures and flows in living cells

    Abstract: Flows in the fluidic interior of living cells can serve biological function or act as signatures of how intracellular forces are exerted. I’ll discuss examples of each. One is understanding the emergence of cell-spanning vortical flows in large developing egg cells, while the other arises in studying the nature of force transduction in single cell embryos moving towards their first cell division. Both involve the cytoskeleton, that set of polymers, cross-linkers, and molecular motors that underlie much of the active mechanics within cells, and has led to the development of new coarse-grained active matter models and novel instabilities.

  • Seminars

    Seminars Colloquia & Seminar
    4-11-2017 Social Science Applications Forum

    1:00 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

    In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

    This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

  • Active Matter Seminar
    1:00 pm-2:26 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-04.07.22

    Abstract: The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.

  • Math Science Literature Lecture Series
    1:00 pm-2:30 pm
    12/01/2024
    Lecture_Ma-1-pdf
    Yi Ma
    Photo Copyright Noah Berger / 2019

     

    Yi Ma (University of California, Berkeley)

    Title: Deep Networks from First Principles

    Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation, both for optimizing the same objective. This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.

    Talk chair: Harry Shum

    Slides | Video

  • Quantum Matter
    1:00 pm-2:30 pm
    12/01/2024
  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review  another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a self-organizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

  • Active Matter Seminar
    1:00 pm-2:20 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-03.24.22

    Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes and second layers within a base monolayer of M xanthus cells. We find that cells align with each other over the majority of the monolayer forming an active nematic liquid crystal with defect point where cell alignment is undefined. We find that new layers and holes form at positive and negative topological defects respectively. We model the cell layer using hydrodynamic modeling and find that this layer and hole formation process is driven by active nematic forces through cell motility and anisotropic substrate friction.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar
    Speaker: Alexander Grosberg (NYU)

    Title: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell

    Abstract: Nucleus of a living cell houses a cell genome – a polymer called chromatin, which is a functional form of DNA.  It is very long, e.g., 2 meters long for every human cell.  Nucleus is also an arena of incessant energy-driven activity.  Experiments show that chromatin undergoes large scale motions sustained over long times of order seconds.  In the talk, after reviewing the phenomenology, I will show how these flows may arise due to a phase transition in which chromatin-driving motors, such as RNA polymerase, form a polar (“ferromagnetic”) order controlled by hydrodynamic interactions.  The talk is based on the joint work with I.Eshghi and A.Zidovska.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-04.28.22

    Speaker: Guillaume Duclos (Brandeis)
    Title: Building active nematic and active polar liquids out of biological machines

    Abstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium, leading to emergent collective behaviors not found in passive materials. In this talk, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics, as well as shine light on the physical mechanisms that regulate self-organization in living matter.

     

    Video (Youtube)

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Active Matter Seminar

     

    Speaker:  Jonathan Bauermann, Max Planck Institute for the Physics of Complex Systems

    Title: Active chemical reactions in phase-separating systems

    Abstract: Motivated by the existence of membrane-less compartments in the chemically active environment of living cells, I will discuss the dynamics of droplets in the presence of active chemical reactions. Therefore, I will first introduce the underlying interplay between phase separation and active reactions, which can alter the droplet dynamics compared to equilibrium systems. A key feature of such systems is the emergence of concentration gradients even at steady states. In the second part of this talk, I will discuss how these gradients can trigger instabilities in the core of chemically active droplets, giving rise to a new non-equilibrium steady state of liquid spherical shells. Finally, I will present experimental and theoretical results discussing the existence and energetic cost of this non-equilibrium steady state in a coacervate system.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Shane McInally, Brandeis

    Title: Control of actin cable length by decelerated growth and network geometry

    Abstract: The sizes of many subcellular structures are coordinated with cell size to ensure that these structures meet the functional demands of the cell. In eukaryotic cells, these subcellular structures are often membrane-bound organelles, whose volume is the physiologically important aspect of their size. Scaling organelle volume with cell volume can be explained by limiting pool mechanisms, wherein a constant concentration of molecular building blocks enables subcellular structures to increase in size proportionally with cell volume. However, limiting pool mechanisms cannot explain how the size of linear subcellular structures, such as cytoskeletal filaments, scale with the linear dimensions of the cell. Recently, we discovered that the length of actin cables in budding yeast (used for intracellular transport) precisely matches the length of the cell in which they are assembled. Using mathematical modeling and quantitative imaging of actin cable growth dynamics, we found that as the actin cables grow longer, their extension rates slow (or decelerate), enabling cable length to match cell length. Importantly, this deceleration behavior is cell-length dependent, allowing cables in longer cells to grow faster, and therefore reach a longer length before growth stops at the back of the cell. In addition, we have unexpectedly found that cable length is specified by cable shape. Our imaging analysis reveals that cables progressively taper as they extend from the bud neck into the mother cell, and further, this tapering scales with cell length. Integrating observations made for tapering actin networks in other systems, we have developed a novel mathematical model for cable length control that recapitulates our quantitative experimental observations. Unlike other models of size control, this model does not require length-dependent rates of assembly or disassembly. Instead, feedback control over the length of the cable is an emergent property due to the cross-linked and bundled architecture of the actin filaments within the cable. This work reveals a new strategy that cells use to coordinate the size of their internal parts with their linear dimensions. Similar design principles may control the size and scaling of other subcellular structures whose physiologically important dimension is their length.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Open mic Swampland Discussion

    Topic: Cobordism

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Nicolas Romeo (UChicago)

    Title: Scaling behavior and control of nuclear wrinkling

    Abstract: The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. We characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behaviour. A spectral analysis of three-dimensional high-resolution live-imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing the mechanical properties of the nuclear envelope, highlighting in passing the importance of nonlinear response to biological robustness.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Mehran Kardar, MIT

    Title: Competition at the front of expanding populations

    Abstract: When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that  integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar

    Speaker: Josef Käs, Leipzig University

    Title: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

    Abstract: Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.

    Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.

    We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.

    Video (Youtube)

  • Quantum Matter
    1:00 pm-2:30 pm
    12/01/2024
  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Open Mic Discussion
    Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 02.02.23

    Active Matter Seminar

    Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen

    Title: Interacting Active Matter

    Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    Jefferson Hal Room 256, 17 Oxford Street, Cambridge MA 02138

    Active Matter Seminar
    Speaker: Sahand Hormoz, Harvard Medical School, Dana-Farber Cancer Institute
    Title: Insights from single cell lineage trees
    Abstract: In this talk, I will discuss two recent projects from my lab that involve lineage trees of cells (the branching diagram that represents the ancestry and division history of individual cells). In the first project, we reconstructed the lineage trees of individual cancer cells from the patterns of randomly occurring mutations in these cells. We then inferred the age at which the cancer mutation first occurred and the rate of expansion of the population of cancer cells within each patient. To our surprise, we discovered that the cancer mutation occurs decades before diagnosis. For the second project, we developed microfluidic ‘mother machines’ that allow us to observe mammalian cells dividing across tens of generations. Using our observations, we calculated the correlation between the duration of cell cycle phases in pairs of cells, as a function of their lineage distance. These correlations revealed many surprises that we are trying to understand using hidden Markov models on trees. For both projects, I will discuss the mathematical challenges that we have faced and open problems related to inference from lineage trees.
  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

  • Seminars

    Seminars Colloquia & Seminar
    5/15/2020 Math Physics Seminar

    1:00 pm-2:00 pm
    12/01/2024
  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Mark Bowick, Kavli Institute for Theoretical Physics, UCSB

    Title: The Role of Orientational Order in Development

    Abstract: Morphogenesis, the process through which genes generate form, establishes tissue scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fueled by cell proliferation, which, naively, should disrupt order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order remains an outstanding question in animal development. I will review the statistical mechanics of orientational order and discuss the observation of a fourfold orientationally ordered phase (tetratic) in the model organism Parhyale hawaiensis. I will also discuss theoretical mechanisms for the formation of orientational order that require both motility and cell division, with support from self-propelled vertex models of tissue. The aim is to uncover a robust, active mechanism for generating global orientational order in a non-equilibrium system that then sets the stage for the development of shape and form.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be “Swampland constraints, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    Lyman Lab, 17 Oxford Street, Cambridge MA 02138
    CMSA Active Matter Seminar 12.08.22

    Active Matter Seminar

    Speaker: Julien Tailleur (MIT)

    Title: Self-organization of motile cells by quorum-sensing or chemotactic interactions

    Abstract: Equilibrium statistical mechanics tells us how to control the self-assembly of passive materials by tuning the competition between energy and entropy to achieve desired states of organization. Out of equilibrium, no such principles apply and self-organization principles are scarce. Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Dissipation and injection of energy are then disconnected at the microscopic scale, hence driving the system strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases in the absence of cohesive attractive forces, but it also leaves us without guiding principles to understand the self-organization of active matter. In this talk, I will review the progress which has been made over the past ten years to control the organization of self-propelled agents using motility control, either externally or through interactions. I will show that generic principles apply and illustrate the theoretical developments presented in the talk using recent experiments on the motility-induced self-organization of bacterial mixtures.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 02.16.23

    Active Matter Seminar

    Speaker: Jörn Dunkel, MIT

    Title: Towards programmable living materials and quantitative models of active matter

    Abstract: Over the last two decades, major progress has been made in understanding the self-organization principles of active matter.  A wide variety of experimental model systems, from self-driven colloids to active elastic materials, has been established, and an extensive theoretical framework has been developed to explain many of the experimentally observed non-equilibrium pattern formation phenomena. Two key challenges for the coming years will be to translate this foundational knowledge into functional active materials, and to identify quantitative mathematical models that can inform and guide the design and production of such materials. Here, I will describe joint efforts with our experimental collaborators to realize self-growing bacterial materials [1], and to implement computational model inference schemes for active and living systems dynamics [2,3].

    [1] Nature 608: 324, 2022
    [2] PNAS 120: e2206994120, 2023
    [3] eLife 10: e68679, 2021

  • CMSA EVENT: Second Annual STAR Lab Conference
    1:01 pm-1:02 pm
    12/01/2024

    The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

    For more information, please consult the event’s website.

  • Colloquium
    1:02 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-10-2017 Mathematical Physics Seminar

    1:07 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:07 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:09 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    1:10 pm-3:00 pm
    12/01/2024
  • Colloquium
    1:10 pm-3:10 pm
    12/01/2024

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

  • Colloquium
    1:10 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-31-2015 Mathematical Physics Seminar

    1:10 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:11 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Differential Geometry Seminar

    1:12 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-12-2017 Random Matrix & Probability Theory Seminar

    1:12 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Evolution Equation Seminar

    1:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-14-2015 Mathematical Physics Seminar

    1:14 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-17-2017 Mathematical Physics Seminar

    1:14 pm
    12/01/2024

    No additional detail for this event.

  • Active Matter Seminar
    1:15 pm-2:30 pm
    12/01/2024

    Abstract: In this talk I will review our ongoing theoretical and experimental efforts toward deciphering the hydrodynamic behavior of confluent epithelia. The ability of epithelial cells to collectively flow lies at the heart of a myriad of processes that are instrumental for life, such as embryonic morphogenesis and wound healing, but also of life-threatening conditions, such as metastatic cancer. Understanding the physical origin of these mechanisms requires going beyond the current hydrodynamic theories of complex fluids and introducing a new theoretical framework, able to account for biomechanical activity as well as for scale-dependent liquid crystalline order.

  • Quantum Matter
    1:15 pm-2:45 pm
    12/01/2024
    CMSA QMMP 1.24.23

    Quantum Matter Seminar

    Speakers: Jacob McNamara (Caltech) and Matthew Reece (Harvard)

    Title: Reflections on Parity Breaking

    Abstract: One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we will describe the formal meaning of parity as a gauge symmetry, and argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. We will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity, as well as their relationship with the Swampland Cobordism Conjecture.

     

    https://www.youtube.com/watch?v=hTeaVGRG3LA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=19

  • Seminars

    Seminars Colloquia & Seminar
    4-18-2017 Social Science Applications Forum

    1:15 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-08-2015 Geometric Analysis Seminar

    1:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-06-2015 Geometric Analysis Seminar

    1:17 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-08-2015 Evolution Equations Seminar

    1:18 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:18 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:20 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:21 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    1:21 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:22 pm-2:22 pm
    12/01/2024

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-19-2017 Random Matrix & Probability Theory Seminar

    1:22 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-13-2015 Geometric Analysis Seminar

    1:22 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-10-2015 Evolution Equations Seminar

    1:23 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: 2016 Big Data Conference & Workshop
    1:24 pm
    12/01/2024-08/23/2016
    1 Oxford Street, Cambridge MA 02138

    ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

    Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

    The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

    The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

    Conference Speakers:

    1. Jörn Boehnke, Harvard CMSA
    2. Joan Bruna, UC Berkeley [Video]
    3. Tamara Broderick, MIT [Video]
    4. Justin Chen, MIT [Video]
    5. Yiling Chen, Harvard University [Video]
    6. Amir Farbin, UT Arlington [Video]
    7. Doug Finkbeiner, Harvard University [Video]
    8. Andrew Gelman, Columbia University [Video]
    9. Nina Holden, MIT [Video]
    10. Elchanan Mossel, MIT
    11. Alex Peysakhovich, Facebook
    12. Alexander Rakhlin, University of Pennsylvania [Video]
    13. Neal Wadhwa, MIT [Video]
    14. Jun Yin, University of Wisconsin
    15. Harry Zhou, Yale University [Video]

    Please click Conference Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Please click here for registration.

    Conference Schedule:

    August 22 – Day 1
    8:30amBreakfast
    8:55amOpening remarks
    9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
    9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
    2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
    4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
    August 23 – Day 2
    8:45amBreakfast
    9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
    9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
    2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

    Workshop Participants:

    Richard Freeman’s Group:

    1. Sen Chai, ESSEC
    2. Brock Mendel, Harvard University
    3. Raviv Muriciano-Goroff, Stanford University
    4. Sifan Zhou, CMSA

    Scott Kominer’s Group:

    1. Bradly Stadie, UC Berkeley
    2. Neal Wadhwa, MIT [Video]
    3. Justin Chen

    Christopher Rogan’s Group:

    1. Amir Farbin, UT Arlington [Video]
    2. Paul Jackson, University of Adelaide

    For more information about the workshops, please reach out directly to the individual group leaders.

    This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

  • Seminars

    Seminars Colloquia & Seminar
    10-01-2015 Evolution Equations Seminar

    1:25 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-15-2015 Geometric Analysis Seminar

    1:26 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-16-2015 Random Matrix & Probability Theory Seminar

    1:27 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5-3-2017 Random Matrix & Probability Theory Seminar

    1:29 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-23-2015 Random Matrix & Probability Theory Seminar

    1:29 pm
    12/01/2024

    No additional detail for this event.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/16/2021 Computer Science for Mathematicians

    1:30 pm-2:30 pm
    12/01/2024

    Speaker: Michael P. Kim (UC Berkeley)

    Title: Outcome Indistinguishability

    Abstract: Prediction algorithms assign numbers to individuals that are popularly understood as individual “probabilities” — e.g., what is the probability of 5-year survival after cancer diagnosis? — and which increasingly form the basis for life-altering decisions. The understanding of individual probabilities in the context of such unrepeatable events has been the focus of intense study for decades within probability theory, statistics, and philosophy. Building off of notions developed in complexity theory and cryptography, we introduce and study Outcome Indistinguishability (OI). OI predictors yield a model of probabilities that cannot be efficiently refuted on the basis of the real-life observations produced by Nature.

    We investigate a hierarchy of OI definitions, whose stringency increases with the degree to which distinguishers may access the predictor in question.  Our findings reveal that OI behaves qualitatively differently than previously studied notions of indistinguishability.  First, we provide constructions at all levels of the hierarchy.  Then, leveraging recently-developed machinery for proving average-case fine-grained hardness, we obtain lower bounds on the complexity of the more stringent forms of OI.  The hardness result provides scientific grounds for the political argument that, when inspecting algorithmic risk prediction instruments, auditors should be granted oracle access to the algorithm, not simply historical predictions.

    Joint work with Cynthia Dwork, Omer Reingold, Guy N. Rothblum, Gal Yona; to appear at STOC 2021.

  • Probability Seminar
    1:30 pm-2:30 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 05.11.23

    Probability Seminar

    Speaker: Giorgio Cipolloni (Princeton)

    Title: How do the eigenvalues of a large non-Hermitian random matrix behave?

    Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues. Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X.

    Location: Science Center Room 232

  • Seminars

    Seminars Colloquia & Seminar
    11/14/2018 Hodge Seminar

    1:30 pm
    12/01/2024
  • Probability Seminar
    1:30 pm-2:30 pm
    12/01/2024
    Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

    Probability Seminar

    Speaker: Arka Adhikari (Stanford)

    Title: Correlation decay for finite lattice gauge theories

    Abstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.

     

  • Seminars
    1:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5-2-2017 Social Sciences Application Forum

    1:30 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA GR Seminar 05.11.23

    General Relativity Seminar

    Speaker: Aghil Alaee, Clark University

    Title: Positivity of Static quasi-local Mass in general relativity

    Abstract: In this talk, we review results on the PMT of quasi-local masses and prove the positivity of static quasi-local masses with respect to the AdS and AdS Schwarzschild spacetimes.

  • Seminars
    1:30 pm-3:00 pm
    12/01/2024
  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 04.24.23 (1)

    General Relativity Seminar

    Speaker: Tin Yau Tsang, University of California Irvine

    Title: Recent advances in scalar curvature and positive mass theorems
    Abstract:  First, we have a review of classical tools for studying scalar curvature and positive mass theorem. Then we are going to discuss some advances and new perspectives on these tools which lead to a deeper understanding of geometry and initial data sets.
  • CMSA EVENT: Current Developments in Mathematics 2019
    1:30 pm-5:00 pm
    12/01/2024-11/23/2019
    CDM-POSTER-2019.email_-662x1024

     

    cdmFriday, Nov. 22, 2019 1:30 pm – 5:20 pm

    Saturday, Nov. 23, 2019  9:00 am – 5:00 pm

    Harvard University Science Center, Hall C

    Speakers:

    ·      Svetlana Jitomirskaya (UC Irvine)

    ·      Subash Khot (NYU)

    ·      Jun Li (Stanford)

    ·      André Neves (Chicago)

    ·      Geordie Williamson (U Sidney)

    Free and open to the public – registration is required.
    Please register in advance online at www.math.harvard.edu/cdm

    CDM_2019-agenda-791x1024

  • Special Seminar
    1:30 pm-2:30 pm
    12/01/2024
  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 02.09.23

    General Relativity Seminar

    Speaker: Maciej Zworski, UC Berkeley

    Title: Quasinormal modes and Ruelle resonances: mathematician’s perspective

    Abstract: Quasinormal modes of gravitational waves and Ruelle resonances in hyperbolic classical dynamics share many general properties and can be considered “scattering resonances”: they appear in expansions of correlations, as poles of Green functions and are associated to trapping of trajectories (and are both notoriously hard to observe in nature, unlike, say, quantum resonances in chemistry or scattering poles in acoustical scattering). I will present a mathematical perspective that also includes zeros of the Riemann zeta function (scattering resonances for the Hamiltonian given by the Laplacian on the modular surface) and stresses the importance of different kinds of trapping phenomena, resulting, for instance, in fractal counting laws for resonances.

  • Seminars

    Seminars Colloquia & Seminar
    11/21/2018 Hodge Seminar

    1:30 pm
    12/01/2024
  • Special Seminar
    1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/23/2019 Hodge Seminar

    1:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/5/2018 Hodge Seminar

    1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/28/2018 Hodge Lecture

    1:30 pm
    12/01/2024
  • Special Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Random Matrix & Probability Theory Seminar
    Speaker: Minh-Binh TRAN (SMU & MIT)

    Location: CMSA, Room G02

    Title: On the wave turbulence theory for a stochastic KdV type equation

    Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic  Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave  kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is  $d\ge 2$, the smallness of the nonlinearity $\lambda$ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation.  Unlike the cubic nonlinear Schrodinger equation, for which such a general result is commonly expected without the noise, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen  as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.

  • Seminars

    Seminars Colloquia & Seminar
    5/27/2020 Quantum Matter Seminar

    1:30 pm-3:00 pm
    12/01/2024
  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 02.16.23

    General Relativity Seminar

    Speaker: Kwinten Fransen (UC Santa Barbara)

    Title: Quasinormal Modes from Penrose Limits

    Abstract: In this talk, I will explain how to describe quasinormal modes with large real frequencies using Penrose limits. To do so, I first recall relevant aspects of the Penrose limit, and its resulting plane wave spacetimes, as well as quasinormal modes to subsequently tie these together. Having established the main principle, I will illustrate the usefulness of this point of view with the geometric realization of the emergent symmetry algebra underlying the quasinormal modes in the large real frequency limit and present its application to the astrophysically important example of Kerr black holes. Based on arXiv:2301.06999.

  • Colloquium
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 04.20.2023

    Speaker: Julio Parra Martinez, Caltech

    Title: Black hole collider physics

    Abstract: Despite more than a century since the development of Einstein’s theory, the general relativistic two-body problem remains unsolved. A precise description of its solution is now essential, as it is necessary for understanding the strong-gravity dynamics of compact binaries observed at LIGO/VIRGO/KAGRA and in future gravitational wave observatories. In this talk, I will describe how considering the scattering of black holes and gravitons can shed new light on this problem. I will explain how using modern ideas from collider and particle physics we can calculate scattering observables in classical gravity, and extract the basic ingredients that describe the bound binary dynamics. Such calculations have produced state-of-art predictions for current and future gravitational wave observatories, which open the door for further discovery as we enter this new era of precision gravitational physics.

  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 03.23.23

    General Relativity Seminar

    Speaker: Prahar Mitra (University of Cambridge)

    Title: New Phases of N=4 SYM

    Abstract: We construct new static solutions to gauged supergravity that, via the AdS/CFT correspondence, are dual to thermal phases in N=4 SYM at finite chemical potential. These solutions dominate the micro-canonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. These are constructed in two distinct truncations of gauged supergravity and can be uplifted to solutions of type IIB supergravity. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials. We will also discuss the status of hairy supersymmetric black hole solutions in this theory.

    Based on: https://arxiv.org/pdf/2207.07134.pdf [hep-th]

  • Seminars

    Seminars Colloquia & Seminar
    09-28-2015 Mathematical Physics Seminar

    1:31 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-24-2017 Mathematical Physics Seminar

    1:31 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:31 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    1:32 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:33 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
    1:34 pm
    12/01/2024-04/10/2016

    The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Speakers:

    1. Lydia Bieri (University of Michigan)
    2. Luis Caffarelli (University of Texas at Austin)
    3. Mihalis Dafermos (Princeton University)
    4. Camillo De Lellis (Universität Zürich)
    5. Pengfei Guan (McGill University)
    6. Slawomir Kolodziej (Jagiellonian University)
    7. Melissa Liu (Columbia University)
    8. Duong H. Phong (Columbia University)
    9. Richard Schoen (UC Irvine)
    10. Cliff Taubes (Harvard University)
    11. Blake Temple (UC Davis)
    12. Valentino Tosatti (Northwestern University)
    13. Tai-Peng Tsai (University of British Columbia)
    14. Mu-Tao Wang (Columbia University)
    15. Xu-jia Wang (Australian National University)

    Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Schedule:

    April 8 – Day 1
    8:30amBreakfast
    8:45amOpening remarks
    9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
    10:00am – 10:15amBreak
    10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
    11:15am – 11:30amBreak
    11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
    April 9 – Day 2
    8:45amBreakfast
    9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
    10:00am – 10:15amBreak
    10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
    11:15am – 11:30amBreak
    11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
    April 10 – Day 3
    8:45amBreakfast
    9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
    10:00am – 10:15amBreak
    10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
    11:15am – 11:30amBreak
    11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    10-22-2015 Evolution Equations Seminar

    1:37 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/11/2017 Mathematical Physics Seminar

    1:38 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-18-17 Mathematical Physics Seminar

    1:39 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-17-2015 Evolution Equations Seminar

    1:39 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    9-27-17 RM&PT Seminar

    1:41 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-27-17 Mathematical Physics Seminar

    1:42 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-23-17 Mathematical Physics Seminar

    1:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/11/2019 Random Matrix

    1:45 pm-2:45 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-25-17 RMPT Seminars

    1:45 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:47 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-10-2017 RM & PT Seminar

    1:48 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:51 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-22-2015 Geometric Analysis Seminar

    1:52 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:52 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-30-2015 Random Matrix & Probability Theory Seminar

    1:53 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-13-2017 Mathematical Physics Seminar

    1:53 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:54 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:54 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-15-17 RM & PT Seminar

    1:55 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    1:56 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:58 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    9/9/2020 RMPT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/18/2020 RMPT

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02/26/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
    2:00 pm-7:00 pm
    12/01/2024-09/17/2014

    The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    12.07.2022

    New Technologies in Mathematics Seminar

    Speaker: Cyril Zhang, Microsoft Research

    Title: How do Transformers reason? First principles via automata, semigroups, and circuits

    Abstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models, leading to dramatic advances in natural language understanding, program synthesis, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses, given that they resist interpretation? In this work, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure.

    Specifically, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory, we characterize shortcut solutions, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore, in synthetic experiments, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness, and discuss mitigations.

    Joint work with Bingbin Liu, Jordan Ash, Surbhi Goel, and Akshay Krishnamurthy.

  • Seminars
    2:00 pm-4:00 pm
    12/01/2024

    References: 

    • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
    • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
    • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
    • Nick Sheridan’s IAS and Jussieu lectures. 
    • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA NTM Seminar 10.26.2022

    New Technologies in Mathematics Seminar

    Speakers: João Araújo, Mathematics Department, Universidade Nova de Lisboa and Michael Kinyon, Department of Mathematics, University of Denver

    Title: From Engine to Auto

    Abstract: Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type, etc.
    In this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups, loops, semigroups, logic algebras, lattices and generalizations, quandles, and many more.
  • Seminars

    Seminars Colloquia & Seminar
    Homological Mirror Symmetry Seminar

    2:00 pm-4:00 pm
    12/01/2024-09/15/2017

    The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    09-15-16
    09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

    Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

    Lecture Slides

    09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

    Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

    Lecture Slides

    10-06-16

    Hansol Hong, CMSAhong

    Title: Homological mirror symmetry for elliptic curves

    Abstract:
    We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
    which use homological algebra techniques and formal deformation theory of Lagrangians etc.

    Notes

    Notes (Baris)

    10-13-16

    Yu-Wei Fan, Harvard

    s_yuwei_fan

    Title: Semi-flat mirror symmetry and Fourier-Mukai transform

    Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

     10-20-16

    Tim Large, MIT

    Title: “Symplectic cohomology and wrapped Fukaya categories”

    Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

    Notes

     10-27-16

    Philip Engel, Columbia

    picture

    Title: Mirror symmetry in the complement of an anticanonical divisor”

    According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

    Notes

    11-03-16

    Yusuf Baris Kartal, MIT

    HMS for Del Pezzo surfaces

    I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

    11-10-16No seminar this week
     12-08-16

    Lino Amorim, Boston University

    Title: The Fukaya category of a compact toric manifold

    Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

    Video

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    12/2/2020 Random Matrix and Probability Theory

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024

    New Technologies in Mathematics Seminar

    Speaker: Timo Schick, Meta AI

    Title: Toolformer: Language Models Can Teach Themselves to Use Tools

    Abstract: Language models exhibit remarkable abilities to solve new tasks from just a few examples or textual instructions, especially at scale. They also, paradoxically, struggle with basic functionality, such as arithmetic or factual lookup, where much simpler and smaller models excel. In this talk, we show how these limitations can be overcome by letting language models teach themselves to use external tools via simple APIs. We discuss Toolformer, a model trained to independently decide which APIs to call, when to call them, what arguments to pass, and how to best incorporate the results into future token prediction. Through this, it achieves substantially improved zero-shot performance across a variety of downstream tasks without sacrificing its core language modeling abilities.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5/20/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024

    New Technologies in Mathematics Seminar

    Speaker: Dmitry Krotov, IBM Research – Cambridge

    Title: Modern Hopfield Networks for Novel Transformer Architectures

    Abstract: Modern Hopfield Networks or Dense Associative Memories are recurrent neural networks with fixed point attractor states that are described by an energy function. In contrast to conventional Hopfield Networks, which were popular in the 1980s, their modern versions have a very large memory storage capacity, which makes them appealing tools for many problems in machine learning and cognitive and neurosciences. In this talk, I will introduce an intuition and a mathematical formulation of this class of models and will give examples of problems in AI that can be tackled using these new ideas. Particularly, I will introduce an architecture called Energy Transformer, which replaces the conventional attention mechanism with a recurrent Dense Associative Memory model. I will explain the theoretical principles behind this architectural choice and show promising empirical results on challenging computer vision and graph network tasks.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speakers: Katherine Collins and Albert Jiang, Department of Computer Science and Technology, University of Cambridge

    Title: Evaluating Language Models for Mathematics through Interactions

    Abstract: There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs based on static pairs of inputs and outputs is insufficient to be able to make an informed decision about which LLMs, and under what assistive settings they can be sensibly utilised. Static assessment fails to take into account the essential interactive element in their deployment, and therefore limits how we understand language model capabilities. In this talk, we present our recent work introducing CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We discuss our study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we identify useful scenarios and existing issues of GPT-4 in mathematical reasoning through a series of case studies contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models which communicate uncertainty, respond well to user corrections, and are more interpretable and concise may constitute better assistants; interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models’ algebraic fallibility and discern where they are appropriate to use.

     

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Jimmy Ba, University of Toronto

    Title: How to steer foundation models?

    Abstract: By conditioning on natural language instructions, foundation models and large language models (LLMs) have displayed impressive capabilities as general-purpose computers. However, task performance depends significantly on the quality of the prompt used to steer the model. Due to the lack of knowledge of how foundation models work, most effective prompts have been handcrafted by humans through a demanding trial-and-error process. To reduce the human effort in this alignment process, I will discuss a few approaches to steer these powerful models to excel in various downstream language and image tasks.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/21/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/04/2020 RMPT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/16/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/14/2020 RM&PT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/8/2019 Topology Seminar

    2:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/7/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/22/2019 Social Science Applications Forum

    2:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Johan Commelin, Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

    Title: Breaking the one-mind-barrier in mathematics using formal verification

    Abstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.

    I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.

    Video
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Random Matrix & Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024

    Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

    In the 2020-2021 AY, the Random Matrix and Probability Theory Seminar will take place on select Wednesdays from 2:00 – 3:00pm virtually. This seminar is organized by Christian Brennecke (brennecke@math.harvard.edu ).

    To learn how to attend this seminar, please fill out this form.

    The schedule below will be updated as the details are confirmed.

    Spring 2021:

    DateSpeakerTitle/Abstract
    3/31/2021Philippe Sosoe, Cornell UniversityTitle:  Fluctuation bounds for O’Connell-Yor type systems

    Abstract: The O’Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about this model thanks to remarkable algebraic structure uncovered by O’Connell, Yor and others, basic estimates for the behavior of the tails of the centered partition function for finite N that are available for zero temperature models are missing. I will present an iterative estimate to obtain strong concentration and localization bounds  for the O’Connell-Yor polymer on an almost optimal scale N^{1/3+\epsilon}.

    In the second part of the talk, I will introduce a system of interacting diffusions describing the successive increments of partition functions of different sizes. For this system, the N^{2/3} variance upper bound known for the OY polymer can be proved for a general class of interactions which are not expected to correspond to integrable models.

    Joint work with Christian Noack and Benjamin Landon.

    4/7/2021Yue M. Lu, HarvardTitleHouseholder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Random Matrices

    Abstract: In many problems in statistical learning, random matrix theory, and statistical physics, one needs to simulate dynamics on random matrix ensembles. A classical example is to use iterative methods to compute the extremal eigenvalues/eigenvectors of a (spiked) random matrix. Other examples include approximate message passing on dense random graphs, and gradient descent algorithms for solving learning and estimation problems with random initialization. We will show that all such dynamics can be simulated by an efficient matrix-free scheme, if the random matrix is drawn from an ensemble with translation-invariant properties. Examples of such ensembles include the i.i.d. Gaussian (i.e. the rectangular Ginibre) ensemble, the Haar-distributed random orthogonal ensemble, the Gaussian orthogonal ensemble, and their complex-valued counterparts.A “direct” approach to the simulation, where one first generates a dense n × n matrix from the ensemble, requires at least O(n^2) resource in space and time. The new algorithm, named Householder Dice (HD), overcomes this O(n^2) bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are O(nT) and O(n T^2), respectively, with T being the number of iterations. When T ≪ n, which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint.Finally, the HD algorithm is not just a computational trick. I will show how its construction can serve as a simple proof technique for several problems in high-dimensional estimation
    4/14/2021Canceled
    4/16/2021
    Friday
    Patrick Lopatto (IAS)Title: Fluctuations in local quantum unique ergodicity for generalized Wigner matrices

    Abstract: In a disordered quantum system, delocalization can be understood in many ways. One of these is quantum unique ergodicity, which was proven in the random matrix context by Bourgade and Yau. It states that for a given eigenvector and set of coordinates J, the mass placed on J by the eigenvector tends to N^{-1}|J|, the mass placed on those coordinates by the uniform distribution. Notably, this convergence holds for any size of J, showing that the eigenvectors distribute evenly on all scales.

    I will present a result which establishes that the fluctuations of these averages are Gaussian on scales where |J| is asymptotically less than N, for generalized Wigner matrices with smooth entries. The proof uses new eigenvector observables, which are analyzed dynamically using the eigenvector moment flow and the maximum principle.

    This is joint work with Lucas Benigni.

    4/21/2021Jean-Christophe Mourrat, Courant Institute, NYUTitleMean-field spin glasses: beyond Parisi’s formula?

    Abstract: Spin glasses are models of statistical mechanics encoding disordered interactions between many simple units. One of the fundamental quantities of interest is the free energy of the model, in the limit when the number of units tends to infinity. For a restricted class of models, this limit was predicted by Parisi, and later rigorously proved by Guerra and Talagrand. I will first show how to rephrase this result using an infinite-dimensional Hamilton-Jacobi equation. I will then present partial results suggesting that this new point of view may allow to understand limit free energies for a larger class of models, focusing in particular on the case in which the units are organized over two layers, and only interact across layers.

    Fall 2020:

    DateSpeakerTitle/Abstract
    9/9/2020Yukun He (Zurich)Title: Single eigenvalue fluctuations of sparse Erdős–Rényi graphs

    Abstract: I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdös-Rényi graph $G(N,p)$. I show that if $N^{-1}\ll p \ll N^{-2/3}, then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. The main technical tool of the proof is a rigidity bound of accuracy $N^{-1-\varepsilon}p^{-1/2}$ for the extreme eigenvalues, which avoids the $(Np)^{-1}$-expansions from previous works. Joint work with Antti Knowles.

    10/14/2020David Belius (University of Basel)TitleThe TAP approach to mean field spin glasses

    Abstract: The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated methods  in theoretical physics and mathematics, such as the replica method, which are largely orthogonal to the TAP approach. The TAP approach has the advantage of being interpretable as a variational principle optimizing an energy/entropy trade-off, as commonly encountered in statistical physics and large deviations theory, and potentially allowing for a more direct characterization of the Gibbs measure and its “pure states”. In this talk I will recall the TAP approach, and present preliminary steps towards a solution of mean field spin glass models entirely within a TAP framework.

    10/28/2020Giuseppe Genovese (University of Basel)TitleNon-convex variational principles for the RS free energy of restricted Boltzmann machines

    Abstract: From the viewpoint of spin glass theory, restricted Boltzmann machines represent a veritable challenge, as to the lack of convexity prevents us to use Guerra’s bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will present old and new results around the topic along with some open problems.

    11/4/2020Benjamin Landon (MIT)Title:  Fluctuations of the spherical Sherrington-Kirkpatrick model

    Abstract:  The SSK model was introduced by Kosterlitz, Thouless and Jones as a simplification of the usual SK model with Ising spins. Fluctuations of its observables may be related to quantities from random matrix theory using integral representations.  In this informal talk we discuss some results on fluctuations of this model at critical temperature and with a magnetic field

    11/11/2020
    3:00 – 4:00pm
    Lucas Benigni (University of Chicago)Title:  Optimal delocalization for generalized Wigner matrices

    Abstract: We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result, known as delocalization, to more general entry distributions. After giving a brief overview of the previous results going in this direction, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.

    11/18/2020Simone Warzel (Technical University of Munich)Title:  Hierarchical quantum spin glasses

    Abstract: Hierarchical spin glasses such as the generalised random energy model are known to faithfully model typical energy landscapes in the classical theory of mean-field spin glasses. Their built-in hierarchical structure is known to emerge spontaneously in the spin-glass phase of, e.g., the Sherrington-Kirkpatrick model. In this talk, I will review recent results on the effects of a transversal magnetic field on such hierarchical quantum spin glasses.
    In particular, I will present a formula of Parisi-type for their free energy which allows to make predictions about the phase diagram.
    12/2/2020Sabine Jansen (LMU Munich)TitleThermodynamics of a hierarchical mixture of cubes

    Abstract: The talk discusses a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes of side-lengths 2^j, j\in \N_0. Cubes belong to an admissible set such that if two cubes overlap, then one cube is contained in the other, a picture reminiscent of Mandelbrot’s fractal percolation model. I will present exact formulas for the entropy and pressure, discuss phase transitions from a fluid phase with small cubes towards a condensed phase with a macroscopic cube, and briefly sketch some broader questions on renormalization and cluster expansions that motivate the model. Based on arXiv:1909.09546 (J. Stat. Phys. 179 (2020), 309-340).

    For information on previous seminars, click here

    The schedule will be updated as details are confirmed.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Gabriel Poesia, Dept. of Computer Science, Stanford University

    Title: Peano: Learning Formal Mathematical Reasoning Without Human Data

    Abstract: Peano is a theorem proving environment in which a computational agent can start tabula rasa in a new domain, learn to solve problems through curiosity-driven exploration, and create its own higher level actions. Gabriel will describe the system, present case studies on learning to solve simple algebra problems from the Khan Academy platform, and describe work on progress on learning the Natural Number Game, a popular introduction to theorem proving in Lean for mathematicians.

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    10.19.2022

    New Technologies in Mathematics Seminar

    Speaker: Antonia Creswell, DeepMind

    Title: Towards Faithful Reasoning Using Language Models

    Abstract: Language models are showing impressive performance on many natural language tasks, including question-answering. However, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this, we will introduce Selection-Inference, a faithful reasoning model, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy.

     

     

  • New Technologies in Mathematics Seminar
    2:00 pm-4:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    10.05.2022

    New Technologies in Mathematics Seminar

    Speaker: Guy Gur-Ari, Google Research

    Title: Minerva: Solving Quantitative Reasoning Problems with Language Models

    Abstract: Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA NTM Seminar 09.28.2022

    New Technologies in Mathematics

    Speaker: Surya Ganguli, Stanford University

    Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
    Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size, sometimes achieving exponential scaling, by collecting small carefully curated datasets rather than large random ones.
    References: Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
    Sorscher, Ben, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/31/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/28/2020 RM&PT seminar

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Sean Welleck, CMU, Language Technologies Institute

    Title: Llemma: an open language model for mathematics

    Abstract: We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of mathematical web data, code, and scientific papers. The resulting models show improved mathematical capabilities, and can be adapted to various tasks. For instance, Llemma outperforms the unreleased Minerva model suite on an equi-parameter basis, and is capable of tool use and formal theorem proving without any further fine-tuning. We openly release all artifacts, including the Llemma models, the Proof-Pile II, and code to replicate our experiments. We hope that Llemma serves as a platform for new research and tools at the intersection of generative models and mathematics.

     

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/29/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5/13/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Quantum Matter
    2:00 pm-3:30 pm
    12/01/2024

    Speaker: Clay Cordova (U Chicago)

    Title: Non-Invertible Duality Defects in 3+1 Dimensions

    Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

  • Topological Quantum Matter Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Ceren Dag, Harvard

    Title: Breaking ergodicity: quantum scars and regular eigenstates

    Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411, in peer review.

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo

    2:00 pm-5:00 pm
    12/01/2024-04/03/2018
    1 Oxford Street, Cambridge MA 02138
    Math Science Lectures in Honor of Raoul Bott

    DSC_0170-e1525711590120

    On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

    The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

     

    Cachazo-e1519325938458

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-20-2017 RM & PT Seminar

    2:00 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Special Seminar

    Speaker: Mayuko Yamashita, Kyoto University

    Title: Topological modular forms and heretoric string theory

    Abstract: In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF.

    Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

     

  • Topological Quantum Matter Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker:  Ken K. W. Ma (Northeastern University)

    Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future

    Abstract: The discovery of fractional quantum Hall (FQH) states started a new chapter in modern physics. Nowadays, more than 70 FQH states at different filling factors have been observed. Among them, the FQH state at the filling factor ν=5/2 in GaAs (or the 5/2 state) remains one of the most special and attractive states. Since its discovery in 1987, different possible topological orders have been proposed to describe the 5/2 state. Some of them can host an exotic type of particles, known as non-Abelian anyons. Recent experiments have provided more insights into the understanding of the 5/2 state, but its underlying nature is still under debate.

    In this talk, I will review the basics of the 5/2 state [1] and a more unified theoretical description of different possible topological orders of the 5/2 state that we have recently proposed [2]. I will also review the groundbreaking thermal Hall conductance experiment [3] and the follow-up quantum Hall interface experiments by the Weizmann Institute group [4, 5], and discuss what possible lessons that we can learn from the experimental results. Lastly, I will talk about some possible directions and related topics for future investigations.

    References:

    [1] K. K. W. Ma, M. R. Peterson, V. W. Scarola, and K. Yang, “Fractional quantum Hall effect at the filling factor ν = 5/2” in Encyclopedia of Condensed Matter Physics (Second Edition), edited by T. Chakraborty, Academic Press (2024).
    [2] K. K. W. Ma and D. E. Feldman, “The sixteenfold way and the quantum Hall effect at half-integer filling factors”, Phys. Rev. B 100, 035302 (2019).
    [3] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern, “Observation of half-integer thermal Hall conductance”, Nature (London) 559, 205 (2018).
    [4] B. Dutta, W. Yang, R. Melcer, H. K. Kundu, M. Heiblum, V. Umansky, Y. Oreg, A. Stern, D. Mross, “Distinguishing between non-Abelian topological orders in a quantum Hall system”, Science 375, 193 (2021).
    [5] B. Dutta, V. Umansky, M. Banerjee, and M. Heiblum, “Isolated ballistic non-Abelian interface channel”, Science 377, 1198 (2022).

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Yuanzhi Li, CMU Dept. of Machine Learning and Microsoft Research

    Title: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation

    Abstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking results about this question. Using a synthetic biography dataset, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence, can mitigate this issue. Using linear probing, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations.

    We then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset, so that it could answer “What is the birthday of XXX” with 100% accuracy.  Even so, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly.  Even using Chain of Thought training data only helps the model answer such questions in a CoT manner, not directly.

    We will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example, is a 1B parameter language model enough to store all the knowledge of a middle school student?

     

     

  • Topological Quantum Matter Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Prashant Kumar, University of Chicago

    Title: Emergent composite-fermion Luttinger liquid at the half-filled Landau level

    Abstract: The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, I will present our numerical calculations of the excitation spectrum of this state on infinite cylinders. By comparing our results with a quasi-1D theory of CFs, we show compelling quantitative evidence for the emergence of a Luttinger liquid of composite-fermions at low energies, distinct from that of electrons. I will comment on some future directions.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5/6/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Abhishek Panigrahi, Dept. of Computer Science, Princeton University

    Title: On the Power of Forward pass through Transformer Architectures

    Abstract: Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of study. This talk studies two interesting phenomena.

    In the first half, we explore how and why pre-trained language models, specifically BERT of moderate sizes, can effectively learn linguistic structures like parse trees during pre-training. Specifically, using synthetic data through PCFGs, we show how moderate-sized transformers can perform forward-backward parsing, also known as the inside-outside algorithm, during inference. We further understand the role of the pre-training loss for the model to learn to parse during pre-training.

    In the second half, we consider in-context learning of large language models, where they learn to reason on the fly. An ongoing hypothesis is that transformers simulate gradient descent at inference to perform in-context learning. We propose the Transformer in Transformer (TinT) framework, which creates explicit transformer architectures that can simulate and fine-tune a small pre-trained transformer model during inference. E.g. a 1.3B parameter TINT model can simulate and fine-tune a 125 million parameter model in a single forward pass. This framework suggests that large transformers might execute intricate sub-routines during inference, and provides insights for enhancing their capabilities through intelligent design considerations.

     

  • Math Science Literature Lecture Series
    2:00 pm-3:00 pm
    12/01/2024

    Shing-Tung Yau (Harvard)

    Title: Shiing-Shen Chern as a Great Geometer of 20th Century

    Video | Slides | Article

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024

    New Technologies in Mathematics Seminar

    Speaker: Ronen Eldan, Microsoft Research

    Title: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent

    Abstract: While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity?

    In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4-year-olds typically understand, generated by GPT-3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the state-of-the-art models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for low-resource or specialized domains, and shed light on the emergence of language capabilities in LMs.

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: François Charton, Meta AI

    Title:  Transformers for maths, and maths for transformers

    Abstract: Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics.

    Problems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic, I show that model predictions can be explained, that trained models do not confabulate, and that carefully choosing the training distributions can help achieve better, and more robust, performance.

     

     

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/1/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • General Relativity Seminar
    2:00 pm-3:00 pm
    12/01/2024
    17 Oxford St, Cambridge, MA 02138

    General Relativity Seminar

    Speaker: Suman Kundu (Weizmann Institute)

    Title: ‘Grey Galaxy’ as the endpoint of the Kerr-AdS super radiant blackhole

    Abstract: Kerr AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses near extremality. We conjecture that these instabilities settle down into Grey Galaxies (GG)s – a new class of solutions to Einstein’s equations which we construct for $d=3$. Grey Galaxies consist of an $mega=1$ black hole in the `centre’ of $AdS$, surrounded by a uniformly thick and very large disk of thermal bulk matter that revolves around the centre of AdS at the speed of light. The parametrically low energy density and parametrically large radius of the gas disk are inversely related; as a consequence, the gas carries a finite fraction of the total energy. Grey Galaxy saddles exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr AdS black holes and the gas. In addition to a smooth piece, the boundary stress tensor of these solutions includes a contribution from a delta function localized at the `equator’ of the boundary sphere, a term which may be used as an order parameter that sharply distinguishes GG solutions from ordinary Kerr-Black hole saddles. We also construct `Revolving Black Hole (RBH) saddles’,  macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, that describe black holes revolving around the centre of $AdS$, at the fixed radial location but in a quantum wave function in the angular directions. RBH saddles turn out to be (marginally) entropically subdominant to GG saddles. We argue that supersymmetric versions of RBH saddles exist and have interesting consequences for the spectrum of SUSY states in, e.g.  ${\cal N}=4$ Yang-Mills theory.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Alex Gu, MIT Dept. of EE&CS

    Title: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models

    Abstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

     

  • Seminars

    Seminars Colloquia & Seminar
    4/22/2020 RM&PT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-29-17 RM & PT Seminar

    2:03 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    09-24-2015 Evolution Equations Seminar

    2:03 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2015 Special Random Matrix & Probability Theory Seminar

    2:05 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-18-2015 Random Matrix & Probability Theory Seminar

    2:07 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:08 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 RM&PT Seminar

    2:08 pm
    12/01/2024
  • Colloquium
    2:10 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-29-2017 Mathematical Physics Seminar

    2:11 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    2:11 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-29-2015 Geometric Analysis Seminar

    2:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-28-2015 CMSA Special Seminar

    2:15 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:15 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    2:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-05-2015 Mathematical Physics Seminar

    2:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-15-2015 Evolution Equations Seminar

    2:17 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-6-2017 Mathematical Physics Seminar

    2:17 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-07-2015 Random Matrix & Probability Theory Seminar

    2:19 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:20 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-29-2015 Evolution Equations Seminar

    2:20 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-14-2015 Random Matrix & Probability Theory Seminar

    2:21 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:21 pm
    12/01/2024-03/06/2018

    During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

    You can watch Prof. Sheshmani describe the series here.

    The Syllabus is as follows:

    Date………..TopicVideo/Audio
    1-25-2018Gromov-Witten invariants 

    Definition, examples via algebraic geometry I

    Video / Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture.

     2-01-2018Gromov-Witten invariants 

    Virtual Fundamental Class I (definition)

    Video Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture

    2-13-2018Gromov-Witten invariants 

    Virtual Fundamental Class II (computation in some cases)

     2-15-2018Computing GW invariants 

    Three level GW classes

    Genus zero invariants of the projective plane

     2-20-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) I

    2-22-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) II

    2-27-2018Quantum Cohomology 

    Big Quantum Cohomology I

     3-1-2018Quantum Cohomology 

    Big Quantum Cohomology II

    GW potential

    WDVV equation

    3-6-2018GW invariants via Quantum Cohomology 

    The Quintic threefold case

    The P^2 case

    GW invariants via Quantum Cohomology 

    Dubrovin (quantum) connection

    Nakajima varieties 

    -Algebraic and symplectic reduction

    Nakajima varieties 

    Quasi maps to Nakajima varieties

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) I

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) I

     
    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) IV

     
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    11/11/21 Interdisciplinary Science Seminar

    2:22 pm-3:22 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-11.11.21

    Title: The Kervaire conjecture and the minimal complexity of surfaces

    Abstract: We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture.
    The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/<<w>> is still nontrivial. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of surfaces in HNN extensions. This gives a conceptually simple proof of Klyachko’s theorem that confirms the Kervaire conjecture for any G torsion-free. I will also explain new results obtained using this approach.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-21-2015 Random Matrix & Probability Theory Seminar

    2:22 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Existence of Canonical Metrics on Non-Kähler Geometry
    2:23 pm-2:24 pm
    12/01/2024

    On Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on “Existence of Canonical Metrics on Non-Kähler Geometry.

    In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses works by Jun Li of Fudan University in Shanghai, Ji-Xiang Fu of Fudan University, Ivan Smith of the University of Cambridge, Richard P. Thomas of Imperial College London, Tristan C. Collins of the Massachusetts Institute of Technology, French mathematician Émile Picard, Teng Fei of Rutgers University in Newark, New Jersey, Adam Jacob of the University of California, Davis, and Duong H. Phong of Columbia University.

    More information about this talk can be found on the Simons Foundation website.

  • Colloquium
    2:23 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:24 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    11/18/2021 Interdisciplinary Science Seminar

    2:25 pm-3:25 pm
    12/01/2024

    Title: Amplituhedra, Scattering Amplitudes and Triangulations

    Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    12/2/2021 Interdisciplinary Science Seminar

    2:28 pm-3:28 pm
    12/01/2024

    Title: Polyhomogeneous expansions and Z/2-harmonic spinors branching along graphs

    Abstract: In this talk, we will first reformulate the linearization of the moduli space of Z/2-harmonic spinorsv branching along a knot. This formula tells us that the kernel and cokernel of the linearization are isomorphic to the kernel and cokernel of the Dirac equation with a polyhomogeneous boundary condition. In the second part of this talk, I will describe the polyhomogenous expansions for the Z/2-harmonic spinors branching along graphs and formulate the Dirac equation with a suitable boundary condition that can describe the perturbation of graphs with some restrictions. This is joint work with Andriy Haydys and Rafe Mazzeo.

  • Colloquium
    2:29 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    12/9/21 Interdisciplinary Science Seminar

    2:29 pm-3:29 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-12.09.21-1583x2048

    Title: Numerical Higher Dimensional Geometry

    Abstract: In 1977, Yau proved that a Kahler manifold with zero first Chern class admits a Ricci flat metric, which is uniquely determined by certain “moduli” data. These metrics have been very important in mathematics and in theoretical physics, but despite much subsequent work we have no analytical expressions for them. But significant progress has been made on computing numerical approximations. We give an introduction (not assuming knowledge of complex geometry) to these problems and describe these methods.

  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-Quantum-Matter-in-Mathematics-and-Physics-11.18.21-1583x2048

    Speaker: B. Andrei Bernevig (Princeton University)

    Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

    Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

  • Seminars

    Seminars Colloquia & Seminar
    9/19/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/12/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-28-2015 Random Matrix & Probability Theory Seminar

    2:30 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    2:30 pm-3:30 pm
    12/01/2024-04/26/2020
  • Seminars

    Seminars Colloquia & Seminar
    12/10/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-QMMP-1.18.22-1544x2048-1

    Speaker: Aavishkar Patel (UC Berkeley)

    Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

    Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

  • Seminars

    Seminars Colloquia & Seminar
    11/26/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024

    Speaker: Jeongwan Haah (Microsoft)

    Title: A degeneracy bound for homogeneous topological order

  • Seminars

    Seminars Colloquia & Seminar
    11/21/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    2/27/2019 Colloquium

    2:30 pm-4:00 pm
    12/01/2024
  • Quantum Matter
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-QMMP-1.28.2022-1544x2048-1

    Speaker: Maria Tikhanovskaya (Harvard)

    Title: Maximal quantum chaos of the critical Fermi surface

    Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

  • Seminars

    Seminars Colloquia & Seminar
    11/14/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Colloquium
    2:30 pm-3:00 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    4/10/2019 Colloquium

    2:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/3/2019 Colloquium

    2:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/31/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Social Science Applications Forum

    2:30 pm-4:00 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-QMMP-12.10.21-1544x2048

    Speaker: Lukasz Fidkowski (U Washington)

    Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

    Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

  • Seminars

    Seminars Colloquia & Seminar
    3/7/2019 Social Science Applications Forum

    2:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/18/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    12/01/2024
  • Colloquium
    2:32 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-19-2015 Mathematical Physics Seminar

    2:33 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-20-2015 Geometric Analysis Seminar

    2:35 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-26-2015 Mathematical Physics Seminar

    2:36 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-02-2015 Mathematical Physics Seminar

    2:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    01-26-2018 Mirror Symmetry Seminar

    2:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-03-2015 Geometric Analysis Seminar

    2:39 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-04-2015 Random Matrix & Probability Theory Seminar

    2:40 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-29-2018 Mathematical Physics Seminar

    2:42 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    2:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2-2-2018 Mirror Symmetry Seminar

    2:44 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:44 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:45 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    12/16/2021 Interdisciplinary Science Seminar

    2:46 pm-3:46 pm
    12/01/2024

    Title: Quadratic reciprocity from a family of adelic conformal field theories

    Abstract: We consider a deformation of the 2d free scalar field action by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it’s no longer invariant under the local conformal symmetry algebra. Furthermore, there is an adelic version of this family of global conformal field theories, parametrized by the choice of a number field, together with a Hecke character. Tate’s thesis plays an important role here in calculating Green’s functions of these theories, and in ensuring the adelic compatibility of these theories. In particular, the local L-factors contribute to prefactors of these Green’s functions. We shall try to see quadratic reciprocity from this context, as a consequence of an adelic version of holomorphic factorization of these theories. This is work in progress with B. Stoica and X. Zhong.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/6/2022 Interdisciplinary Science Seminar

    2:47 pm-3:47 pm
    12/01/2024

    Title: The smooth closing lemma for area-preserving surface diffeomorphisms

    Abstract: In this talk, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing result of twisted Seiberg- Witten Floer homology. This is joint work with Dan Cristofaro-Gardiner and Rohil Prasad.

  • Colloquium
    2:47 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:48 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/13/2022 Interdisciplinary Science Seminar

    2:48 pm-3:48 pm
    12/01/2024

    Title: A universal triangulation for flat tori

    Abstract: A celebrated theorem of Nash completed by Kuiper implies that every smooth Riemannian surface has a C¹ isometric embedding in the Euclidean 3-space E³. An analogous result, due to Burago and Zalgaller, states that every polyhedral surface, obtained by gluing Euclidean triangles, has an isometric PL embedding in E³. In particular, this provides PL isometric embeddings for every flat torus (a quotient of E² by a rank 2 lattice). However, the proof of Burago and Zalgaller is partially constructive, relying on the Nash-Kuiper theorem. In practice, it produces PL embeddings with a huge number of vertices, moreover distinct for every flat torus. Based on a construction of Zalgaller and on recent works by Arnoux et al. we exhibit a universal triangulation with less than 10.000 vertices, admitting for any flat torus an isometric embedding that is linear on each triangle. Based on joint work with Florent Tallerie.

  • Seminars

    Seminars Colloquia & Seminar
    11-19-2015 Evolution Equations Seminar

    2:50 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 CMSA Special Lecture

    2:51 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/20/2022 – Interdisciplinary Science Seminar

    2:52 pm-4:52 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-01.20.22-1577x2048

    Title: Markov chains, optimal control, and reinforcement learning

    Abstract: Markov decision processes are a model for several artificial intelligence problems, such as games (chess, Go…) or robotics. At each timestep, an agent has to choose an action, then receives a reward, and then the agent’s environment changes (deterministically or stochastically) in response to the agent’s action. The agent’s goal is to adjust its actions to maximize its total reward. In principle, the optimal behavior can be obtained by dynamic programming or optimal control techniques, although practice is another story.

    Here we consider a more complex problem: learn all optimal behaviors for all possible reward functions in a given environment. Ideally, such a “controllable agent” could be given a description of a task (reward function, such as “you get +10 for reaching here but -1 for going through there”) and immediately perform the optimal behavior for that task. This requires a good understanding of the mapping from a reward function to the associated optimal behavior.

    We prove that there exists a particular “map” of a Markov decision process, on which near-optimal behaviors for all reward functions can be read directly by an algebraic formula. Moreover, this “map” is learnable by standard deep learning techniques from random interactions with the environment. We will present our recent theoretical and empirical results in this direction.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/27/2022 – Interdisciplinary Science Seminar

    2:54 pm-4:54 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-1.27.2022-1583x2048

    Title: Polynomials vanishing at lattice points in convex sets

    Abstract: Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number, which we compute for many (but maybe not all) triangles P.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 Mathematical Physics Seminar

    2:54 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:54 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:55 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:56 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-19-2015 Random Matrix and Probability Theory Seminar

    2:57 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:57 pm
    12/01/2024

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    2/3/2022 – Interdisciplinary Science Seminar

    2:57 pm-4:57 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.03.2022-1583x2048-1

    Title:Quasiperiodic prints from triply periodic blocks

    Abstract: Slice a triply periodic wooden sculpture along an irrational plane. If you ink the cut surface and press it against a page, the pattern you print will be quasiperiodic. Patterns like these help physicists see how metals conduct electricity in strong magnetic fields. I’ll show you some block prints that imitate the printing process described above, and I’ll point out the visual features that reveal conductivity properties.

    Interactive slides:https://www.ihes.fr/~fenyes/seeing/slices/

  • Colloquium
    2:59 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-16-2015 Mathematical Physics Seminar

    2:59 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/31/2020 Quantum Matter Seminar

    3:00 pm-4:30 pm
    12/01/2024
  • Special Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11-17-2015 Geometric Analysis Seminar

    3:00 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2/25/2020 Fluid Dynamics

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2-27-2018 HMS Lecture

    3:00 pm-4:00 pm
    12/01/2024-03/01/2018
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024

    Speaker: Jason Rute, CIBO Technologies

    Title: Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models

    Abstract: Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.

  • New Technologies in Mathematics Seminar
  • Seminars

    Seminars Colloquia & Seminar
    Algebraic Geometry Seminar, Thursdays

    3:00 pm-4:00 pm
    12/01/2024

    This seminar will not be held in the Spring 2018 Semester.

    The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated as details are confirmed.

     

     

    DateNameTitle/Abstract
    09-14-17 Yu-Wei Fan (Harvard Math)

    Entropy of an autoequivalence on Calami-Yau manifolds

    Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

    11-1-17

    *5:00pm, G10*

     Shamil Shakirov, Harvard Math

    Undulation invariants of plane curves

    Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

    11-2-17

     

    Alexander Moll, IHES

    Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

    ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

    11-9-17  TBD  TBD
    11-16-17 TBD TBD
    11-23-17  TBD  TBD
    11-30-17  TBD  TBD
    12-7-17  TBD  TBD
    12-15-17  TBD  TBD
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/4/2019 Special Seminar

    3:00 pm
    12/01/2024
  • Math Science Literature Lecture Series
    3:00 pm-4:00 pm
    12/01/2024
    Lecture_Donaldson-pdf

    Simon Donaldson (Stony Brook)

    Title: The ADHM construction of Yang-Mills instantons

    Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the Yang-Mills instanton equations over the 4-sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics,  and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof,  using Penrose’s twistor theory and results on algebraic vector bundles over projective 3-space. As time permits, we will also discuss some further developments, for example, the work of Nahm on monopoles and connections to Mukai duality for bundles over complex tori.

    Video | Slides

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Quantum Groups

    3:00 pm-4:00 pm
    12/01/2024-05/05/2020
    Lecture_Etingof-pdf

    Pavel Etingof (MIT)

    Title: Quantum Groups

    Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum Yang-Baxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as representation theory, the Langlands program, low-dimensional topology, category theory, enumerative geometry, quantum computation, algebraic combinatorics, conformal field theory, integrable systems, integrable probability, and others. I will review some of the main ideas and examples of quantum groups and try to briefly describe some of the applications.

    Video | Slides

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    10/9/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Probability Seminar
    3:00 pm-4:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 04.10.23

    Probability Seminar

    *Please note room change: Science Center 232*

    Speaker: Ron Peled (Tel Aviv University)

    Title: Localization for random band matrices

    Abstract: I will explain an approach via “an adaptive Mermin-Wagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}.

    Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/03/2018 RMPT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Dmytro Shklyrov HMS Focused Lecture Series

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/25/2019 Math Physics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Fluid Dynamics Seminar

    3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • CMSA EVENT: 2018 Ding Shum Lecture
    3:00 pm-4:00 pm
    12/01/2024
    ding-shum-2018

     

    Screen-Shot-2018-06-14-at-1.41.25-PM

    On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

    This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

    Pictures of the event can be found here.

  • Seminars

    Seminars Colloquia & Seminar
    2/14/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Fluid Dynamics Seminar

    3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/31/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Special Seminar
    3:00 pm-4:30 pm
    12/01/2024-05/09/2019

    In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

    Click here for reference material

    Click here for a syllabus

    Schedule:

    Section 1: Basic setting of derived geometry

    The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

    2/05/2019Lecture 1: Model and с-categoriesVideo
    2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
    2/12/2019Lecture 3: Derived Artin stacksVideo 
    2/14/2019Lecture 4: Cotangent complexes

    Section 2: Loop spaces and differential forms

    The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

    2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
    2/21/2019Lecture 6: Chern characterVideo
    2/26/2019

    Room G02

    Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
    2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
    3/05/2019Lecture 9: Cyclic homologyVideo

    Section 3: Shifted symplectic structures
    Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

    3/07/2019Lecture 10: Definition and existence resultsVideo
    3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
    3/14/2019

    Room G02

    Lecture 12: Lagrangians and Lagrangian fibrationsVideo
    3/26/2019Lecture 13: Intersections of LagrangiansVideo
    3/28/2019

    Room G02

    Lecture 14: Examples and applications 2 (Part I)Video
    4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

    Section 4: Uhlenbeck–Yau construction and correspondence

    4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
    4/09/2019

    Room G02

    Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/7/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/11/2020 RM&PT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars
    3:00 pm-4:00 pm
    12/01/2024
  • Quantum Matter
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/24/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Quantum Matter
    3:00 pm-4:30 pm
    12/01/2024

    Speaker: Jie Wang (Simons Foundation)

    Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

    Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

    [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
    [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
    [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

  • Seminars

    Seminars Colloquia & Seminar
    2/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Probability Seminar
    3:00 pm-4:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 11.30.22

    Probability Seminar

    Title: Lipschitz properties of transport maps under a log-Lipschitz condition

    Abstract: Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting, for applications, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition.

    I will present a construction of a transport map, constructed infinitesimally along the Langevin flow, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds, and which, at the moment, seem to be out of reach of the classically studied optimal transport theory.

    Joint work with Max Fathi and Yair Shenfeld.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/6/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/8/2019 Special Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024

    Speaker: Josef Urban, Czech Technical University

    Title: AI and Theorem Proving

    Abstract: The talk will discuss the main approaches that combine machine learning with automated theorem proving and automated formalization. This includes learning to choose relevant facts for “hammer” systems, guiding the proof search of tableaux and superposition automated provers by interleaving learning and proving (reinforcement learning) over large ITP libraries, guiding the application of tactics in interactive tactical systems, and various forms of lemmatization and conjecturing. I will also show some demos of the systems, and discuss autoformalization approaches such as learning probabilistic grammars from aligned informal/formal corpora, combining them with semantic pruning, and using neural methods to learn direct translation from Latex to formal mathematics.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/28/2018 Random Matrix and Probability Theory Seminar

    3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/7/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024

    Speaker: Thomas Hales, Univ. of Pittsburgh Dept. of Mathematics

    Title: A Mathematical Language

    Abstract: A controlled natural language for mathematics is an artificial language that is designed in an explicit way with precise computer-readable syntax and semantics.  It is based on a single natural language (which for us is English) and can be broadly understood by mathematically literate English speakers.  This talk will describe the design of a controlled natural language for mathematics that has been influenced by the Lean theorem prover, by TeX, and by earlier controlled natural languages. The semantics are provided by dependent type theory.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/14/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/22/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12/5/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/15/2019 Fluid Dynamics

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/1/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    2/10/2022 – Interdisciplinary Science Seminar

    3:00 pm-4:00 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.10.2022-1

    Title: Metric Algebraic Geometry

    Abstract: A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a distance metric. In this talk, we introduce metric algebraic geometry through a discussion of Voronoi cells, bottlenecks, and the reach of an algebraic variety. We also show applications to the computational study of the geometry of data with nonlinear models.

  • Seminars

    Seminars Colloquia & Seminar
    11-23-2015 Mathematical Physics Seminar

    3:01 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Random Matrix & Probability Theory Seminar (2016-2017)

    3:01 pm
    12/01/2024-12/14/2017
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    DSC_0025-768x512

    The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

  • Member Seminar
    3:02 pm
    12/01/2024-01/01/2021

    The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below.

    Previous seminars can be found here.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/29/2021Cancelled
    2/5/2021Itamar ShamirTitle: Boundary CFT and conformal anomalies

    Abstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.

    2/12/2021Louis FanTitle:  Joint distribution of Busemann functions in corner growth models

    Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.

    2/19/2021Daniel JunghansTitle: Control issues of the KKLT scenario in string theory

    Abstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular, we show that, generically, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.

    2/26/2021Tsung-Ju LeeTitle: SYZ fibrations and complex affine structures

    Abstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.

    3/5/2021Cancelled
    3/11/2021

    9:00pm ET

    Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification

    Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

    3/18/2021

    9:00pm ET

    Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification
    Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.
    3/26/2021

    8:30am ET

    Aghil AlaeeTitle:  Rich extra dimensions are hidden inside black holes

    Abstract: In this talk, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.

    4/2/2021
    8:30am ET
    Enno KeßlerTitle: Super Stable Maps of Genus Zero

    Abstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.

    4/9/2021Juven Wang

    Video

    Title: Ultra Unification

    Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate more on the nonperturbative global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.

    4/16/2021Sergiy VerstyukTitle: Deep learning methods for economics

    Abstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way, interpretability of neural networks features prominently.

    4/23/2021Yifan WangTitle: Virtues of Defects in Quantum Field Theories

    Abstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra, precision studies of defect observables, and the implications thereof for strongly coupled dynamics. In this talk, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics, and that open new windows to nonperturbative effects in quantum gravity.

    4/30/2021Yun ShiTitle: D-critical locus structure for local toric Calabi-Yau 3-fold

    Abstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.

    5/7/2021Thérèse Yingying WuTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2

    Abstract: In this talk, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.

    5/14/2021Du PeiTitle: Three applications of TQFTs

    Abstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds, and 3) smooth structures on 4-manifolds.

    5/21/2021Farzan VafaTitle: Active nematic defects and epithelial morphogenesis

    Abstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/11/2020Moran KorenTitle:  Observational Learning and Inefficiencies in Waitlists

    Abstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents, upon receiving an offer, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.

    9/18/2020Michael DouglasTitle: A talk in two parts, on strings and on computers and math

    Abstract: I am dividing my time between two broad topics. The first is string theory, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert,GPT) which have led to breakthroughs on natural language processing, describe their potential for helping us do math, and sketch some related theoretical problems.

    9/25/2020Cancelled – Math Science Lecture
    10/2/2020Cancelled – Math Science Lecture
    10/9/2020Wai Tong (Louis) FanTitle: Stochastic PDE as scaling limits of interacting particle systems

    Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
    In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.

    10/16/2020Tianqi WuTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

    Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.

    10/23/2020Changji XuTitle: Random Walk Among Bernoulli Obstacles

    Abstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk, we will discuss some recent results about the behaviors of the conditional random walk, in quenched, annealed, and biased settings.

    10/30/2020Michael SimkinTitle: The differential equation method in Banach spaces and the $n$-queens problem

    Abstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
    We apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.

    11/6/2020Kenji KawaguchiTitle: Deep learning: theoretical results on optimization and mixup

    Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization, robustness, and generalization, during the optimization process of a neural network. In this talk, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.

    11/13/2020Omri Ben-EliezerTitle: Sampling in an adversarial environment

    Abstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations, the existing statistical literature does not apply.

    We propose a new sequential adversarial model capturing these situations, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results, techniques, and applications reveal close connections to various areas in mathematics and computer science, including VC theory, discrepancy theory, online learning, streaming algorithms, and computational geometry.

    Based on joint works with Noga Alon, Yuval Dagan, Shay Moran, Moni Naor, and Eylon Yogev.

    11/20/2020Charles DoranTitle: The Calabi-Yau Geometry of Feynman Integrals

    Abstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.

    Colloquia & Seminars,Seminars

  • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
    3:02 pm-3:03 pm
    12/01/2024-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Participants:

    Gerard Ben Arous, Courant Institute of Mathematical Sciences

    Alex Bloemendal, Broad Institute

    Arup Chakraburty, MIT

    Zhou Fan, Stanford University

    Alpha Lee, Harvard University

    Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

    David R. Nelson, Harvard University

    Nick Patterson, Broad Institute

    Marc Potters, Capital Fund management

    Yasser Roudi, IAS

    Tom Trogdon, UC Irvine

    Organizers:

    Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

    Please click Program for a downloadable schedule with talk abstracts.

    Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

    Schedule:

    January 9 – Day 1
    9:30am – 10:00amBreakfast & Opening remarks
    10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
    11:00am – 12:00pmYasser Roudi
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 10 – Day 2
    8:30am – 9:00amBreakfast
    9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
    10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
    11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 11 – Day 3
    8:30am – 9:00amBreakfast
    9:00am – 10:00amNick Patterson
    10:00am – 11:00amLucy Colwell
    11:00am – 12:00pmAlpha Lee
    12:00pm – 2:00pmLunch
    2:00pm-4:00pmAfternoon Discussion
    4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
    January 12 – Day 4
    8:30am – 9:00amBreakfast
    9:00am – 10:00amGovind Menon
    10:00am – 11:00amAlex Bloemendal
    11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 13 – Day 5
    8:30am – 9:00amBreakfast
    9:00am – 12:00pmFree for Working
    12:00pm – 2:00pmLunch
    2:00pmFree for Working

    * This event is sponsored by CMSA Harvard University.

  • Colloquium
    3:03 pm-4:00 pm
    12/01/2024

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

  • Colloquium
    3:03 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    3:03 pm-4:03 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.11.22-1583x2048

    Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.

  • Seminars

    Seminars Colloquia & Seminar
    11-24-2015 Geometric Analysis Seminar

    3:03 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-04-2016 Evolution Equations Seminar

    3:04 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    3:05 pm-4:05 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.12.22-1583x2048-1

    Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Sparse Markov Models for High-dimensional Inference

    3:05 pm-4:05 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.17.2022-1-1583x2048-1

    Abstract: Finite order Markov models are theoretically well-studied models for dependent data.  Despite their generality, application in empirical work when the order is larger than one is quite rare.  Practitioners avoid using higher order Markov models because (1) the number of parameters grow exponentially with the order, (2) the interpretation is often difficult. Mixture of transition distribution models (MTD)  were introduced to overcome both limitations. MTD represent higher order Markov models as a convex mixture of single step Markov chains, reducing the number of parameters and increasing the interpretability. Nevertheless, in practice, estimation of MTD models with large orders are still limited because of curse of dimensionality and high algorithm complexity. Here, we prove that if only few lags are relevant we can consistently and efficiently recover the lags and estimate the transition probabilities of high order MTD models. Furthermore, we show that using the selected lags we can construct non-asymptotic confidence intervals for the transition probabilities of the model. The key innovation is a recursive procedure for the selection of the relevant lags of the model.  Our results are  based on (1) a new structural result of the MTD and (2) an improved martingale concentration inequality. Our theoretical results are illustrated through simulations.

  • Colloquium
    3:06 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-02-2016 Geometric Analysis Seminar

    3:06 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Hodge and Noether-Lefschetz Loci Seminar

    3:06 pm
    12/01/2024

    In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

    The schedule below will be updated as talks are confirmed.

    DateTitle/Abstract
    11/7/2018

    Video

    Title: Hodge and Noether-Lefschetz loci

    Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

    In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

    11/14/2018

    Video

    Title:  Integral Hodge conjecture for Fermat varieties

    Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

    11/21/2018

    Video

    Title:  Periods of algebraic cycles

    Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

    11/28/2018

    Video

    Title: Periods of Complete Intersection Algebraic Cycles

    Speaker: Roberto Villaflor

    Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

    12/05/2018

    Room G02

    Title: Some explicit Hodge cycles

    Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

    12/12/2018

    Video

    Title: A conjectural Hodge locus for cubic tenfold

    Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

    1/16/2019Title: Algebraic BCOV anomaly equation

    Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

    1/23/2019

    Video

    Title: A new model for modular curves

    Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

    The talk is based on the article arXiv:1808.01689.

    1/30/2019

    Video

    Title: Constant Yukawa couplings

    Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

    2/6/2019

    Video

    Title: Integrality properties of CY modular forms

    Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

    We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

    2/13/2019Title: Foliations and Hodge loci

    Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

     

    References:

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Singular Set in Obstacle Problems

    3:08 pm-4:08 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.24.2022-1583x2048

    Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.

  • Colloquium
    3:09 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
    3:09 pm-3:10 pm
    12/01/2024-04/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

    Workshop Locations:

    April 4 – 7 (Monday ~ Thursday)

    Room G10,
    20 Garden Street, Cambridge, MA 02138 

    April 8 (Friday)

    EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
    20 Oxford Street, Cambridge, MA 02138

     Participants:

    • Peter Hubyers (Harvard University)
    • Eli Tziperman (Harvard University)
    • Andrew Rhines (University of Washington)
    • Karen McKinnon (UCAR)
    • Douglas MacMartin (Caltech)
    • Thomas Laepple (Alfred Wegener Institute)
    • Yossi Ashkenazy (Ben-Gurion University)
    • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
    • Natesh Pillai (Harvard University)
    • Judah Cohen (Atmospheric and Environmental Research)
    • Cristian Proistosescu (Harvard University)

    Please click Workshop Agenda for a downloadable agenda.

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    02-11-2016 Evolution Equations Seminar

    3:09 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-16-2018 RM & PT Seminar

    3:09 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    3:11 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-03-2016 Random Matrix & Probability Theory Seminar

    3:11 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:11 pm-4:11 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.03.2022-1583x2048-1

    Abstract: While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573.

    Bio: Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research, New England. In 2019, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text, images, and other forms of data, using techniques such as non-convex optimization and tensor decompositions.

  • Colloquium
    3:12 pm-4:12 pm
    12/01/2024

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

  • Interdisciplinary Science Seminar
    3:13 pm-4:13 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.10.2022-1583x2048-1

    Abstract: The gig economy provides workers with the benefits of autonomy and flexibility, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms, an unexplored aspect is the organization identity. In a series of studies, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach, combining methodologies from randomized field experiments, recommender systems, and counterfactual machine learning. Together, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy.

    Bio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning, causal inference, and field experiments in his research, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences, including PNAS, ACM TOIS, WWW, and ICWSM.

  • Colloquium
    3:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 RM & PT Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 RM & PT Seminar

    3:15 pm
    12/01/2024
  • Colloquium
    3:15 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2019 Random Matrix and Probability Theory Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Interdisciplinary Science Seminar
    3:15 pm-4:15 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048

    Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization, during the optimization process. In this talk, I will discuss some mathematical properties of optimization and generalization for deep neural networks.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/6/2019 Random Matrix and Probability Theory Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 RMPT Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02-16-2016 Geometric Analysis Seminar

    3:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-15-2016 Mathematical Physics Seminar

    3:17 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    An operadic structure on supermoduli spaces

    3:17 pm-5:17 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048 (1)

    Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin. Based joint work with Yu. I. Manin and Y. Wu. https://arxiv.org/abs/2202.10321

  • Seminars

    Seminars Colloquia & Seminar
    02-18-2016 Evolution Equations Seminar

    3:19 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:20 pm-5:20 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.231.2022-1583x2048-1

    Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space.  Many fundamental questions have been open for these classical objects.  We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry.  Key objects involve compactifications of embedded vector spaces, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector bundles and the cohomology ring of stellahedral varieties.

  • Seminars

    Seminars Colloquia & Seminar
    02-22-2016 Mathematical Physics Seminar

    3:20 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:22 pm-5:22 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.07.2022-1583x2048-1

    Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson, as well as joint work with (separately) Larson and Jim Bryan.

  • Seminars

    Seminars Colloquia & Seminar
    02-23-2016 Geometric Analysis Seminar

    3:22 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-24-2016 Random Matrix & Probability Theory

    3:23 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
    3:23 pm
    12/01/2024-12/02/2016

    The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

    Organizers:

    Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

    Speakers:

    1. Conan Leung, Chinese University of Hong Kong
    2. Junwu Tu, University of Missouri
    3. Jingyu Zhao, Columbia University
    4. David Treumann, Boston College
    5. Hiro Lee Tanaka, Harvard University
    6. Fabian Haiden, Harvard University
    7. Hansol Hong, Harvard CMSA/Brandeis University
    8. Netanel Blaier, Harvard CMSA/Brandeis University
    9. Garret Alston, The University of Oklahoma

    Please click Workshop Program for a downloadable schedule with talk abstracts.

    Conference Schedule:

    Monday, November 28 – Day 1
    10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
    Lunch
    1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
    4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
    Tuesday, November 29 – Day 2
    10:30am –11:30amConan Leung, “Remarks on SYZ”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
    4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
    Wednesday, November 30 – Day 3
    10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30-2:45pm Break
    2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
    Thursday, December 1 – Day 4
    10:30am –11:30amDavid Treumann“Some examples in three dimensions”
    Lunch
    1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
     2:30-2:45pm Break
    2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

    * This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    02-25-2016 Evolution Equations Seminar

    3:25 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    3:25 pm
    12/01/2024

    During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

    The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

    To learn how to attend, please fill out this form.

    Information on previous colloquia can be found here.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

    Slides

    Video

    Title: Topology protects chiral edge currents in stochastic systems

    Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

    2/3/2021André Luiz de Gouvêa (Northwestern)

    Video

    Title: The Brave Nu World

    Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

    2/10/2021Mykhaylo Shkolnikov (Princeton)

    Video

    Title: Probabilistic approach to free boundary problems and applications

    Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

    2/17/2021
    9:00 – 10:00PM ET
    C. Seshadhri (UC Santa Cruz)

    Video

    Title: Studying the (in)effectiveness of low dimensional graph embeddings

    Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

    2/24/2021David Ben-Zvi (U Texas)

    Video

    Title: Electric-Magnetic Duality for Periods and L-functions

    Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
    A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
    We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

    3/3/2021

    9:00pm ET

    Omer Tamuz (Caltech)Title: Monotone Additive Statistics

    Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

    (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

    3/10/2021

    9:00pm ET

    Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

    Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

    3/17/2021
    9:00pm ET
    Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

    Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

    3/24/2021Weinan E (Princeton)

    Video

    Title: Machine Learning and PDEs

    Abstract: I will discuss two topics:
    (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
    (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

    3/31/2021Thore Graepel (DeepMind/UCL)

    Video

    Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

    Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

    4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

    Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

    4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

    Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

    4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
    Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
    4/28/2021

    9:00 – 10:00pm ET

    Shamit Kachru (Stanford)

    Slides

    Title: K3 Metrics from String Theory

    Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

    Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

    10/7/2020

    10:00am

    Mariangela Lisanti (Princeton University)

    Video

    Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

    Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

    10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

    Video

    Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

    Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
    a) My general argument “against” quantum computers,
    b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
    Relevant papers:
    Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
    wordpress.com/2019/11/stat-quantum2.pdf

    Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
    wordpress.com/2020/08/laws-blog2.pdf

    Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
    wordpress.com/2019/09/main-pr.pdf

    10/21/2020Marta Lewicka (University of Pittsburgh)

    Video

    Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

    Abstract: We propose results that relate the following two contexts:
    (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
    (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
    For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
    geometry and mechanics of materials in the prediction of patterns and shape formation.

    10/28/2020Jonathan Heckman (University of Pennsylvania)

    Video

    Title: Top Down Approach to Quantum Fields

    Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

    11/4/2020
    9:00pm ET
    Surya Ganguli (Stanford)

    Video

    Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

    Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
    Selected References:
    M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
    M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
    A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
    H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
    S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
    B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
    Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
    S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

    11/11/2020Kevin Buzzard (Imperial College London)

    Video

    Title: Teaching proofs to computers

    Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
    I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

    11/18/2020Jose A. Scheinkman (Columbia)

    Video

    Title: Re-pricing avalanches

    Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

    11/25/2020

    10:45am

    Eric J. Heller (Harvard)

    Video

    Title: Branched Flow

    Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

    12/2/2020Douglas Arnold (U of Minnesota)

    Video

    Title: Preserving geometry in numerical discretization

    Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

    12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

    Video

    Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

    Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
    After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

  • Seminars

    Seminars Colloquia & Seminar
    03-03-2016 Evolution Equations Seminar

    3:26 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-5-2018 Mathematical Physics Seminar

    3:27 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    03-29-2016 Geometric Analysis Seminar

    3:27 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    3:28 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
    3:29 pm
    12/01/2024-05/02/2017

    In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

    Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

    Confirmed Speakers

    * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Tomas Berggren (MIT)

    Title: Geometry of the doubly periodic Aztec dimer model

    Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions — known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.

     

     

  • Colloquium
    3:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 05.03.23

    Probability Seminar

    Speaker: Boris Hanin (Princeton)

    Title: Random Neural Networks

    Abstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially L) are large. The first set of results are for deep linear networks, which are simply products of L random matrices of size N x N. I’ll explain how the setting where the ratio L / N is fixed with both N and L large reveals a number of phenomena not present when only one of them is large. I will then state several results about non-linear networks in which this depth-to-width ratio L / N again plays a crucial role and gives an effective notion of depth for a random neural network.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 04.26.23

    Probability Seminar

    Speaker: Jimmy He (MIT)

    Title: Boundary current fluctuations for the half space ASEP

    Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

  • Seminars

    Seminars Colloquia & Seminar
    11/12/2019 Spacetime Seminar

    3:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Spacetime Seminar

    3:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    Harvard Science Center, 1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 04.19.23

    Probability Seminar

    Speaker: Evita Nestoridi (Stonybrook)

    Title: Diagonalizing Transition Matrices of Card Shuffles

    Abstract: In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 04.12.23

    Probability Seminar

    Speaker: Emma Bailey (CUNY)

    Title: Large deviations of Selberg’s central limit theorem

    Abstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance.  It is natural to investigate how far into the tails this Gaussianity persists, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials.  It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations, as well as certain maxima and moments. In this talk I will focus more on the techniques we apply to approach this problem and I will assume no number theoretic knowledge. This is joint work with Louis-Pierre Arguin.

  • Seminars

    Seminars Colloquia & Seminar
    7/29/2020 Quantum Matter Seminar

    3:30 pm-5:00 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 04.05.23

    Probability Seminar

    Speaker: Ahmed El Alaoui (Cornell)

    Title: Sampling from the SK and mixed p-spin measures with stochastic localization

    Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model. This is based on a joint work with Andrea Montanari and Mark Sellke.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/17/2018 RM & PT Seminar

    3:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA Probability Seminar 03.22.23

    Probability Seminar

    Speaker: Wei-Kuo Chen (Minnesota)

    Title: Some rigorous results on the Lévy spin glass model

    Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024

    Probability Seminar

    Speaker: Benjamin Landon (University of Toronto)

    Title: Tail estimates for stationary KPZ models

    Abstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size, including the stochastic six vertex model, the ASEP and a class of non-integrable interacting diffusions.

    Joint work with Christian Noack and Phil Sosoe.

     

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main)

    Title: Solving spin systems, the Babylonian way

    Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues, but quite astonishingly, evidence is mounting that Parisi’s ultrametricity assumption, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024

    Probability Seminar

    Speaker: Vishesh Jain (University of Illinois Chicago)
    Title: Thresholds for edge colorings
    Abstract: We show that if each edge of the complete bipartite graph K_{n,n} is given a random list of C(\log n) colors from [n], then with high probability, there is a proper edge coloring where the color of each edge comes from the corresponding list. We also prove analogous results for Latin squares and Steiner triple systems. This resolves several related conjectures of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-Osthus. I will discuss some of the main ingredients which go into the proof: the Kahn-Kalai conjecture, absorption, and the Lovasz Local Lemma distribution. Based on joint work with Huy Tuan Pham.
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 02.15.23

    Probability Seminar

    Speaker: Zhigang Yao (Harvard CMSA/National University of Singapore)

    Title: Manifold Fitting: An Invitation to Statistics

    Abstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference: https://arxiv.org/abs/1909.10228

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Youngtak Sohn (MIT)

    Title: Universality of max-margin classifiers

    Abstract: Many modern learning methods, such as deep neural networks, are so complex that they perfectly fit the training data. Despite this, they generalize well to the unseen data. Motivated by this phenomenon, we consider high-dimensional binary classification with linearly separable data. First, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule, namely the max-margin classification, has near-optimal prediction accuracy. Then, we discuss universality of max-margin classification. In particular, we characterize the prediction accuracy of the non-linear random features model, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally, we consider the wide-network limit, where the number of neurons tends to infinity, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective.

    Joint work with Andrea Montanari, Feng Ruan, Jun Yan, and Basil Saeed.

  • Quantum Matter
    3:30 pm-5:00 pm
    12/01/2024

    Title: Electric-magnetic duality and the Geometric Langlands duality

    Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    Virtual and in 20 Garden Street, Room G10
    CMSA Probability Seminar 02.08.23

    Probability Seminar

    Speaker: Roland Bauerschmidt (Cambridge)

    Title: Bakry-Emery theory and renormalisation

    Abstract: I will discuss an approach to log-Sobolev inequalities that
    combines the Bakry-Emery theory with renormalisation and present several
    applications. These include log-Sobolev inequalities with polynomial
    dependence for critical Ising models on Z^d when d>4 and singular SPDEs
    with uniform dependence of the log-Sobolev constant on both the
    regularisation and the volume. The talk is based on joint works with
    Thierry Bodineau and Benoit Dagallier.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024

    Probability Seminar

    Speaker: Antoine Maillard (ETH Zürich)

    Title: Fitting ellipsoids to random points

    Abstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science, and is conjectured to undergo a sharp transition: with high probability, it has a solution if n < d^2/4, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture, and highlight some recent progress, in three different directions:

    • A proof that the problem is feasible for n < d^2 / C, for some (large) constant C, significantly improving over previously-known bounds.
    • A non-rigorous characterization of the conjecture, as well as significant generalizations, using analytical methods of statistical physics.
    • A rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.

    This talk is based on the three manuscripts: arXiv:2307.01181, arXiv:2310.01169, arXiv:2310.05787, which are joint works with A. Bandeira, Tim Kunisky, Shahar Mendelson and Elliot Paquette.

  • Seminars

    Seminars Colloquia & Seminar
    4/4/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 12.07.22

    Probability Seminar

    Note location change: Science Center Room 300H

    Speaker: Lior Alon (MIT)

    Title: Fourier quasicrystals and stable polynomials

    Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A, such that the sum of exp(iat), over a in A, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial, and the measures associated with each irreducible factor is either supported on an arithmetic progression, or its support has a bounded intersection with any arithmetic progression. Finally, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix.

    Based on joint work with Pravesh Kothari.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 11.16.22

    Probability Seminar

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 11.09.22 (1)

    Probability Seminar

    Speaker: Hugo Falconet (Courant Institute, NYU)

    Title: Liouville quantum gravity from random matrix dynamics

    Abstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary group at equilibrium, then the measures $|det(U_t – e^{i theta}|^gamma dt dtheta$ converge to the 2d LQG measure with parameter $gamma$, in the limit of large dimension. This extends results from Webb, Nikula and Saksman for fixed time. The proof relies on a new method for Fisher-Hartwig asymptotics of Toeplitz determinants with real symbols, which extends to multi-time settings. I will explain this method and how to obtain multi-time loop equations by stochastic analysis on Lie groups.

    Based on a joint work with Paul Bourgade.

     

  • Seminars

    Seminars Colloquia & Seminar
    3/14/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Social Science Application Forum

    3:30 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-23-2018 RM & PT Seminar

    3:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Quantum Matter
    3:30 pm-5:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-04.22.22-1583x2048-1

    Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Jinyoung Park (NYU)

    Title: Thresholds

    Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a “threshold.” Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Catherine Wolfram (MIT)

    Title: Large deviations for the 3D dimer model

    Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is different from two, explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.

     

  • Seminars

    Seminars Colloquia & Seminar
    10/15/2019 Spacetime Seminar

    3:30 pm-5:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Mathematical Physics Seminar

    3:31 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-01-2016 Geometric Analysis Seminar

    3:32 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:33 pm-5:33 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.28.22-1583x2048-1

    Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole,  length of the shortest closed geodesic on X.

  • Seminars

    Seminars Colloquia & Seminar
    03-10-2016 Evolution Equations Seminar

    3:34 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
    3:34 pm
    12/01/2024-03/30/2017

    The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Photos of the event can be found on CMSA’s Blog.

     Participants:

    Organizers:

    * This event is sponsored by CMSA Harvard University.

    Schedule:

    Monday, March 27

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
    10:00am – 11:00amKieron Burke, University of California, Irvine

    The density functionals machines can learn

    11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

    Tuesday, March 28

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amRyan Adams, HarvardTBA
    10:00am – 11:00amGábor Csányi, University of Cambridge

    Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

     Wednesday, March 29 

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
    10:00am – 11:00amJörg Behler, University of GöttingenTBA
    11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
    4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

    CMSA Colloquium

    Thursday, March 30

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
    10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-09-2016 Random Matrix & Probability Theory

    3:35 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    3:35 pm-4:35 pm
    12/01/2024

    Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Fluid Dynamics Seminar

    3:35 pm
    12/01/2024
  • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
    3:35 pm-3:36 pm
    12/01/2024-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Participants:

    Dan Freed, UT Austin

    Anton Kapustin, California Institute of Technology

    Alexei Y. Kitaev, California Institute of Technology

    Greg Moore, Rutgers University

    Constantin Teleman, University of Oxford

    Organizers:

    Mike Hopkins, Shing-Tung Yau

    * This event is sponsored by CMSA Harvard University.

  • Interdisciplinary Science Seminar
    3:36 pm-5:36 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.05.2022-1583x2048

    Abstract: Although everyone talks about AI + healthcare, many people were unaware of the fact that there are two possible outcomes of the collaboration, due to the inherent dissimilarity between the two giant subjects. The first possibility is healthcare-leads, and AI is for building new tools to make steps in healthcare easier, better, more effective or more accurate. The other possibility is AI-leads, and therefore the protocols of healthcare can be redesigned or redefined to make sure that the whole infrastructure and pipelines are ideal for running AI algorithms.

    Our system Qianfang belongs to the second category. We have designed a new kind of clinic for the doctors and patients, so that it will be able to collect high quality data for AI algorithms. Interestingly, the clinic is based on Traditional Chinese Medicine (TCM) instead of modern medicine, because we believe that TCM is more suitable for AI algorithms as the starting point.

    In this talk, I will elaborate on how we convert TCM knowledge into a modern type-safe large-scale system, the mini-language that we have designed for the doctors and patients, the interpretability of AI decisions, and our feedback loop for collecting data.

    Our project is still on-going, not finished yet.Bio: Yang Yuan is now an assistant professor at IIIS, Tsinghua. He finished his undergraduate study at Peking University in 2012. Afterwards, he received his PhD at Cornell University in 2018, advised by Professor Robert Kleinberg. During his PhD, he was a visiting student at MIT/Microsoft New England (2014-2015) and Princeton University (2016 Fall). Before joining Tsinghua, he spent one year at MIT Institute for Foundations of Data Science (MIFODS) as a postdoc researcher. He now works on AI+Healthcare, AI Interpretability and AI system.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-23-2016 Random Matrix & Probability Theory

    3:37 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Geometric Models for Sets of Probability Measures

    3:38 pm-5:38 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.12.22-1583x2048

    Abstract: Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models.  In this setting, we often are unable to match individual data points but rather need to deduce relationships between entire weighted and unweighted point sets. In this talk, I will summarize our team’s recent efforts to apply geometric techniques to problems in this space, using tools from optimal transport and spectral geometry. Motivated by applications in dataset comparison, time series analysis, and robust learning, our work reveals how to apply geometric reasoning to data expressed as probability measures without sacrificing computational efficiency.

  • Seminars
    3:38 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
    3:40 pm-3:41 pm
    12/01/2024-05/02/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Speakers:

    Orr Ashenberg, Fred Hutchinson Cancer Research Center

    John Barton, Massachusetts Institute of Technology

    Simona Cocco, Laboratoire de Physique Statistique de l’ENS

    Sean Eddy, Harvard University

    Efthimios Kaxiras, Harvard University

    Michael Laub, Massachusetts Institute of Technology

    Debora S. Marks, Harvard University

    Govind Menon, Brown University

    Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

    Andrew Murray, Harvard University

    Ilya Nemenman, Emory College

    Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

    Dave Thirumalai, University of Texas at Austin

    Martin Weigt, IBPS, Université Pierre et Marie Curie

    Matthieu Wyart, EPFL

    More speakers will be confirmed soon.

     

    Schedule:

    (Please click here for a downloadable version of the schedule.)

    Please note that the schedule for both days is currently tentative and is subject to change.

    May 1, Monday

    TimeSpeakerTopic
    9:00-10:00amSean EddyTBA
    10:00-11:00amMike LaubTBA
    11:00am-12:00pmIlya NemenmanTBA
    May 2, Tuesday
    TimeSpeakerTopic
    9:00-10:00amOrr AshenbergTBA
    10:00-11:00amDebora MarksTBA
    11:00am-12:00pmMartin WeigtTBA
    4:30pm-5:30pmSimona CoccoCMSA Colloquia

     

    May 3, Wednesday
    TimeSpeakerTopic
    9:00-10:00amAndrew MurrayTBA
    10:00-11:00amMatthieu WyartTBA
    11:00am-12:00pmRémi MonassonTBA

     

    May 4, Thursday
    TimeSpeakerTopic
    9:00-10:00amDavid ThirumalaiTBA
    10:00-11:00amChris SanderTBA
    11:00am-12:00pmJohn BartonTBA

     

    Organizers:

    Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    03-07-2016 Mathematical Physics Seminar

    3:41 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-26-2018 Mathematical Physics Seminar

    3:42 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-11-2016 Random Matrix & Probability Theory

    3:42 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-08-2016 Geometric Analysis Seminar

    3:44 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
    3:44 pm
    12/01/2024-05/04/2017

    In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

    To register for this event, please click here.

    Confirmed speakers:

    The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

    For a list of lodging options convenient to the Center, please see our recommended lodgings page.

    Schedule:

    The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

    June 5, Monday (Full day)

    TimeSpeakerTopic
    8:30am – 9:0amBreakfast
    9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
    10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

    Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

    Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

    Video

    3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

    Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

    4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
    Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

    June 6, Tuesday (Full day)

    TimeSpeakerTopic
    8:30am – 9:00amBreakfast
    9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

    Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

    Video

    10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

    Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

    Video

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

    Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

    Video

    3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

    Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

    Video


  • Seminars

    Seminars Colloquia & Seminar
    03-21-2016 Mathematical Physics Seminar

    3:46 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-24-2016 Evolution Equations Seminar

    3:47 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: 2017 Big Data Conference
    3:47 pm
    12/01/2024-08/19/2017
    1 Oxford Street, Cambridge MA 02138

    The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

    The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

    Confirmed Speakers:

     

    Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

    • Jörn Boehnke, Harvard University
    • Nikhil Naik, Harvard University
    • Bradly Stadie, Open AI, University of California, Berkeley

     

    Conference Schedule

    A PDF version of the schedule below can also be downloaded here.

    August 18, Friday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amMohammad Akbarpour

    Video

    Title: Information aggregation in overlapping generations and the emergence of experts

    Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

    9:40 am – 10:20 amLucas Janson

    Video

    Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

    Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

    Slides

    10:20 am – 10:50 amBreak
    10:50 pm – 11:30 pmNoureddine El Karoui

    Video

    Title: Random matrices and high-dimensional statistics: beyond covariance matrices

    Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

    11:30 am – 12:10 pmNikhil Naik

    Video

    Title: Understanding Urban Change with Computer Vision and Street-level Imagery

    Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

    (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

    12:10 pm – 12:25 pmVideo #1

    Video #2

    Data Science Lightning Talks
    12:25 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmTracy Ke

    Video

    Title: A new SVD approach to optimal topic estimation

    Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

    We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

    For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

    2:10 pm – 2:50 pmAlbert-László Barabási

    Video

    Title: Taming Complexity: From Network Science to Controlling Networks

    Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

     

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmMarena Lin

    Video

    Title: Optimizing climate variables for human impact studies

    Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

    4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

    Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

    4:40 pm – 5:20 pmTze Leung Lai

    Video

    Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

    Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

    August 19, Saturday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amNatesh Pillai

    Video

    Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

    Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

    9:40 am – 10:20 amRavi Jagadeesan

    Video

    Title: Designs for estimating the treatment effect in networks with interference

    Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

    10:20 am – 10:50 amBreak
    10:50 am – 11:30 amAnnie Liang

    Video

    Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

    Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

    11:30 am – 12:10 pmZak Stone

    Video

    Title: TensorFlow: Machine Learning for Everyone

    Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

    12:10 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmJann Spiess

    Video

    Title: (Machine) Learning to Control in Experiments

    Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

    2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

    Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
    We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmHau-Tieng Wu

    Video

    Title: When Medical Challenges Meet Modern Data Science

    Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

    4:00 pm – 4:40 pmSifan Zhou

    Video

    Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

    Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

     

    To view photos and video interviews from the conference, please visit the CMSA blog.

     

  • Seminars

    Seminars Colloquia & Seminar
    12-07-2015 Mathematical Physics Seminar

    3:49 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-22-2016 Geometric Analysis Seminar

    3:51 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: CMSA/Math Fall Gathering
    4:00 pm-6:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA
    Friday, Sep 22, 2022
    4:00 pm
    All CMSA and Math affiliates are invited.
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Quantum cohomology as a deformation of symplectic cohomology

    4:00 pm-5:00 pm
    12/01/2024
    20211124_Nick-Sheridan_RESCHEDULED_poster

    Abstract: Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Mina Aganagic

    4:00 pm
    12/01/2024-04/10/2019
    1 Oxford Street, Cambridge MA 02138

    On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

    The lectures took place in Science Center, Hall C

    “Two math lessons from string theory”

    Lecture 1:

     

     

     

     

     

    April 9, 2019

    Title: “Lesson on Integrability”

     

    Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

    Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

    Lecture 2:

     

     

     

     

     

    April 10, 2019

    Title: “Lesson on Knot Categorification”

     

    Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

    The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

    This talk is mostly based on joint work with Andrei Okounkov.

     

    Information about last year’s Math Science Bott lecture can be found here. 

    Aganagic

  • Seminars
    4:00 pm-5:00 pm
    12/01/2024

  • Topological Quantum Matter Seminar
    4:00 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Yizhuang You, UC San Diego

    Title: Symmetric Mass Generation
    Abstract: Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Higher rank DT theory from rank 1

    4:00 pm-5:00 pm
    12/01/2024
    20211110_Richard-Thomas_poster

    Abstract: Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

  • Yip Lecture Series

    Yip Lecture Series Event
    Yip Annual Lecture

    4:00 pm-5:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

    The lecture was held from 4:00-5:00pm in Science Center, Hall A.

    Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
  • Math Science Lectures in Honor of Raoul Bott
    4:00 pm-5:30 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    Fibered ribbon knots vs. major 4D conjectures

    Location: Harvard University Science Center Hall A & via Zoom webinar

    Dates: Feb 20 & 22, 2024

    Time: 4:00-5:30 pm

    Directions and Recommended Lodging

    Registration is required.

    Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin and a Clay Research Fellow.

    This will be the fourth annual Math Science Lecture Series held in Honor of Raoul Bott.

    Talk topic:  Fibered ribbon knots vs. major 4D conjectures

    Feb. 20, 2024

    Title: Fibered ribbon knots and the Poincaré conjecture

    Abstract: A knot is “fibered” if its complement in S^3 is the total space of a bundle over the circle, and ribbon if it bounds a smooth disk into B^4 with no local maxima with respect to radial height. A theorem of Casson-Gordon from 1983 implies that if a fibered ribbon knot does not bound any fibered disk in B^4, then the smooth 4D Poincaré conjecture is false. I’ll show that unfortunately (?) many ribbon disks bounded by fibered knots are fibered, giving some criteria for extending fibrations and discuss how one might search for non-fibered examples.

    Feb. 22, 2024

    Title: Fibered knots and the slice-ribbon conjecture

    Abstract: The slice-ribbon conjecture (Fox, 1962) posits that if a knot bounds any smooth disk into B^4, it also bounds a ribbon disk. The previously discussed work of Casson-Gordon yields an obstruction to many fibered knots being ribbon, yielding many interesting potential counterexamples to this conjecture — if any happy to bound a non-ribbon disk. In 2022, Dai-Kong-Mallick-Park-Stoffregen showed that unfortunately( ?) many of these knots don’t bound a smooth disk into B^4 and thus can’t disprove the conjecture. I’ll show a simple alternate proof that a certain interesting knot (the (2,1)-cable of the figure eight) isn’t slice and discuss remaining open questions. This talk is joint with Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.

     

    Talk Chair: Cliff Taubes (Harvard Mathematics)

    Moderator: Freid Tong (Harvard CMSA)


    Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.

  • Probability Seminar
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Wei-Kuo Chen (University of Minnesota)

    Title: A Gaussian convexity for logarithmic moment generating function

    Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy.

     

  • Quantum Matter
    4:00 pm-5:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.18.22-1583x2048-1

    Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045

  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 Colloquium

    4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/12/2020 Colloquium

    4:00 pm-5:00 pm
    12/01/2024
  • Colloquium
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 03.02.2023

    Speaker: Erez Urbach, Weizmann Institute of Science

    Title: The string/black hole transition in anti de Sitter space

    Abstract: String stars, or Horowitz-Polchinski solutions, are string theory saddles with normalizable condensates of thermal-winding strings. In the past, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux), their possible connection to small black holes in AdS, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model, and their relation to the deconfined phase of 3+1 pure Yang-Mills.

  • Colloquium
    4:00 pm
    12/01/2024
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Lagrangians and mirror symmetry in the Higgs bundle moduli space

    4:00 pm-5:00 pm
    12/01/2024

    Abstract: The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed, but  also to open up new features involving finite-dimensional algebras which are deformations of cohomology algebras. Answering some of the questions raised  requires revisiting basic constructions of stable bundles on curves.

  • Probability Seminar
    4:00 pm-5:00 pm
    12/01/2024
    Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

    Probability Seminar

    Speaker: Marius Lemm, University of Tuebingen

    Title: Light cones for open quantum systems
    Abstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely, if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound on the slope of this light cone (i.e., on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang.

     

  • Topological Quantum Matter Seminar
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Roman Geiko, UCLA

    Title: Homotopy classes of loops of Clifford unitaries

    Abstract: We study Clifford locality-preserving unitaries and stabilizer Hamiltonians by means of Hermitian K-theory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two short-range entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu.  https://arxiv.org/abs/2306.09903.

  • Joint Harvard-CUHK-YMSC Differential Geometry
    4:00 pm-5:00 pm
    12/01/2024

    Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class S[A1]. I will describe the resulting geometric structures using a kind of complexified Hitchin system parameterising bundles on curves equipped with pencils of flat connections.

  • Topological Quantum Matter Seminar
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Daniele Guerci, Flatiron Institute

    Title: Chern Mosaic and ideal bands in helical trilayer graphene

    Abstract: In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat bands features the superposition of a Chern -1 and a Chern 2 bands described by the superposition of two lowest Landau level [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [3]. Building on this knowledge, I will discuss the properties of the zero-modes at higher magic angles.

    [1] Y.Mao,D.Guerci,C.Mora, PRB 107, 125423 (2023) [Editors’ Suggestion]

    [2] D.Guerci,Y.Mao,C.Mora, arXiv:2305.03702 (2023)

    [3] D.Guerci,Y.Mao,C.Mora, arXiv:2308.02638 (2023)

  • Colloquium
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.05.22 (1)

    Colloquium

    Please note this colloquium will be held at a special time:  4:00-5:00 pm.

    Speaker: Subir Sachdev (Harvard)

    Title: Quantum statistical mechanics of charged black holes and strange metals
    Abstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.
    Slides: cmsa22
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-28-2016 Mathematical Physics Seminar

    4:08 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-06-2016 Random Matrix & Probability Theory

    4:10 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-30-2016 Random Matrix & Probability Theory Seminar

    4:11 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:12 pm-5:12 pm
    12/01/2024

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Fast Point Transformer

    4:13 pm-5:13 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-06.02.2022-1583x2048-1

    Abstract: The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine the local predictions together. However, this scheme inevitably involves additional stages for pre- and post-processing and may also degrade the final output due to predictions in a local perspective. This talk introduces Fast Point Transformer that consists of a new lightweight self-attention layer. Our approach encodes continuous 3D coordinates, and the voxel hashing-based architecture boosts computational efficiency. The proposed method is demonstrated with 3D semantic segmentation and 3D detection. The accuracy of our approach is competitive to the best voxel-based method, and our network achieves 129 times faster inference time than the state-of-the-art, Point Transformer, with a reasonable accuracy trade-off in 3D semantic segmentation on S3DIS dataset.

    Bio: Jaesik Park is an Assistant Professor at POSTECH. He received his Bachelor’s degree from Hanyang University in 2009, and he received his Master’s degree and Ph.D. degree from KAIST in 2011 and 2015, respectively. Before joining POSTECH, He worked at Intel as a research scientist, where he co-created the Open3D library. His research interests include image synthesis, scene understanding, and 3D reconstruction. He serves as a program committee at prestigious computer vision conferences, such as Area Chair for ICCV, CVPR, and ECCV.

  • Seminars

    Seminars Colloquia & Seminar
    04-14-2016 Evolution Equations Seminar

    4:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-12-2016 Geometric Analysis Seminar

    4:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Special Seminar

    4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Duality String Seminar, Thursdays

    4:15 pm-6:00 pm
    12/01/2024-10/12/2016

    The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

    For details, please visit the website.

    * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

  • Seminars

    Seminars Colloquia & Seminar
    03-31-2016 Evolution Equations Seminar

    4:15 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    4:15 pm-5:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    04-04-2016 Mathematical Physics Seminar

    4:20 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-05-2016 Geometric Analysis Seminar

    4:21 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-11-2016 Mathematical Physics Seminar

    4:22 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    4:23 pm-5:23 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-06.30.22-1583x2048-1

    Abstract: Entanglement is a type of correlation found in composite quantum systems, connected with various non-classical phenomena. Currently, entanglement plays a key role in quantum information applications such as quantum computing, quantum communication, and quantum sensing. In this talk the concept of entanglement will be introduced along with various methods that have been proposed to detect and quantify it. The fundamental role of entanglement in both quantum theory and quantum technology will also be discussed.

    Bio: Spyros Tserkis is a postdoctoral researcher at Harvard University, working on quantum information theory. Before joining Harvard in Fall 2021, he was a postdoctoral researcher at MIT and the Australian National University. He received his PhD from the University of Queensland.

  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    4:24 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-06-2016 Seminar on General Relativity

    4:25 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-11-2016 Random Matrix & Probability Theory Seminar

    4:28 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-13-2016 General Relativity Seminar

    4:29 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Colloquium

    Speaker: Justin Moore (Cornell University)

    Title: Homology, higher derived limits, and set theory

    Abstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the “shape” of the space and can give counterintuitive information about its dimension. One remedy of this is to develop a homology theory based on approximating spaces by polyhedra, computing their homologies, and then taking a limit. This is the approach taken by Steenrod-Sitnikov homology and Lisica and Mardesic’s strong homology. Even within the class of locally compact second countable spaces though, the properties of these homology theories — and the higher derived limits which underly them — are dependent on axioms of set theory beyond ZFC. Recently it was shown that it is consistent with (and therefore independent of) ZFC that strong homology and Steenrod Sitnikov homology coincide in the class of locally compact second countable spaces — and therefore each of these homology theories enjoys the desirable properties of the other. These results also point to how we might develop variants of these homology theories which enjoy their desirable properties, but which are less sensitive to set theory. This is joint work with Nathaniel Bannister, Jeff Bergfalk, and Stevo Todorcevic.

  • Seminars

    Seminars Colloquia & Seminar
    04-20-2016 General Relativity Seminar

    4:30 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: CMSA/MATH Fall Gathering
    4:30 pm-6:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    CMSA/MATH Fall Gathering

    Friday, Sep 23, 2022
    4:30–6:00 pm
    All CMSA and Math affiliates are invited.
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/13/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Joel D. Hamkins (Notre Dame and Oxford)

    Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers

    Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually, and in the talk I shall begin slowly with some easy elementary observations. By the end, however, we shall engage with sophisticated ideas in descriptive set theory, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses, for example, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.

  • Colloquium
    4:30 pm
    12/01/2024
  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Cenke Xu (UCSB)

    Title: Quantum field theory approach to quantum information

    Abstract: We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement and decoherence. The Euclidean space-time path integral allows us to map this problem to a quantum field theory with (temporal) boundary or defects. We therefore investigate two types of quantum many-body systems with nontrivial boundary physics: quantum critical points, and states with nontrivial topology, such as Chern insulator and symmetry protected topological states. For example, we demonstrate that a Wilson-Fisher quantum critical point can be driven into an “extraordinary-log” phase after weak-measurement. Another example is that, we argue that a system with higher form symmetry may be driven to a self-dual phase transition under weak measurement.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Seth Koren (Notre Dame)

    Title: Non-invertible symmetries, leptons, quarks, and why multiple generations

    Abstract: Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof.  After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this theory works by virtue of the SM having the same numbers of colors and generations.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    2/20/2019 Colloquium

    4:30 pm-5:00 pm
    12/01/2024
  • Topological Quantum Matter Seminar
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Kaifeng Bu (Harvard University)

    Title: Quantum information: the interplay of mathematics and physics

    Abstract: I will provide an introduction to quantum information, which points to a new connection with experiment on the one hand, and a potential new area of mathematical analysis on the other. I will introduce two recent results about the application of this new area in quantum information: (1) a novel Quantum Central Limit Theorem (QCLT), and (2) a physically realizable protocol for testing and measuring quantum advantage. This talk is based on a collaboration with Arthur Jaffe, and Weichen Gu (PNAS120(25)2023, arXiv: 2302.08423, arXiv:2306.09292).

     

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Yu-Shen Lin (Boston University)

    Title: Gravitational Instantons

    Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk, we will discuss the Torelli theorem of gravitational instantons, how the cohomological invariants of a gravitational instanton determine them. As a consequence, this leads to a description of the moduli space of gravitational instantons.

  • Colloquium
    4:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02/21/2020 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/25/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Colloquium 12/4/2019

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    4:30 pm-5:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Seminars
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Dana Bartosova (University of Florida)

    Title: What do topological dynamics, combinatorics, and model theory have in common?

    Abstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory.  Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front, however, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts, which is an AIMSQuaRE project with Džamonja, Patel, and Scow.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Jeff W. Lichtman (Harvard University)

    Title: The analytical challenges of connectomics

    Abstract: Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2/14/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/30/2019 Colloquium

    4:30 pm
    12/01/2024
  • Topological Quantum Matter Seminar
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar

    Speaker: Liujun Zou (Perimeter Institute)

    Title: Landscape of quantum phases in quantum materials

    Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.

  • CMSA EVENT: CMSA/MATH Bi-Annual Gathering
    4:30 pm-6:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    On Friday, March 24th, 4:30PM – 6PM, the CMSA will host the CMSA/MATH Bi-Annual Gathering for Harvard CMSA and Math affiliates in the Common Room at 20 Garden Street, Cambridge MA 02138.

  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Topological Quantum Matter Seminar
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Bruno Mera, Instituto Superior Tecnico

    Title: Uniqueness of Landau levels and their analogs with higher Chern numbers

    Abstract: Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged par- ticle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this talk, using the Stone-von Neumann the- orem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions.

    Ref: Bruno Mera and Tomoki Ozawa. Uniqueness of Landau levels and their analogs with higher Chern numbers. arXiv:2304.00866, 2023. arXiv:2304.00866.

     

  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Matthew Foreman (UC Irvine)

    Title: Impossibility results in classical dynamical systems

    Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.

     

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Manuel Cortés-Izurdiaga (University of Malaga)

    Title:  Homotopy categories of rings: some properties and consequences in module categories

    Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the first step in studying other (algebraic) homotopy categories, such as those associated to a scheme. To study these categories, one can use results from the category of modules or the category of complexes. In the first part of the talk, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes, for a natural number N greater than or equal to 2, using some techniques from module categories, such us the deconstruction of a class of modules.

    Another approximation is to use other methods for studying homotopy categories, like those coming from triangulated categories. In some cases, the results obtained in homotopy categories imply some consequences in the category of modules. In the second part of the talk, we will see how to prove the existence of Gorenstein-projective precovers for some specific rings using this approach.

  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/28/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Cameron Krulewski (MIT) and Leon Liu (Harvard)

    Title: A Long Exact Sequence in Symmetry Breaking

    Abstract: We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES).

    The mathematical backbone of the SBLES is the Smith homomorphism, which gives a family of maps between twisted bordism groups. Though many examples have been studied, we give the first completely general account of the Smith homomorphism. We lift it to a map of Thom

    spectra and identify the cofiber, producing a long exact sequence of twisted bordism groups; the SBLES is the Anderson dual of that long exact sequence. Our work develops further the theory of higher Berry phase and its bulk-boundary correspondence and serves as a new computational tool for classifying symmetry protected topological phases.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Boaz Barak (Harvard)

    Title: On Provable Copyright Protection for Generative Model

    Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set.

    Roughly speaking, a generative model p is k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content.

    Joint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870

  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Clay Córdova (U Chicago)

    Title: Anomalies of Non-Invertible Symmetries

  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 RM & PT Seminar

    4:30 pm-5:00 pm
    12/01/2024
  • Seminars
    4:30 pm-5:30 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/4/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/2/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Brian Williams (Boston University)

    Title: Koszul duality in QFT

    Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello, Gaiotto, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory.

     

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Sean Cox, Virginia Commonwealth University

    Title: Predicting non-continuous functions

    Abstract: One of the strangest consequences of the Axiom of Choice is the following Hardin-Taylor 2008 result: there is a “predictor” such that for every function $f$ from the reals to the reals—even nowhere continuous $f$—the predictor applied to $f \restriction (-\infty,t)$ correctly predicts $f(t)$ for *almost every* $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$-invariant predictors? Bajpai-Velleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular, do there exist analytic-invariant predictors? We have partially answered that question: assuming the Continuum Hypothesis (CH), the answer is “no”. Regarding other subgroups of Homeo^+(R), we have affirmative answers that rely solely on topological group-theoretic properties of the subgroup. But these properties are very restrictive; e.g., all known positive examples are metabelian. So there remain many open questions. This is joint work with Aldi, Buffkin, Cline, Cody, Elpers, and Lee.

  • Seminars

    Seminars Colloquia & Seminar
    3/11/2020 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Xuwen Zhu (Northeastern)

    Title: Analysis of ALH* gravitational instantons

    Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.

  • Seminars

    Seminars Colloquia & Seminar
    4/15/2020 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Social Science Application Forum

    4:31 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:33 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-19-2016 Geometric Analysis Seminar

    4:33 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:34 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Mathematical Physics Seminar

    4:34 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-21-2016 Evolution Equations Seminar

    4:35 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:36 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-20-2016 Random Matrix & Probability Theory Seminar

    4:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-26-2016 Geometric Analysis Seminar

    4:38 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:39 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-25-2016 Mathematical Physics Seminar

    4:39 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:41 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-27-2016 Random Matrix & Probability Theory Seminar

    4:42 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-27-2016 General Relativity Seminar

    4:44 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-28-2016 CMSA Special Seminar

    4:45 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/4/2020 Colloquium

    4:45 pm-5:45 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    04-28-2016 Evolution Equations Seminar

    4:46 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-04-2016 General Relativity Seminar

    4:48 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-29-2016 CMSA Special Seminar

    4:49 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    05-02-2016 Mathematical Physics Seminar

    4:50 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-05-2016 Evolution Equations Seminar

    4:51 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-25-2016 General Relativity Seminar

    4:52 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar
    4:54 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    4:56 pm-5:56 pm
    12/01/2024

    Abstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learning-based approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, data-hungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.

  • General Relativity Seminar
    4:58 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    4:59 pm-6:59 pm
    12/01/2024

    Abstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible, and after considerable work by many authors, it is generally conjectured by computer scientists that as the size of matrices becomes large, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk, no knowledge of algebraic geometry or representation theory will be needed.

  • CMSA EVENT: 2017 Ding Shum Lecture
    5:00 pm-6:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

    Learning as a Theory of Everything

    Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

     

  • Seminars

    Seminars Colloquia & Seminar
    2018 HMS Focused Lecture Series

    5:00 pm
    12/01/2024

    As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated below.

    DateSpeakerTitle/Abstract
    January 23, 25, 30 and February 1 

    3-5pm

    *Room G10*

    Ivan Losev 

    (Northeastern)

    Title: BGG category O: towards symplectic duality 

    Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

    Approximate (optimistic) plan of the lectures:

    1) Preliminaries and BGG category O.

    2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

    3) Localization theorem continued. Soergel modules.

    4) Koszul algebras and Koszul duality for categories O.

    Time permitting: other instances of Symplectic duality.

    Prerequisites:

    Semi-simple Lie algebras and their finite dimensional representation theory.

    Some  Algebraic geometry. No prior knowledge of category O/ Geometric

    Representation theory is assumed.

    Scanned from a Xerox Multifunction Device

    February 27, 

    and March 1

    3-5pm

    Colin Diemer 

    (IHES)

    Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

    Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

    March 6 and 8 

    4-5pm

    Adam Jacob 

    (UC Davis)

    Title: The deformed Hermitian-Yang-Mills equation 

    Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

    March 6, 8, 13, 15 

    3-4pm

    Dmytro Shklyarov 

    (TU Chemnitz)

    Title: On categories of matrix factorizations and their homological invariants 

    Abstract: The talks will cover the following topics:

    1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

    2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

    3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

    April 10 & 12 

    3-4pm

    Mauricio Romo 

    (IAS)

    Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

    Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

    Lecture notes

    April 17, 19, 26 

    3-5pm

    Andrew  Harder 

    (University of Miami)

    Title: Perverse sheaves of categories on surfaces 

    Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

    I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

     

    May 15, 17 

    1-3pm

    Charles Doran 

    (University of Alberta)

    Lecture One:
    Title: Picard-Fuchs uniformization and Calabi-Yau geometry
    Abstract:
    Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
    Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

     

    Lecture Two:
    Title: Calabi-Yau fibrations: construction and classification
    Abstract:

    Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

    Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    05-11-2016 Random Matrix & Probability Theory Seminar

    5:00 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
    5:00 pm-6:00 pm
    12/01/2024

    Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Network Science: From the Online World to Cancer Genomics

    Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

     

  • Math Science Literature Lecture Series
    5:00 pm-6:30 pm
    12/01/2024
    Lecture_Sahai-pdf

    Amit Sahai  (UCLA)

    Title: Indistinguishability Obfuscation: How to Hide Secrets within Software

    Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way compiler” remained elusive for decades.

    In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running time) be indistinguishable to any efficient adversary. Leveraging the notion of punctured programming, introduced in our work with Waters in 2013, well over a hundred papers have explored the remarkable power of iO.

    We’ll then discuss the intense effort that recently culminated in our 2020 work with Jain and Lin, finally showing how to construct iO in such a way that, for the first time, we can prove the security of our iO scheme based on well-studied computational hardness conjectures in cryptography.

    Talk chair: Sergiy Verstyuk

    Video

  • Colloquium
    5:00 pm
    12/01/2024
  • CMSA EVENT: 2023 Ding Shum Lecture
    5:00 pm-6:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    Cynthia Dwork

    On March 21, 2023, the CMSA will host the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS and Microsoft Research).

    Time: 5:00-6:00 pm ET

    Location: Harvard University Science Center Hall D

    This event will be held in person and via Zoom webinar.

    Registration is required.

    In-person registration (link)

    Zoom Webinar registration (link)

    Title: Measuring Our Chances: Risk Prediction in This World and its Betters

    Abstract: Prediction algorithms score individuals, assigning a number between zero and one that is often interpreted as an individual probability: a 0.7 “chance” that this child is in danger in the home; an 80% “probability” that this woman will succeed if hired; a 1/3 “likelihood” that they will graduate within 4 years of admission. But what do words like “chance,” “probability,” and “likelihood” actually mean for a non-repeatable activity like going to college? This is a deep and unresolved problem in the philosophy of probability. Without a compelling mathematical definition we cannot specify what an (imagined) perfect risk prediction algorithm should produce, nor even how an existing algorithm should be evaluated. Undaunted, AI and machine learned algorithms churn these numbers out in droves, sometimes with life-altering consequences.

    An explosion of recent research deploys insights from the theory of pseudo-random numbers – sequences of 0’s and 1’s that “look random” but in fact have structure – to yield a tantalizing answer to the evaluation problem, together with a supporting algorithmic framework with roots in the theory of algorithmic fairness.

    We can aim even higher. Both (1) our qualifications, health, and skills, which form the inputs to a prediction algorithm, and (2) our chances of future success, which are the desired outputs from the ideal risk prediction algorithm, are products of our interactions with the real world. But the real world is systematically inequitable. How, and when, can we hope to approximate probabilities not in this world, but in a better world, one for which, unfortunately, we have no data at all? Surprisingly, this novel question is inextricably bound with the very existence of nondeterminism.

    Professor Cynthia Dwork is Gordon McKay Professor of Computer Science at the Harvard University John A. Paulson School of Engineering and Applied Sciences, Affiliated Faculty at Harvard Law School, and Distinguished Scientist at Microsoft. She uses theoretical computer science to place societal problems on a firm mathematical foundation.

    Her recent awards and honors include the 2020 ACM SIGACT and IEEE TCMF Knuth Prize, the 2020 IEEE Hamming Medal, and the 2017 Gödel Prize.

    Talk Chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)
    Moderator: Faidra Monachou (Harvard CMSA)

    The 2020-2022 Ding Shum lectures were postponed due to Covid-19.


    Watch the Lecture on Youtube:

    https://youtu.be/wGpZE8QrCKY

  • CMSA EVENT: Noga Alon Public Talk, 9-7-17
    5:00 pm-6:00 pm
    12/01/2024

    Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Graph Coloring: Local and Global

    Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

  • General Relativity Seminar
    5:02 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:02 pm-6:02 pm
    12/01/2024

    Abstract: Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the ““game” of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.

  • New Technologies in Mathematics Seminar
    5:03 pm-6:03 pm
    12/01/2024

    Abstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions, has allowed major progress on other related questions about M theory, and briefly discuss other applications in field theory and beyond.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-01-2016 Random Matrix & Probability Theory Seminar

    5:03 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-08-2016 Random Matrix & Probability Theory Seminar

    5:04 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:04 pm-6:04 pm
    12/01/2024

    Abstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size.

    We demonstrate the effectiveness of the SAT approach by presenting some recent successes, including the solution of the Boolean Pythagorean Triples problem, computing the fifth Schur number, and resolving the remaining case of Keller’s conjecture. Moreover, we constructed and validated a proof for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular, we discuss our progress on applying SAT solving techniques to the chromatic number of the plane (Hadwiger-Nelson problem), optimal schemes for matrix multiplication, an

  • Seminars

    Seminars Colloquia & Seminar
    07-12-2016 Chinese Economy Seminar

    5:06 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:07 pm-6:07 pm
    12/01/2024

    Speaker: Patrick Massot, Laboratoire de Mathématiques d’Orsay and CNRS

    Title: Why explain mathematics to computers?

    Abstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics, and I won’t assume any prior knowledge about formalization.

  • Seminars

    Seminars Colloquia & Seminar
    07-19-2016 Chinese Economy Seminar

    5:07 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-02-2016 China Gazetteer Seminar

    5:08 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-12-2016 Mathematical Physics Seminar

    5:10 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-19-2016 Mathematical Physics Seminar

    5:11 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:12 pm-6:12 pm
    12/01/2024
    CMSA-NTM-Seminar-11.03.21

    Abstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms.  This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers.  This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-21-2016 Random Matrix & Probability Theory Seminar

    5:13 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    5:15 pm-6:15 pm
    12/01/2024

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-23-2018 Math Physics

    5:15 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    5:15 pm-6:15 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    3/27/2019 Colloquium

    5:15 pm-6:15 pm
    12/01/2024
  • Colloquium
    5:15 pm-6:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4-16-2018 Social Science Applications Forum

    5:16 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:17 pm-6:17 pm
    12/01/2024
    CMSA-NTM-Seminar-12.01.21

    Abstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data.

    In terms of their “microscopic” definition, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem, analogous to criticality, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting, we will explain how the interactions induce representation learning.

    This talk is based on a book, The Principles of Deep Learning Theory, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.

  • Seminars

    Seminars Colloquia & Seminar
    4-20-2018 Social Science Applications Forum

    5:18 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:32 pm-6:32 pm
    12/01/2024
    CMSA-NTM-Seminar-12.08.21

    Abstract: Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured images produced by DALL-E. These large language models are impressive but also very inefficient and costly, which limits their applications and accessibility. We postulate that having an explicit hierarchical architecture is the key to Transformers that efficiently handle long sequences. To verify this claim, we first study different ways to upsample and downsample activations in Transformers so as to make them hierarchical. We use the best performing upsampling and downsampling layers to create Hourglass – a hierarchical Transformer language model. Hourglass improves upon the Transformer baseline given the same amount of computation and can yield the same results as Transformers more efficiently. In particular, Hourglass sets new state-of-the-art for Transformer models on the ImageNet32 generation task and improves language modeling efficiency on the widely studied enwik8 benchmark.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-26-16 Mathematical Physics Seminar

    5:32 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Fluid Dynamics Seminar

    5:33 pm
    12/01/2024

    Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. Links to connect can be found in the schedule below once they are created. 

    In the Spring 2019 Semester, the Center of Mathematical Sciences and Applications will be hosting a seminar on Fluid Dynamics. The seminar will take place on Wednesdays from 3:00-4:00pm in CMSA G10.

    Spring 2020:

    DateSpeakerTitle/Abstract
    2/25/2020Keaton Burns, MITTitle: Flexible spectral simulations of low-Mach-number astrophysical fluids

    Abstract: Fluid dynamical processes are key to understanding the formation and evolution of stars and planets. While the astrophysical community has made exceptional progress in simulating highly compressible flows, models of low-Mach-number stellar and planetary flows typically use simplified equations based on numerical techniques for incompressible fluids. In this talk, we will discuss improved numerical models of three low-Mach-number astrophysical phenomena: tidal instabilities in binary neutron stars, waves and convection in massive stars, and ice-ocean interactions in icy moons. We will cover the basic physics of these systems and how ongoing additions to the open-source Dedalus Project are enabling their efficient simulation in spherical domains with spectral accuracy, implicit timestepping, phase-field methods, and complex equations of state.

    3/4/2020

    G02

    3/11/2020
    3/18/2020
    3/25/2020
    4/1/2020
    4/8/2020 G02
    4/15/2020
    4/22/2020
    4/29/2020

    G02

    5/6/2020
    5/13/2020

    Fall 2019:

    DateSpeakerTitle/Abstract
    9/18/2019Jiawei Zhuang (Harvard)Title: Simulation of 2-D turbulent advection at extreme accuracy with machine learning and differentiable programming

     Abstract: The computational cost of fluid simulations grows rapidly with grid resolution. With the recent slow-down of Moore’s Law, it can take many decades for 10x higher resolution grids to become affordable. To break this major barrier in high-performance scientific computing, we used a data-driven approach to learn an optimal numerical solver that can retain high-accuracy at much coarser grids. We applied this method to 2-D turbulent advection and achieved 4x effective resolution than traditional high-order flux-limited advection solvers. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The model can achieve near-peak FLOPs on CPUs and accelerators via convolutional filters.

    9/25/2019Yantao Yang (Peking University)Title: Double diffusive convection and thermohaline staircases 

    Abstract: Double diffusive convection (DDC), i.e. the buoyancy-driven flow with fluid density depending on two scalar components, is omnipresent in many natural and engineering environments. In ocean this is especially true since the seawater density is mainly determined by temperature and salinity. In upper water of both (sub-) tropical and polar oceans, DDC causes the intriguing thermohaline staircases, which consist of alternatively stacked convection layers and sharp interfaces with high gradients of temperature and salinity. In this talk, we will focus on the fingering DDC usually found in (sub-)tropical ocean, where the mean temperature and salinity decrease with depth. We numerically investigate the formation and the transport properties of finger structures and thermohaline staircases. Moreover, we show that multiple states exit for the exactly same global condition, and individual finger layers and finger layers within staircases exhibit very different transport behaviors.

    10/2/2019No talk
    10/9/2019Samuel Rudy (MIT)Title: Data-driven methods for discovery of partial differential equations and forecasting

    Abstract: A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for partial differential equations with or without parametric dependencies and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will also be discussed.​

    10/16/2019No talk
    10/23/2019Kimee Moore (Harvard)Title: Using magnetic fields to investigate Jupiter’s fluid interior

    Abstract: The present-day interior structure of a planet is an important reflection of the formation and subsequent thermal evolution of that planet. However, despite decades of spacecraft missions to a variety of target bodies, the interiors of most planets in our Solar System remain poorly constrained. In this talk, I will discuss how actively generated planetary magnetic fields (dynamos) can provide important insights into the interior properties and evolution of fluid planets. Using Jupiter as a case study, I will present new results from the analysis of in situ spacecraft magnetometer data from the NASA Juno Mission (currently in orbit about Jupiter). The spatial morphology of Jupiter’s magnetic field shows surprising hemispheric asymmetry, which may be linked to the dissolution of Jupiter’s rocky core in liquid metallic hydrogen. I also report the first definitive detection of time-variation (secular variation) in a planetary dynamo beyond Earth. This time-variation can be explained by the advection of Jupiter’s magnetic field by the zonal winds, which places a lower bound on the velocity of Jupiter’s winds at depth. These results provide an important complement to other analysis techniques, as gravitational measurements are currently unable to uniquely distinguish between deep and shallow wind scenarios, and between solid and dilute core scenarios. Future analysis will continue to resolve Jupiter’s interior, providing broader insight into the physics of giant planets, with implications for the formation of our Solar System.

    10/30/2019No Talk
    11/6/2019Federico Toschi (Eindhoven University of Technology)Title: Deep learning and reinforcement learning for turbulence

    Abstract: This talk tells two stories.

    Chapter 1: We investigate the capability of a state-of-the-art deep neural model at learning features of turbulent velocity signals. Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected. We consider turbulent velocity signals, spanning decades in Reynolds numbers, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of the turbulent signals, we focus on the fundamental question of whether a deep neural network (DNN) is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. Can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning?

    Chapter 2: Thermally driven turbulent flows are common in nature and in industrial applications. The presence of a (turbulent) flow can greatly enhance the heat transfer with respect to its conductive value. It is therefore extremely important -in fundamental and applied perspective- to understand if and how it is possible to control the heat transfer in thermally driven flows. In this work, we aim at maintaining a Rayleigh–Bénard convection (RBC) cell in its conductive state beyond the critical Rayleigh number for the onset of convection. We specifically consider controls based on local modifications of the boundary temperature (fluctuations). We take advantage of recent developments in Artificial Intelligence and Reinforcement Learning (RL) to find -automatically- efficient non-linear control strategies. We train RL agents via parallel, GPU-based, 2D lattice Boltzmann simulations. Trained RL agents are capable of increasing the critical Rayleigh number of a factor 3 in comparison with state-of-the-art linear control approaches. Moreover, we observe that control agents are able to significantly reduce the convective flow also when the conductive state is unobtainable. This is achieved by finding and inducing complex flow fields.

    11/13/2019

     

    2:10pm

    G02

    Martin Lellep (Philipps University of Marburg, Germany)Title: Predictions of relaminarisation in turbulent shear flows using deep learning

     

    Abstract: Given the increasing performance of deep learning algorithms in tasks such as classification during the last years and the vast amount of data that can be generated in turbulence research, I present one application of deep learning to fluid dynamics in this talk. We train a deep learning machine learning model to classify if turbulent shear flow becomes laminar a certain amount of time steps ahead in the future. Prior to this, we use a 2D toy example to develop an understanding how the performance of the deep learning algorithm depends on hyper parameters and how to understand the errors. The performance of both algorithms is high and therefore opens up further steps towards the interpretation of the results in future work.

    11/19/2019

    Tuesday

    3-4 pm

    Pierce Hall 209, 29 Oxford Street 

    Detlef Lohse (University of Twente)Title: Rayleigh vs. Marangoni Abstract: In this talk I will show several examples of an interesting and surprising competition between buoyancy and Marangoni forces. First, I will introduce the audience to the jumping oil droplet – and its sudden death – in a density stratified liquid consisting of water in the bottom and ethanol in the top : After sinking for about a minute, before reaching the equilibrium the droplet suddenly jumps up thanks to the Marangoni forces. This phenomenon repeats about 30-50 times, before the droplet falls dead all the sudden. We explain this phenomenon and explore the phase space where it occurs.

    Next, I will focus on the evaporation of multicomponent droplets, for which the richness of phenomena keeps surprising us. I will show and explain several of such phenomena, namely evaporation-triggered segregation thanks to either weak solutal Marangoni flow or thanks to gravitational effects. The dominance of the latter implies that sessile droplets and pending droplets show very different evaporation behavior, even for Bond number << 1. I will also explain the full phase diagram in the Marangoni number vs Rayleigh number phase space, and show where Rayleigh convections rolls prevail, where Marangoni convection rolls prevail, and where they compete.

    The research work shown in this talks combines experiments, numerical simulations, and theory. It has been done by and in collaboration with Yanshen Li, Yaxing Li, and Christian Diddens, and many others.

    11/20/2019Time: 3:00-3:35 pm

    Speaker:  Haoran Liu

    Title: Applications of Phase Field method: drop impact and multiphase turbulence 

    Abstract: Will a mosquito survive raindrop collisions? How the bubbles under a ship reduce the drag force? In nature and industry, flows with drops and bubbles exist everywhere. To understand these flows, one of the powerful tools is the direct numerical simulation (DNS). Among all the DNS methods, we choose the Phase Field (PF) method and develop some models based on it to simulate the complicated flows, such as flows with moving contact lines, fluid-structure interaction, ternary fluids and turbulence. In this talk, I will firstly introduce the advantages and disadvantages of PF method. Then, I will show its applications: drop impact on an object, compound droplet dynamics, water entry of an object and multiphase turbulence.


    Time: 3:35-4:10 pm

    Speaker:  Steven Chong

    Title: Confined Rayleigh-Bénard, rotating Rayleigh-Bénard, double diffusive convection and quasi-static magnetoconvection: A unifying view on their scalar transport enhancement 

    Abstract: For Rayleigh-Bénard under geometrical confinement, under rotation or the double diffusive convection with the second scalar component stabilizing the convective flow, they seem to be the three different canonical models in turbulent flow. However, previous research coincidentally reported the scalar transport enhancement in these systems. The results are counter-intuitive because the higher efficiency of scalar transport is bought about by the slower flow. In this talk, I will show you a fundamental and unified perspective on such the global transport behavior observed in the seemingly different systems. We further show that the same view can be applied to the quasi-static magnetoconvection, and indeed the regime with heat transport enhancement has been found. The beauty of physics is to understand the seemingly unrelated phenomena by a simplified concept. Here we provide a simplified and generic view, and this concept could be potentially extended to other situations where the turbulent flow is subjected to an additional stabilization.

    11/27/2019
    12/4/2019
    12/11/2019

     

    See previous seminar information here.
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2016 Random Matrix & Probability Theory Seminar

    5:35 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:35 pm-6:35 pm
    12/01/2024
    CMSA-NTM-Seminar-12.15.21

    Abstract: A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular, we will consider the gapped ground states and Gibbs states on low dimensional lattices, which are believed to exhibit ‘low complexity’ due to the widely studied area law behaviour. Here, we will see the crucial role of complexity-theoretic methods in progress on the ‘area law conjecture’ and in the development of efficient algorithms to classically simulate quantum many-body systems.

  • Seminars
    5:36 pm
    12/01/2024

    As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    DateSpeakerTitle/Abstract
    8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

    Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

    9/10/2018Dominic Else, MIT

    Video

    Title: Phases and topology in periodically driven (Floquet) systems

    Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

    9/17/2018Adrian Po, MIT

    Video

    Title: A modern solution to the old problem of symmetries in band theory

    Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

    9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

    Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

    10/1/2018Cancelled
    10/9/2018

    Tuesday

    3:00-4:30pm

    Sagar VijayTitle: Fracton Phases of Matter

    Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

    10/15/2018Ethan LakeTitle: A primer on higher symmetries

    Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

    10/22/2018

    Room G02

    Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

    Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

    10/29/2018Dominic Williamson, Yale

    Video

    Title: Symmetry and topological order in tensor networks

    Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

    11/13/2018

    Tuesday

    3:00-4:30pm

    Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
    11/19/2018X. G. Wen, MIT

    Video

    Title: A classification of 3+1D topological orders

    Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

    12/3/2018

    *Room G02*

    Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

    Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

    12/10/2018

    Room G02

    Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

    Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

    1/8/2019Lukasz Fidkowski, Univ. of Washington

    Video

    Title: Non-trivial quantum cellular automata in 3 dimensions

    Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

    3/18/2019Ari Turner, Technion

    Video

    Title:  Trapping Excitations at Phantasmagoric Wave Vectors

    Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

    4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

    Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

    4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

    Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

    4/16/2019

    Lyman 425

    1:30pm

    Xie Chen (Calthech)Title: Foliated Fracton Order

    Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

    4/24/2019

    10:30am

    Michael Freedman (Microsoft Station Q)

    Video

    Title: Quantum cellular automata in higher dimensions

    Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

    4/26/2019

    10:30am

    Maissam Barkeshli (University of Maryland)

    Video

    Title: Relative anomalies in (2+1)D symmetry enriched topological states

    Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

    5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

    Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

    5/9/2019

    10:30am

    Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

    Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

    5/28/2019

    10:30am

    Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

     

    Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

    7/18/2019Eslam Khalaf (Harvard)

    Title: Dynamical correlations in anomalous disordered wires

    Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
    The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
    The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
  • Seminars

    Seminars Colloquia & Seminar
    Spacetime and Quantum Mechanics Seminar

    5:38 pm
    12/01/2024

    As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

    DateSpeakerTitle/Abstract
    9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
    19/18/2019

    2:00pm

    G02

    Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
    9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

    Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

    Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

    These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

    Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

    9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
    10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
    10/10/2019

    3:30pm

    Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
    10/15/2019

    Tuesday

    3:30pm

     

    Sergey Fomin (Univ. of Michigan)

     

    Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
    10/18/2019

    Friday 

    G02

    Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
    10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
    11/1/2019

    SC 232

    1:30pm

    George Lusztig (MIT)Title: Total positivity in Springer fibres
    11/12/2019

    Tuesday

    G02

    3:30pm

     

    Pierpaolo Mastrolia (University of Padova)

    Title: Feynman Integrals and Intersection Theory
    11/14/2019

    G02

    Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
    11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
    11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
    12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

    Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

     12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
    12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

    Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/10/2018 Math-Physics Seminar

    5:41 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-05-2016 Random Matrix & Probability Theory Seminar

    5:41 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    5:42 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/14/2019 Random Matrix and Probability Theory Seminar

    5:45 pm
    12/01/2024
  • Seminars
    5:48 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    5:52 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    5:52 pm-6:52 pm
    12/01/2024

    Abstract:  Online marketplaces are the main engines of legal and illegal e-commerce, yet the aggregate properties of buyer-seller networks behind them are poorly understood. We analyse two datasets containing 245M transactions (16B USD)  between 2010 and 2021 involving online marketplaces: 28 dark web marketplaces (DWM), unregulated markets whose main currency is Bitcoin, and 144 product markets of one regulated e-commerce platform. We show how transactions in online marketplaces exhibit strikingly similar patterns of aggregate behavior despite significant differences in language, products, time, regulation, oversight, and technology. We find remarkable regularities in the distributions of (i) transaction amounts, (ii) number of transactions, (iii) inter-event times, (iv) time between first and last transactions. We then show how buyer behavior is affected by the memory of past interactions, and draw on these observations to propose a model of network formation able to reproduce the main stylised facts of the data. Our findings have important implications for understanding market power on online marketplaces as well as inter-marketplace competition.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/17/2018 Math-Physics Seminar

    5:53 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/24/2018 Math-Physics Seminar

    5:55 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    5:56 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    5:59 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
    6:00 pm-6:01 pm
    12/01/2024-10/06/2017

    The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

    • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
    • Linear patterns in the primes (Green, Tao, Ziegler);
    • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
    • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

    Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

    • Constructions of pseudorandom objects (eg. extractors and expanders);
    • Constructions of extremal objects (eg. BCH codes);
    • Property testing (eg. testing linearity);
    • Algebraic algorithms (eg. matrix multiplication).

    The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

    Monday, October 2

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

    Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

    The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    10:20-11:00amCoffee Break 
    11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

    Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    12:00-1:30pmLunch 
    1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

    Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

    Joint work with Sivakanth Gopi

    2:20-3:00pmCoffee Break 
    3:00-3:50pmFernando Shao

    Large deviations for arithmetic progressions

    Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

    4:00-6:00pmWelcome Reception

    Tuesday, October 3

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amEmanuele ViolaInterleaved group products

    Authors: Timothy Gowers and Emanuele Viola

    Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

    These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

    10:20-11:00amCoffee Break
    11:00-11:50amVsevolod LevOn Isoperimetric Stability

    Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

    As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

    We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

    12:00-1:30pmLunch
    1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

    Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

    Joint work with Venkata Gandikota and Badih Ghazi.

    2:20-3:00pmCoffee Break
    3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

    Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

    Wednesday, October 4

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

    Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

    Joint work with Thomas Bloom.

    10:20-11:00amCoffee Break 
    11:00-11:50amThomas BloomBounds on capsets via properties of spectra

    This is a continuation of the previous talk by Olof Sisask.

    12:00-1:30pmLunch 
    1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

    Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

    2:20-3:00pmCoffee Break
    3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

    Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

    When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

    Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

    Thursday, October 5

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

     Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

    I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

    Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

    10:20-11:00amCoffee Break
    11:00-11:50amJulia WolfStable arithmetic regularity

    The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

    Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

    This is joint work with Caroline Terry.

    12:00-1:30pmLunch 
    1:30-2:20pmWill Sawin

    Constructions of Additive Matchings

    Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

    2:20-3:00pmCoffee Break
    3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

    Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

    Friday, October 6

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

    Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

    Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

    10:20-11:00amCoffee Break
    11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

    Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

    This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

    Joint work with Hamed Hatami and Shachar Lovett

    12:00-1:30pmLunch
    1:30-2:20pmGuy Kindler

    From the Grassmann graph to Two-to-Two games

    Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

    The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

    These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

    This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

  • CMSA EVENT: Current Developments In Mathematics 2018
    6:00 pm-5:00 pm
    12/01/2024-11/17/2018
    CDM2018

    Current Developments in Mathematics 2018 Conference.

    Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

    Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

    Harvard University Science Center, Hall B

    Visit the conference page here 

  • New Technologies in Mathematics Seminar
    6:00 pm-7:00 pm
    12/01/2024
    CMSA-New-Technologies-Seminar-01.26.2022-1553x2048-1

    Abstract: Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the four colour theorem are among the most notable. Up until now there hasn’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk we will discuss the results of our recent Nature paper, where we worked together with top mathematicians to use machine learning to achieve two new results – proving a new connection between the hyperbolic and geometric structure of knots, and conjecturing a resolution to a 50-year problem in representation theory, the combinatorial invariance conjecture. Through these examples we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/01/2018 Math-Physics Seminar

    6:01 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
    6:02 pm
    12/01/2024-03/15/2018
    Fluid turbulence

    The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Speakers: 

  • General Relativity Seminar
    6:03 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/08/2018 Math-Physics Seminar

    6:04 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:05 pm-7:05 pm
    12/01/2024
    CMSA-NTM-Seminar-02.02.2022-2-1583x2048

    Abstract: In this talk, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry, it is possible to provide a principled view on such GNN architectural choices as positional encoding and graph rewiring as well as explain and remedy the phenomena of oversquashing and bottlenecks.

  • CMSA EVENT: Blockchain Conference
    6:05 pm
    12/01/2024-01/25/2018
    Blockchain

    On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

    https://youtu.be/FyKCCutxMYo

    List of registrants

    Photos

    Speakers: 

  • Seminars
    6:05 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    6:06 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
    6:07 pm
    12/01/2024-11/17/2017

    The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

    Click here for a list of registrants.

    Monday, Nov. 13

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Jozsef Solymosi

     

    On the unit distance problem

    Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

     

    Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

    Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Andrew Hoon Suk

    Ramsey numbers: combinatorial and geometric

    Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Josh Zahl

    Cutting curves into segments and incidence geometry

    4:00-6:00pmWelcome Reception

    Tuesday, Nov. 14

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Péter Pál Pach

    Polynomials, rank and cap sets

    AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

    10:30-11:00amCoffee Break
    11:00-12:00pmJordan Ellenberg

    The Degeneration Method

    Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Larry GuthThe polynomial method in Fourier analysis

    Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

     

    2:30-3:00pm

    Coffee Break
    3:00-4:00pmOpen Problem

    Wednesday, Nov. 15

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

     

    Avi Wigderson

    The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

    Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

    In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

    In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

    This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

    I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

    (despite the fact that a random such tensor has rank quadratic in n).

    No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Venkat Guruswami

    Subspace evasion, list decoding, and dimension expanders

     Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

    Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

    This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

    (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

    12:00-1:30pmLunch
    1:30-2:30pm

     

    David Conlon

    Finite reflection groups and graph norms

    Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

     

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Laszlo Miklós Lovasz

    Removal lemmas for triangles and k-cycles.

    Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

    In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

    The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

    Thursday, Nov. 16

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Janos PachLet’s talk about multiple crossings

    Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Misha Rudnev

    Few products, many sums

    Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

    $$

    |A|^{10} \ll |A-A|^4|AA|^4

    $$

    to

    $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

    The other is the bound 

    $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Adam Sheffer

    Geometric Energies: Between Discrete Geometry and Additive Combinatorics

    Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Boris Bukh

    Ranks of matrices with few distinct entries

    Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

    Friday, Nov. 17

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Benny Sudakov

    Submodular minimization and set-systems with restricted intersections

    AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

    We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

    Joint work with M. Nagele and R. Zenklusen

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Robert Kleinberg 

    Explicit sum-of-squares lower bounds via the polynomial method

    AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

    Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

    Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

    This is joint work with Sam Hopkins.

    12:00-1:30pmLunch

     

  • New Technologies in Mathematics Seminar
    6:07 pm-7:07 pm
    12/01/2024
    CMSA-NTM-Seminar-02.09.2022-1553x2048

    Abstract: Over the past several years, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning, leading to advances in natural language processing, computer vision, code synthesis, protein structure prediction, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet, there is at present limited principled understanding of the reasons for its success. In this talk, I’ll explain how attention mechanisms and Transformers work, and then I’ll share the results of a preliminary investigation into why they work so well. In particular, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions, with statistical generalization guarantees akin to sparse regression.

  • New Technologies in Mathematics Seminar
    6:09 pm-7:09 pm
    12/01/2024
    CMSA-NTM-Seminar-02.16.2022-1553x2048

    Abstract: Hyperbolic manifolds are a class of Riemannian manifolds that are important in mathematics and physics, playing a prominent role in topology, number theory, and string theory. Associated with a given hyperbolic metric is a sequence of numbers corresponding to the discrete eigenvalues of the Laplace-Beltrami operator. While these eigenvalues usually cannot be calculated exactly, they can be found numerically and must also satisfy various bounds. In this talk, I will discuss a new approach for finding numerical bounds on the eigenvalues of closed hyperbolic manifolds using general consistency conditions and semidefinite programming, inspired by the approach of the conformal bootstrap from physics. Although these bootstrap bounds follow from seemingly trivial consistency conditions, they are surprisingly strong and are sometimes almost saturated by actual manifolds; for example, one such bound implies that the first nonzero eigenvalue of a closed hyperbolic surface must be less than 3.83890, and this is very close to being saturated by a particular genus-2 surface called the Bolza surface. I will show how to derive this and other bounds and will discuss some possible future directions for this approach.

  • Special Seminar
    6:10 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:11 pm-6:12 pm
    12/01/2024-10/25/2016

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/10/2018 RM & PT Seminar

    6:11 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:11 pm-7:11 pm
    12/01/2024
    03.2.2022-1553x2048-1

    Abstract:  Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes, and prospects for RL and other techniques.

  • General Relativity Seminar
    6:12 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:13 pm-7:13 pm
    12/01/2024
    CMSA-NTM-Seminar-03.09.2022

    Abstract: We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time.
    We curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics, Chemical Engineering, Chemistry, Computer Science, Economics, Electrical Engineering, Materials Science, Mathematics, Mechanical Engineering, Nuclear Science, Physics, and Statistics.
    We generate new questions and use them in a Columbia University course, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations, again for the first time.
    Our approach consists of five steps:
    (i) Given course questions, turn them into programming tasks;
    (ii) Automatically generate programs from the programming tasks using a Transformer model, OpenAI Codex, pre-trained on text and fine-tuned on code;
    (iii) Execute the programs to obtain and evaluate the answers;
    (iv) Automatically explain the correct solutions using Codex;
    (v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.
    This work is a significant step forward in applying machine learning for education, automating a considerable part of the work involved in teaching.
    Our approach allows personalization of questions based on difficulty level and student backgrounds, and scales up to a broad range of courses across the schools of engineering and science.

    This is joint work with students and colleagues at MIT, Harvard University, Columbia University, Worcester Polytechnic Institute, and the University of Waterloo.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-03-16 Mathematical Physics Seminar

    6:13 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:14 pm-7:14 pm
    12/01/2024
    CMSA-NTM-Seminar-03.23.2022-1553x2048-1

    Abstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems,  without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark,  automatically solving multiple challenging problems drawn from high school olympiads.

  • Seminars

    Seminars Colloquia & Seminar
    10/15/2018 Topology Seminar

    6:14 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:15 pm-7:15 pm
    12/01/2024
    CMSA-NTM-Seminar-03.30.2022-1583x2048-1

    Abstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this talk, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.

    Video

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/15/2018 Math Physics Seminar

    6:15 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-12-2016 Random Matrix & Probability Theory Seminar

    6:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:17 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-24-2016 Random Matrix & Probability Theory Seminar

    6:18 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:19 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2018 RM & PT Seminar

    6:19 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:20 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:22 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/22/2018 Mathematical Physics Seminar

    6:24 pm
    12/01/2024
  • Member Seminar
    6:24 pm
    12/01/2024

    No additional detail for this event.

  • Member Seminar
    6:26 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:27 pm
    12/01/2024

    No additional detail for this event.

  • Member Seminar
    6:29 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:30 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:31 pm-7:31 pm
    12/01/2024

    Title: Naturalness and muon anomalous magnetic moment

    Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:32 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    6:34 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:34 pm-7:34 pm
    12/01/2024

    Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

    Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

  • Seminars
    6:36 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:37 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:37 pm-7:37 pm
    12/01/2024

    Title: Cornering the universal shape of fluctuations and entanglement

    Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

    Ref: arXiv:2102.06223

  • Quantum Matter
    6:38 pm-7:38 pm
    12/01/2024

    Title: Quantum gravity from quantum matter

    Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    9/23/2021 Interdisciplinary Science Seminar

    6:40 pm-8:40 pm
    12/01/2024

    Title: The number of n-queens configurations

    Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

    Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

  • Member Seminar
    6:40 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-17-16 Mathematical Physics Seminar

    6:41 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    10/7/2021 Interdisciplinary Science Seminar

    6:41 pm
    12/01/2024

    Title: SiRNA Targeting TCRb: A Proposed Therapy for the Treatment of Autoimmunity

    Abstract: As of 2018, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent, treatment options remain relatively poor, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness over time. Given this, new forms of therapy are needed. To this end, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted, novel means of therapy for the treatment of autoimmune disorders.

    This talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    10/14/2021 Interdisciplinary Science Seminar

    6:42 pm-8:42 pm
    12/01/2024

    Title: D3C: Reducing the Price of Anarchy in Multi-Agent Learning

    Abstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.

  • Quantum Matter
    6:44 pm-7:44 pm
    12/01/2024

    Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

    Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
    Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    10/21/2021 Interdisciplinary Science Seminar

    6:44 pm-8:44 pm
    12/01/2024

    Title: Mathematical resolution of the Liouville conformal field theory.

    Abstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David, Kupiainen, Rhodes, Vargas.

    Many works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable », the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras, representations of Virasoro algebras, the theory of conformal blocks). However, for Liouville Theory this was not done at the mathematical level by algebraic methods.

    I’ll explain how to combine probabilistic, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure, which is viewed as the space of fields, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space.

    This is joint work with A. Kupiainen, R. Rhodes and V. Vargas.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    ARCH: Know What Your Machine Doesn’t Know

    6:45 pm-8:45 pm
    12/01/2024

    Speaker: Jie Yang, Delft University of Technology

    Title: ARCH: Know What Your Machine Doesn’t Know

    Abstract: Despite their impressive performance, machine learning systems remain prohibitively unreliable in safety-, trust-, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk, I will present our ongoing work on ARCH, a knowledge-driven, human-centered, and reasoning-based tool, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk, I will present several applications in which ARCH is currently being developed and tested, including health, finance, and smart buildings.

  • Quantum Matter
    6:46 pm-7:46 pm
    12/01/2024

    Title: Three-particle mechanism for pairing and superconductivity

    Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

    [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
    [2] V. Crepel and L. Fu, arXiv:2103.12060
    [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    11/4/21 CMSA Interdisciplinary Science Seminar

    6:46 pm-8:46 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-11.04.21-1583x2048-1

    Title: Exploring Invertibility in Image Processing and Restoration

    Abstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., image-to-video conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:46 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:47 pm-7:47 pm
    12/01/2024

    Title: The Hilbert Space of large N Chern-Simons matter theories

    Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

  • Member Seminar
    6:52 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:53 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:54 pm-7:54 pm
    12/01/2024

    Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

    Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:54 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    6:59 pm
    12/01/2024

    No additional detail for this event.

  • Yip Lecture Series

    Yip Lecture Series Event
    Third Annual Yip Lecture

    7:00 pm-8:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

    Time: 7:00-8:00 pm ET

    Location: Harvard Science Center Hall A

    Registration is required.

    In-person Registration

    Zoom Webinar Registration

    Title: Black Holes: The Most Mysterious Objects in the Universe

    Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.

    Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.

    Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)

    Moderator: Daniel Kapec (Harvard CMSA)

    The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

     

    https://youtu.be/RpQhQ855WUY


    The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

  • Seminars
    7:00 pm
    12/01/2024

    No additional detail for this event.

  • Yip Lecture Series
    7:00 pm-8:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    Yip2022_poster_web

    Harvard CMSA hosted the second annual Yip Lecture on April 4, 2022.

    The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.
    This year’s speaker was Avi Loeb (Harvard).

     

    Extraterrestrial Life

    Abstract: Are we alone? It would be arrogant to think that we are, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System, such as `Oumuamua.

    Abraham (Avi) Loeb is the Frank B. Baird, Jr., Professor of Science at Harvard University and a bestselling author (in lists of the New York Times, Wall Street Journal, Publishers Weekly, Die Zeit, Der Spiegel, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986), led the first international project supported by the Strategic Defense Initiative (1983–1988), and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books, including most recently, Extraterrestrial (Houghton Mifflin Harcourt, 2021), and nearly a thousand papers (with an h-index of 118) on a wide range of topics, including black holes, the first stars, the search for extraterrestrial life, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences, the American Physical Society, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade.

    Click here for Loeb’s commentaries on innovation and diversity.

    Website: https://www.cfa.harvard.edu/~loeb/

    See the Harvard Gazette article featuring Avi Loeb: “Oh, if I could talk to the aliens” published March 8, 2022.

    Prof. Loeb’s books:
    Extraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)
    Life in the Cosmos: From Biosignatures to Technosignatures (2021)

    Avil Loeb is the head of the Galileo Project at Harvard.


    The previous Yip Lecture featured Peter Galison (Harvard), who spoke on the EHT’s hunt for an objective image of a black hole.

  • Seminars
    7:03 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-31-16 Mathematical Physics Seminar

    7:05 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    7:30 pm-9:00 pm
    12/01/2024
  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
    CMSA-QMMP-02.09.2022-1544x2048-1

    Speaker: Yuji Tachikawa (Kavli IPMU, U Tokyo)

    Title: On the absence of global anomalies of heterotic string theories

    Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.

    In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.

    The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.

  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
    CMSA-QMMP-02.02.2022-1544x2048

    Title: Kramers-Wannier-like duality defects in higher dimensions

    Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/15/2020 Quantum Matter Seminar

    8:30 pm-10:00 pm
    12/01/2024
  • Quantum Matter
    8:30 pm-10:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-04.13.22-1583x2048-1

    Youtube Video

    Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.

    We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.

    We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.

    Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.

  • Quantum Matter
    8:30 pm-10:30 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.18.22-1583x2048-1

    Speaker: Linhao Li (ISSP, U Tokyo)

    Title: Boundary conditions and LSM anomalies of conformal field theories in 1+1 dimensions

    Abstract: In this talk, we will study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state which is invariant under a symmetry, then the CFT can be gapped with a unique ground state by adding the corresponding gapping potential. This means that the symmetry of the CFT is anomaly free. Using this approach, we will systematically deduce the anomaly-free conditions for various types of CFTs with several different symmetries. When the symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis type ingappability of the system. Our results are consistent with, where available, known results in the literature. Moreover, we extend the discussion to other symmetries including spin groups and generalized time-reversal symmetries. As an application, we propose 1d LSM theorem involving magnetic space group symmetries on the lattice. The extended LSM theorems apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and chiral three-spin interactions.

  • Quantum Matter
    8:30 pm-10:00 pm
    12/01/2024

    Speaker: Nima Arkani-Hamed (IAS Princeton)

    Title: UV/IR and Effective Field Theory

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Tropical disk counts

    8:30 pm-9:30 pm
    12/01/2024

    Abstract: (joint with S. Venugopalan)  I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan)  which is an open analog of the twenty-seven lines.  As an application, I will explain why the Floer cohomology of such tropical fibers is well-defined; this is a generalization fo a result of Fukaya-Oh-Ohta-Ono for toric varieties.

  • Quantum Matter
    8:30 pm-9:30 pm
    12/01/2024
    CMSA-QMMP-03.10.2022-1544x2048-1-1

    Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field.

    This work is based on arxiv: 2201.11681

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/10/2018 Mathematical Physics Seminar

    8:42 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/10/2018 Topology Seminar

    8:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/12/2018 Hodge Seminar

    8:43 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar
    8:45 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    1/16/2019 Hodge Seminar

    8:46 pm
    12/01/2024

    No additional detail for this event.

  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    4/3/2019 Fluid Dynamics Seminar

    8:54 pm
    12/01/2024

    No additional detail for this event.

  • Program
    9:27 pm
    12/01/2024-12/31/2021

    The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications. This program is funded by the Simons Foundation.

    Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model).

    We envision that our goal of proving HMS in full generality can be accomplished by combining three main viewpoints:

    1. categorical algebraic geometry and non-commutative (nc) spaces: in this language, homological mirror symmetry is the statement that the same nc-spaces can arise either from algebraic geometry or from symplectic geometry.
    2. the Strominger-Yau-Zaslow (SYZ) approach, which provides a global geometric prescription for the construction of mirror pairs.
    3. Lagrangian Floer theory and family Floer cohomology, which provide a concrete path from symplectic geometry near a given Lagrangian submanifold to an open domain in a mirror analytic space.

    The Center of Mathematical Sciences and Applications is hosting the following short-term visitors for an HMS focused semester:

    • Jacob Bourjaily (Neils Bohr Institute)  4/1/2018 – 4/14/2018
    • Colin Diemer (IHES)  2/25/2018 – 3/10/2018
    • Charles Doran (University of Alberta) 5/13/2018 – 5/25/2018
    • Baohua Fu (Chinese Academy of Sciences)  4/15/2018 – 4/28/2018
    • Andrew Harder (University of Miami)  4/15/2018 – 4/28/2018
    • Shinobu Hosono (Gakushuin University) 2/25/2018 – 3/10/2018
    • Adam Jacob (UC Davis) 3/5/2018 – 3/16/2018
    • Tsung-Ju Lee (National Taiwan University) 4/18/2018 – 5/13/2018
    • Ivan Loseu (Northeastern University) 1/21/2018 – 2/3/2018
    • Cheuk-Yu Mak (Cambridge University) 4/1/2018 – 4/15/2018
    • Daniel Pomerleano (Imperial College) 3/19/2018 – 3/23/2018
    • Mauricio Romo (Tsinghua University) 4/1/2018 – 4/18/ 2018
    • Emanuel Scheidegger (Albert Ludwigs University of Freiburg) 2/22/2018 – 3/22/2018
    • Dmytro Shklyarov (Technische Universität Chemnitz) 3/4/2018 – 3/17/2018
    • Alan Thompson (University of Cambridge) 4/15/2018 – 4/21/2018
    • Weiwei Wu (University of Georgia) 4/27/2018 – 5/6/2018
    • Matt Young (Chinese University of Hong Kong) 1/15/2018 – 2/9/2018
    • Jeng-Daw Yu (National Taiwan University) 4/2/2018 – 4/6/2018
    • Minxian Zhu (Yau Mathematical Sciences Center, Tsinghua University) 1/ 22/2018 – 2/25/2018

    As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester.  Click here for information.

    The Collaboration will include two workshops hosted by The Center. The workshops will take place January 10-13, 2018  and April 5-7, 2018 at CMSA. Click here for more information.

  • Seminars

    Seminars Colloquia & Seminar
    7/13/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/27/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/8/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/16/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/22/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds

    9:30 pm-10:30 pm
    12/01/2024

    Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

  • Seminars

    Seminars Colloquia & Seminar
    7/20/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Program
    9:32 pm
    12/01/2024-12/31/2021

    The methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example, the first topological states of matter discovered were the integer quantum Hall states. The two dimensional integer quantum Hall effect was characterized by an integral number which can be understood as a Chern number of the Berry phase. Chern numbers are topological invariants that play an important role in different areas of mathematics. More recently, new topological states of matter known as topological insulators and topological superconductors have been realized theoretically and experimentally. The characterization of new phases of matter using topological invariants has allowed for a better understanding and even predictions of new phases of matter. The use of topology could lead to the discovery of new electronic, photonic, and ultracold atomic states of matter previously unknown. The concrete problems in the physical phenomena could inspire new developments in the study of topological invariants in mathematics.

    Here is a list of the scholars participating in this program.

  • Program
    9:35 pm
    12/01/2024-12/31/2021

    A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as
    cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs, using tools such as random walk theory and harmonic analysis.

     

    Here is a list of the scholars participating in this program.

  • Program
    9:36 pm
    12/01/2024-12/31/2021

    In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory, general relativity, and quantum many-body theory.

    String theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as dramatic progress in old branches.

    Several examples from the recent past exemplifying this synergy include the prediction from string theory of mirror symmetry, a highly unexpected mathematical equivalence between distinct pairs of Calabi-Yau manifolds. This fueled exciting developments in algebraic, enumerative and symplectic geometry. At the same time the realization of string theory as a phenomenologically viable physical theory depends crucially on detailed mathematical properties of these manifolds. In Einstein’s theory of general relativity the proofs of the positive energy theorem and the stability of flat spacetime were accompanied by fundamental new results in functional analysis, differential geometry and minimal surface theory. In the coming decades we expect many more important discoveries to arise from the interface of mathematics and physics. The Cheng Fund will foster these efforts.

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

    NameTentative Visiting Dates
    Po-Ning Chen2/1/15-4/30/15
    Hong-Jian He3/5/15-5/5/15
    Monica Guica12/1/14-3/15/15
    Amer Iqbal1/8/15-4/8/15
    Suvrat Raju2/25/15-5/25/15
    Mithat Ünsal9/1/15-12/31/15
  • Program
    9:37 pm
    12/01/2024-12/31/2021

    Most physical phenomena, from the gravitating universe to fluid dynamics, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations.

    The subject underwent rapid developments in the last century and foundational results were established. Compared to linear equations, the difficulty of solving nonlinear equations is of a different order of magnitude and the methods employed in solving them are also much more diversified. To this date, it is an active field with recent exciting discoveries and renewed interests, and several long standing problems seem to be within reach. The special year aims to spur activity in this subject, to provide a natural setting for the most cutting edge results to be communicated, and to facilitate interaction among researchers of different backgrounds.

    During the year, there will be two weekly seminar programs.  Each program participants will be asked to give a talk on geometric analysis, or the evolution of equations, hyperbolic equations, and fluid dynamics.   

    Seminar on Geometric Analysis

    Seminar on Evolution Equations

    Seminar on General Relativity

    Concluding Conference on Nonlinear Equations Program

    Mini-School on Nonlinear Equations, Dec. 2016

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

    NameHome InstitutionTentative Visiting Dates
    Stefano BianchiniSISSA04/01/2016 – 05/31/2016
    Lydia BieriUniversity of Michigan02/01/2016 – 04/30/2016
    Albert ChauUniversity of British Columbia02/26/2016 – 05/26/2016
    Binglong ChenSun Yat-sen University09/01/2015 – 11/30/2015
    Qingtao ChenETHZ (Swiss Federal Institute of Technology in Zurich)03/17/2016 – 04/04/2016
    Piotr ChruscielUniversity of Vienna03/01/2016 – 05/30/2016
    Fernando Coda MarquesPrinceton University04/25/2016 – 04/29/2016 05/23/2016 – 05/27/2016
    Mihalis DafermosPrinceton University04/01/2016 – 04/30/2016
    Camillo De LellisUniversity of Zurich02/01/2016 – 4/30/2016
    Michael EichmairUniversity of Vienna03/21/2016 – 04/01/2016
    Felix FinsterUniversitat Regensburg09/20/2015 – 10/20/2015 03/20/2016 – 04/20/2016
    Xianfeng David GuSUNY at Stony Brook04/01/2016 – 04/30/2016
    Zheng-Cheng GuPerimeter Institute for Theoretical Physics08/15/2015 – 09/15/2015
    Pengfei GuanMcGill University10/10/2015 – 10/17/2015
    Xiaoli HanTsinghua University01/20/2016 – 04/19/2016
    Thomas HouCalifornia Institute of Technology11/01/2016 – 11/30/2016
    Feimin HuangChinese Academy of Sciences02/15/2016 – 04/15/2016
    Xiangdi HuangChinese Academy of Sciences09/10/2015 – 12/10/2015
    Tom IlmanenETH Zurich10/19/2015 – 12/18/2015
    Niky KamranMcGill Univeristy04/04/2016 – 04/08/2016
    Nicolai KrylovUniversity of Minnesota11/01/2015 – 11/30/2015
    Junbin LiSun Yat-sen University02/01/2016 – 04/30/2016
    Yong LinRenmin University of China02/01/2016 – 03/31/2016
    Andre NevesImperial College London4/25/2016 – 4/29/2016; 5/23/2016 – 5/27/2016
    Duong H. PhongColumbia University04/08/2016 – 04/10/2016
    Ovidiu SavinColumbia University10/15/2015 – 12/14/2015
    Richard SchoenStanford University03/21/2016 – 03/25/2016
    Mao ShengUniversity of Science and Technology of China01/15/2016 – 01/28/2016
    Valentino TosattiNorthwestern University02/01/2016 – 04/15/2016
    John TothMcGill University04/04/2016 – 04/08/2016
    Chung-Jun TsaiNational Taiwan University05/01/2016 – 05/08/2016
    Tai-Peng TsaiUniversity of British Columbia03/20/2016 – 05/31/2016
    Li-Sheng TsengUC Irvine02/08/2016 – 02/19/2016; 04/27/2016 – 05/11/2016
    Chun Peng WangJilin University02/01/2016 – 04/30/2016
    Xu-Jia WangAustralian National University04/01/2016 – 05/31/2016
    Ben WeinkoveNorthwestern University02/28/2016 – 03/18/2016
    Sijue WuUniversity of Michigan04/01/2016 – 04/30/2016
    Chunjing XieShanghai Jiao Tong University09/08/2015 – 12/07/2015
    Zhou Ping XinThe Chinese University of Hong Kong10/01/2015 – 11/30/2015
    Hongwei XuZhejiang University09/01/2015 – 11/30/2015
    Peng YeUniversity of Illinois at Urbana-Champaign11/15/2015 – 11/22/2015
    Pin YuTshinghua University09/07/2015 – 12/10/2015
    Yi ZhangFudan University01/18/2016 – 05/31/2016
  • Program
    9:39 pm
    12/01/2024-12/18/2014

    arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

    Here is a partial list of the mathematicians who are participating in this program

  • Program
    9:44 pm
    12/01/2024-12/28/2013

    During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

    As part of the Program, the CMSA will be hosting two workshops:

    .

    Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
    NameTentative Visiting Dates

    Jason Alicea

    11/12/2018-11/16/2018
    Maissam Barkeshli4/22/2019 – 4/26/2019
    Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

    Lukasz Fidkowski

    1/7/2019-1/11/2019

    Zhengcheng Gu

    8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

    Yin Chen He

    10/14/2018-10/27/2018
    Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

    Michael Levin

    3/11/2019-3/15/2019
    Yuan-Ming Lu4/29/2019-6/01/2019

    Adam Nahum

    4/2/2019- 4/19/2019

    Masaki Oshikawa

    4/22/2019-5/22/2019
    Chong Wang 10/22/2018-11/16/2018

    Juven Wang

    4/1/2019-4/16/2019
    Cenke Xu 8/26/2018-10/1/2018

    Yi-Zhuang You

    4/1/2019-4/19/2019

    Mike Zaletel

    5/1/2019-5/10/2019
  • Program
    9:45 pm-9:46 pm
    12/01/2024-12/31/2010

    During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

    Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

    In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

    In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

    The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

    A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

    A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

  • Program
    9:48 pm
    12/01/2024-12/31/2010

    Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

    Organizers:

    .

    Workshops:

     

    Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

  • Program
    9:49 pm
    12/01/2024-12/23/2010

    The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

    A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


    Directors:


    Shing-Tung Yau (Harvard University)

    Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


    Professor Bong Lian (Brandeis University)

    BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


    Denis Auroux (Harvard University)

    AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
    Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




    Senior Personnel:

    Artan Sheshmani (Harvard CMSA)

    unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

    Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

    An Huang (Brandeis University)

    unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

    An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



    Siu Cheong Lau (Boston University)
    unnamed

    The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

    Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


    Affiliates:

    • Netanel Rubin-Blaier (Cambridge)
    • Kwokwai Chan (Chinese University of Hong Kong)
    • Mandy Cheung (Harvard University, BP)
    • Chuck Doran (University of Alberta)
    • Honsol Hong (Yonsei University)
    • Shinobu Hosono (Gakushuin University, Japan)
    • Conan Leung (Chinese University of Hong Kong)
    • Yu-shen Lin (Boston University)
    • Hossein Movassati (IMPA Brazil)
    • Arnav Tripathhy (Harvard University, BP)

     

    Postdocs:

    • Dennis Borisov
    • Tsung-Ju Lee
    • Dingxin Zhang
    • Jingyu Zhao
    • Yang Zhou

    Jobs:

    Postdoctoral Fellowship in Algebraic Geometry

    Postdoctoral Fellowship in Mathematical Sciences

     

    To learn about previous programming as part of the Simons Collaboration, click here.

  • More events
    • Quantum Matter
      12:00 am-1:30 pm
      12/01/2024-03/19/2021
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-9-2018 Math Physics Seminar
      12:00 am
      12/01/2024
    • Program
      All day
      12/01/2024-03/29/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Arithmetic Quantum Field Theory Program

      To receive email updates and program announcements, visit this link to sign up for the CMSA Arithmetic Quantum Field Theory Program mailing list.

      Dates: Feb. 5–Mar. 29, 2024

      Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138

      Directions to CMSA

      Organizers:

      This program will feature a weekly seminar series, workshops, and a conference.

      The object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions.

      On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions.

      The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions. Conversely, we will explore potential geometric and physical consequences of arithmetic ideas, for example, the Langlands correspondence theory of L-functions for 3-manifolds.


      Schedule

      The first week of the program will feature several lecture series aimed at a broad local community of mathematicians and physicists, aiming to introduce the main ideas underlying our program and help establish a common reference point.

      The program will host a weekly seminar series on Fridays.

      The speakers will be selected with the aim of covering a wide panorama of the subjects over the course of the program.

      The program will conclude with a week-long Conference on Arithmetic Quantum Field Theory March 25–29, 2024.


      AQFT Youtube Playlist

      Lecture series

      All lectures take place in Room G10, Harvard CMSA, 20 Garden Street Cambridge.

      Week 1: Feb. 5–9, 2024

      Abstract: In this lecture series we will introduce some of the themes underlying the CMSA program on Arithmetic Quantum Field Theory taking place this winter and the upcoming conference March 25-29, 2024.

      Some of the themes we plan to discuss include:

      Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.

      The setup of arithmetic topology as a bridge between the background of QFT to that of arithmetic (both “global” and “local”), including the “middle realm” of positive characteristic function fields.

      Questions and structures in arithmetic that have been / might be amenable to inspiration from QFT, in particular the theory of L-functions and the Langlands program.

      Schedule

       

      Monday, Feb. 5, 2024  
      11:00 am – 12:00 pm Minhyong KimArithmetic topology and field theory (Slides part 1 pdf)
      1:30 – 2:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
      2:30 – 3:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      Wednesday, Feb. 7, 2024  
      11:00 am – 12:00 pmMinhyong KimArithmetic topology and field theory (Slides part 2 pdf)
      2:30 – 3:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
      Thursday, Feb.8, 2024  
      2:30 – 3:30 pmMinhyong KimArithmetic topology and field theory (Slides part 3 pdf)
      4:00 – 5:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      Friday, Feb. 9, 2024  
      1:00 – 2:00 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
      2:00 – 3:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      3:30 – 4:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      Monday, Feb. 26, 2024
      1:00 – 2:00 pmOmer Offen (Brandeis)Period integrals of automorphic forms and the residue method
      Tuesday, Feb. 27, 2024
      2:00 – 3:00 pmWei Zhang (MIT)Shtuka special cycles and their generating series
      Friday, March 1, 2024
      11:00 am – 12:00 pmChen Wan (Rutgers Newark)Some examples of the relative Langlands duality
      2:00 – 3:00 pmPeng Shan (Tsinghua)Skein algebras and quantized Coulomb branches
      Thursday, March 7, 2024
      1:30 – 2:30 pmAn Huang (Brandeis)Tate’s thesis and p-adic strings
      3:00 – 4:00 pmJohn Francis (Northwestern)Integrating braided categories over 3-manifolds
      Friday, March 8, 2024
      1:00 – 2:00 pmDihua Jiang (U Minnesota)Shalika Periods: Functoriality and Arithmetic
      Friday, March 15, 2024
      11:45 – 1:00 pmBaiying Liu (Purdue)Recent progress on certain problems related to local Arthur packets of classical groups
      2:15 – 3:30 pmTasho Kaletha (Michigan)Covers of reductive groups and functoriality
      Monday, March 18, 2024
      1:00 – 3:00 pmXinwen Zhu (Stanford)The tame categorical local Langlands correspondence (Slides)
      4:30 – 5:30 pmNatalie Paquette (U  Washington)Koszul duality & twisted holography for asymptotically flat spacetimes (CMSA)
      Wednesday, March 20, 2024
      11:00 – 12:15 pmStephen D. Miller (Rutgers)What 4-graviton scattering amplitudes had to say about the unitary dual
      Friday, March 22, 2024
      1:45 – 3:00 pmJayce Getz (Duke)The Poisson summation conjecture and the fiber bundle method
      3:30 – 4:30 pmTBATBA

       


      Program Visitors

      • Mina Aganagic, University of California, Berkeley
      • Anne-Marie Aubert, Institut de Mathématiques de Jussieu-Paris Rive Gauche, March 15-29
      • Clark Barwick, University of Edinburgh, February 19-March 15
      • Alexander Braverman, Perimeter Institute
      • Alejandra Castro, Cambridge University, March 25-29
      • YoungJu Choie, Pohang University of Science and Technology, February 12-16; March 22-28
      • John Francis, Northwestern University, March 1-14
      • David Gaiotto, Perimeter Institute, March 25-29
      • Jayce Getz, Duke University, March 18-22
      • Ezra Getzler, Northwestern University, March 11-22
      • Sam Gunningham, Montana State University, February 9-12
      • Sarah Harrison, Northeastern University
      • Dihua Jiang, University of Minnesota, February 29-March 9
      • Tasho Kaletha, University of Michigan, March 12-20
      • Minhyong Kim, University of Edinburgh, February 1-29
      • Axel Kleinschmidt, Max Planck Institute for Gravitational Physics, Potsdam, March 18-28
      • Kim Klinger-Logan, Kansas State University, March 25-29
      • Kobi Kremnitzer, Oxford University, March 25-29
      • Baiying Liu, Purdue University, March 13-16
      • Steven Miller, Rutgers University
      • Greg Moore, Rutgers University, February 5-9
      • David Nadler, University of California, Berkeley, March 17-30
      • Bảo Châu Ngô, University of Chicago, March 25-29
      • George Pappas, Michigan State University, March 25-29
      • Daniel Persson, Chalmers Institute of Technology, March 25-29
      • Sam Raskin, Yale University, March 26-29
      • Yiannis Sakellaridis, Johns Hopkins University, March 18-22
      • Peng Shan, Tsinghua University, February 12-April 14
      • Akshay Venkatesh, Institute for Advanced Study
      • Roberto Volpato, University of Padova, February 4-10
      • Chen Wan, Rutgers University, February 29-March 9
      • Fei Yan, Brookhaven National Laboratory, March 18-29
      • Xinwen Zhu, Stanford University

       

    • CMSA EVENT: Big Data Conference 2021
      All day
      12/01/2024

      On August 24, 2021, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The 2021 Big Data Conference took place virtually on Zoom.

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
      • Sergiy Verstyuk, CMSA, Harvard University

      Speakers:

      Time (ET; Boston time)SpeakerTitle/Abstract
      9:00AMConference OrganizersIntroduction and Welcome
      9:10AM – 9:55AMAndrew Blumberg, University of Texas at AustinTitle: Robustness and stability for multidimensional persistent homology

      Abstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However, for many data sets, it is very natural to consider multiple filtrations, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.

      10:00AM – 10:45AMKatrina Ligett, The Hebrew University of JerusalemTitle: Privacy as Stability, for Generalization

      Abstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity, via a connection to the notion of differential privacy. In this talk, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open.

      Joint work with: Christopher Jung (UPenn), Seth Neel (Harvard), Aaron Roth (UPenn), Saeed Sharifi-Malvajerdi (UPenn), and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020

      10:50AM – 11:35AMHima Lakkaraju, Harvard UniversityTitle: Towards Reliable and Robust Model Explanations

      Abstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP, and also introduce novel methods to address some of these vulnerabilities. More specifically, I will first demonstrate that these methods are brittle, unstable, and are vulnerable to a variety of adversarial attacks. Then, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.

      11:40AM – 12:25PMMoran Koren, Harvard CMSATitle: A Gatekeeper’s Conundrum

      Abstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e., ignore her private information with some probability).

      12:25PMConference OrganizersClosing Remarks
    • CMSA EVENT: Mathematics in Science: Perspectives and Prospects
      All day
      12/01/2024-10/28/2023
      1 Oxford Street, Cambridge MA 02138
      Mathematics in Science: Perspectives and Prospects

      A showcase of mathematics in interaction with physics, computer science, biology, and beyond.

      October 27–28, 2023

      Location: Harvard University Science Center Hall D & via Zoom.

      Directions and Recommended Lodging

      Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

      Youtube Playlist

       

      Speakers

      Organizers

      • Michael R. Douglas (Harvard CMSA)
      • Dan Freed (Harvard Math & CMSA)
      • Mike Hopkins (Harvard Math)
      • Cumrun Vafa (Harvard Physics)
      • Horng-Tzer Yau (Harvard Math)

      Schedule

      Friday, October 27, 2023

      2:00–3:15 pmGreg Moore (Rutgers)

      Title: Remarks on Physical Mathematics

      Abstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting, I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet, so I don’t know how it will end any more than you do.

      Slides (PDF)

      3:15–3:45 pmBreak
      3:45–5:00 pmBernd Sturmfels (MPI Leipzig)

      Title: Algebraic Varieties in Quantum Chemistry

      Abstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.

      Slides (PDF)

       

      Saturday, October 28, 2023

      9:00 amBreakfast
      9:30–10:45 amMike Freedman (Harvard CMSA)

      Title: ML, QML, and Dynamics: What mathematics can help us understand and advance machine learning?

      Abstract: Vannila deep neural nets DNN repeatedly stretch and fold. They are reminiscent of the logistic map and the Smale horseshoe.  What kind of dynamics is responsible for their expressivity and trainability. Is chaos playing a role? Is the Kolmogorov Arnold representation theorem relevant? Large language models are full of linear maps. Might we look for emergent tensor structures in these highly trained maps in analogy with emergent tensor structures at local minima of certain loss functions in high-energy physics.

      Slides (PDF)

      10:45–11:15 amBreak
      11:15 am–12:30 pm
      via Zoom
      Nima Arkani-Hamed (IAS)

      Title: All-Loop Scattering as A Counting Problem

      Abstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model, the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

      12:30–2:00 pmLunch break
      2:00–3:15 pmConstantinos Daskalakis (MIT)

      Title: How to train deep neural nets to think strategically

      Abstract: Many outstanding challenges in Deep Learning lie at its interface with Game Theory: from playing difficult games like Go to robustifying classifiers against adversarial attacks, training deep generative models, and training DNN-based models to interact with each other and with humans. In these applications, the utilities that the agents aim to optimize are non-concave in the parameters of the underlying DNNs; as a result, Nash equilibria fail to exist, and standard equilibrium analysis is inapplicable. So how can one train DNNs to be strategic? What is even the goal of the training? We shed light on these challenges through a combination of learning-theoretic, complexity-theoretic, game-theoretic and topological techniques, presenting obstacles and opportunities for Deep Learning and Game Theory going forward.

      Slides (PDF)

      3:15–3:45 pmBreak
      3:45–5:00 pmAlison Etheridge (Oxford)

      Title: Modelling hybrid zones

      Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection, spatial structure, and, if time permits, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection.

      Slides (PDF)

       


      Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to mathsci2023@cmsa.fas.harvard.edu no later than October 9, 2023.

      Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV.

       

    • Holiday
      All day
      12/01/2024

      Holiday: Friday after Thanksgiving

      The CMSA will be closed on Friday, November 25, 2022.

    • Seminars
      Seminars Colloquia & Seminar
      1/27/2020 Math Physics Seminar
      12:00 am-1:00 pm
      12/01/2024
    • CMSA EVENT: Quantum Matter Workshop
      All day
      12/01/2024
      Layer-2-600x338

      Please note: this workshop has been postponed to a later date. Details will be posted to this page when they are available.

      Throughout the summer, scheduled speakers for the Quantum Matter Workshop will give talks on Zoom for the Quantum Matter/Condensed Matter seminar.

      The CMSA will be hosting our second workshop on Quantum Matter. Both of these workshops are part of our program on Quantum Matter in Mathematics and Physics. The first workshop took place in December 2019, and was extremely successful, attracting participants worldwide. Learn more about the first workshop here.

       

      Organizers: Du Pei, Ryan Thorngren, Juven Wang, Yifan Wang, and Shing-Tung Yau.

      Speakers:

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-16-2018 Mathematical Physics Seminar
      12:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/7/2018 Hodge Seminar
      1:30 am-3:00 pm
      12/01/2024
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Some remarks on contact Calabi-Yau 7-manifolds
      3:00 am-4:00 am
      12/01/2024

      Abstract: In geometry and physics it has proved useful to relate G2 and Calabi-Yau geometry via circle bundles. Contact Calabi-Yau 7-manifolds are, in the simplest cases, such circle bundles over Calabi-Yau 3-orbifolds. These 7-manifolds provide testing grounds for the study of geometric flows which seek to find torsion-free G2-structures (and thus Ricci flat metrics with exceptional holonomy). They also give useful backgrounds to examine the heterotic G2 system (also known as the G2-Hull-Strominger system), which is a coupled set of PDEs arising from physics that involves the G2-structure and gauge theory on the 7-manifold. I will report on recent progress on both of these directions in the study of contact Calabi-Yau 7-manifolds, which is joint work with H. Sá Earp and J. Saavedra.

    • Colloquium
      5:00 am
      12/01/2024

      No additional detail for this event.

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Arthur Jaffe (Harvard University)

      Title: Is relativity compatible with quantum theory?

      Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.”  Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed.

      Talk chair: Zhengwei Liu

      Video

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Edward Witten (IAS)

      Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions

      Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification.

      Talk chair: Cliff Taubes

      Video

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Nigel Hitchin (University of Oxford)

      Title: Michael Atiyah: Geometry and Physics

      Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists.

      Talk chair: Peter Kronheimer

      Video

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Alain Connes (Collège de France)

      Title: Noncommutative Geometry, the Spectral Aspect

      Abstract: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function.

      Talk chair: Peter Kronheimer

      Video 

    • CMSA EVENT: Workshop on Quantum Information
      8:00 am-6:07 pm
      12/01/2024-04/24/2017
      banner-image-1

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 23-24, 2018. In the days leading up to the conference, the American Mathematical Society will also be hosting a sectional meeting on quantum information on April 21-22. You can find more information here.

      Register for the event here.

      The following speakers are confirmed:

    • Math Science Literature Lecture Series
      8:00 am-9:00 am
      12/01/2024
      Lecture-Series-Don-pdf

      Donald Rubin (Harvard)

      Title: Why do some universities have separate departments of statistics? And are they all anachronisms, destined to follow the path of other dinosaurs?

      Video | Slides

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Yuri Manin (Max Planck Institute for Mathematics)

      Title: Homotopy spectra and Diophantine equations

      Abstract: For a long stretch of time in the history of mathematics, Number Theory and Topology formed vast, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC)  that contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory, named after Diophantus of Alexandria (about 250 BC). Topology was born much later, but arguably, its cousin — modern measure theory, — goes back to Archimedes, author of Psammites (“Sand Reckoner”), who was approximately a contemporary of Diophantus. In modern language, Archimedes measures the volume of observable universe by counting the number of small grains of sand necessary to fill this volume. Of course, many qualitative geometric models and quantitative estimates of the relevant distances precede his calculations. Moreover, since the estimated numbers of grains of sand are quite large (about $10^{64}$), Archimedes had to invent and describe a system of notation for large numbers going far outside the possibilities of any of the standard ancient systems. The construction of the first bridge between number theory and topology was accomplished only about fifty years ago: it is the theory of spectra in stable homotopy theory. In particular, it connects $Z$, the initial object in the theory of commutative rings, with the sphere spectrum $S$. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this talk based upon the authors’ (Yu. Manin and M. Marcolli) joint research project, I suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.

      Talk chair: Michael Hopkins

      Slides | Video

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrations
      8:00 am-9:30 am
      12/01/2024

      Caucher Birkar (University of Cambridge)

      Title: Log Calabi-Yau fibrations

      Abstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry, differential geometry, arithmetic geometry, mathematical physics, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties, their fibrations, as well as their local birational counterparts such as flips and singularities. Such fibrations can be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations, to remind some known results, and to state some open problems.

      Video

       

    • Special Seminar
      8:00 am-9:00 am
      12/01/2024
      Gromov-Witten

      During the Spring 2021 Semester Artan Sheshmani (CMSA/ I.M. A.U.) will be teaching a CMSA special lecture series on Gromov-Witten/Donaldson Thomas theory and Birational/Symplectic invariants for algebraic surfaces.

      In order to attend this series, please fill out this form.

      The lectures will be held Mondays from 8:00 – 9:30 AM ET and Wednesdays from 8:00 – 9:00 AM ET beginning January 25 on Zoom.

      You can watch Prof. Sheshmani describe the series here. 

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Andrei Okounkov (Columbia University)

      Title: Classical and quantum integrable systems in enumerative geometry

      Abstract: For more than a quarter of a century, thanks to the ideas and questions originating in modern high-energy physics, there has been a very fruitful interplay between enumerative geometry and integrable system, both classical and quantum. While it is impossible to summarize even the most important aspects of this interplay in one talk, I will try to highlight a few logical points with the goal to explain the place and the role of certain more recent developments.

      Talk chair: Cumrun Vafa

      Video

    • Quantum Matter
      8:00 am-9:30 am
      12/01/2024
    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Yujiro Kawamata (University of Tokyo)

      Title: Kunihiko Kodaira and complex manifolds

      Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions.  After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces.  Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts.

      Talk chair: Baohua Fu

      Video 

    • CMSA EVENT: Geometric Analysis Approach to AI Workshop
      8:30 am-5:30 pm
      12/01/2024-01/21/2019
      Geo-Analysis-Poster-final-e1547584167900

      Geo-Analysis-1-e1543848888343

      Due to inclement weather on Sunday, the second half of the workshop has been moved forward one day. Sunday and Monday’s talks will now take place on Monday and Tuesday.

      On January 18-21, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI.

      This workshop will focus on the theoretic foundations of AI, especially various methods in Deep Learning. The topics will cover the relationship between deep learning and optimal transportation theory, DL and information geometry, DL Learning and information bottle neck and renormalization theory, DL and manifold embedding and so on. Furthermore, the recent advancements, novel methods, and real world applications of Deep Learning will also be reported and discussed.

      The workshop will take place from January 18th to January 23rd, 2019. In the first four days, from January 18th to January 21, the speakers will give short courses; On the 22nd and 23rd, the speakers will give conference representations. This workshop is organized by Xianfeng Gu and Shing-Tung Yau.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please register here

      Speakers: 

    • CMSA EVENT: Big Data Conference 2018
      8:30 am-2:50 pm
      12/01/2024-08/24/2018
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2018-1

       

      shutterstock_547250785-e1527881194717

      On August 23-24, 2018 the CMSA will be hosting our fourth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The talks will take place in Science Center Hall B, 1 Oxford Street.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

      Please register here. 

      Confirmed Speakers: 

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
      • Jun Liu, Professor of Statistics, Harvard University
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • CMSA EVENT: 2019 Big Data Conference
      8:30 am-4:40 pm
      12/01/2024-08/20/2019
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2019-Poster-5-2

      shutterstock_547250785-e1527881194717

      On August 19-20, 2019 the CMSA will be hosting our fifth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The talks will take place in Science Center Hall D, 1 Oxford Street.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

      Videos can be found in this Youtube playlist or in the schedule below.

    • CMSA EVENT: Workshop on Aspects of General Relativity
      8:30 am-3:30 pm
      12/01/2024-05/26/2017

      The Center of Mathematical Sciences and Applications will be hosting a workshop on General Relativity from May 23 – 24, 2016. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138The workshop will start on Monday, May 23 at 9am and end on Tuesday, May 24 at 4pm.

      Speakers:

      1. Po-Ning Chen, Columbia University
      2. Piotr T. Chruściel, University of Vienna
      3. Justin Corvino, Lafayette College
      4. Greg Galloway, University of Miami
      5. James Guillochon, Harvard University
      6. Lan-Hsuan Huang, University of Connecticut
      7. Dan Kapec, Harvard University
      8. Dan Lee, CUNY
      9. Alex Lupsasca, Harvard University
      10. Pengzi Miao, University of Miami
      11. Prahar Mitra, Harvard University
      12. Lorenzo Sironi, Harvard University
      13. Jared Speck, MIT
      14. Mu-Tao Wang, Columbia University

      Please click Workshop Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Please click here for registration – Registration is capped at 70 participants.

      Schedule:

      May 23 – Day 1
      8:30amBreakfast
      8:55amOpening remarks
      9:00am – 9:45amGreg Galloway, “Some remarks on photon spheres and their uniqueness
      9:45am – 10:30amPrahar Mitra, “BMS supertranslations and Weinberg’s soft graviton theorem
      10:30am – 11:00amBreak
      11:00am – 11:45amDan Kapec, “Area, Entanglement Entropy and Supertranslations at Null Infinity
      11:45am – 12:30pmPiotr T. Chruściel, “The cosmological constant and the energy of gravitational radiation”
      12:30pm – 2:00pmLunch
      2:00pm – 2:45pmJames Guillochon, “Tidal disruptions of stars by supermassive black holes: dynamics, light, and relics”
      2:45pm – 3:30pmMu-Tao Wang, “Quasi local conserved quantities in general relativity
      3:30pm – 4:00pmBreak
      4:00pm – 4:45pmPo-Ning Chen, “Quasi local energy in presence of gravitational radiations
      4:45pm – 5:30pmPengzi Miao, “Total mean curvature, scalar curvature, and a variational analog of Brown York mass
      May 24 – Day 2
      8:45amBreakfast
      9:00am – 9:45amJustin Corvino, “Scalar curvature deformation and the Bartnik mass
      9:45am – 10:30amLan-Hsuan Huang, “Constraint Manifolds with the Dominant Energy Condition
      10:30am – 11:00amBreak
      11:00am – 11:45amDan Lee, “Lower semicontinuity of Huisken’s isoperimetric mass
      11:45am – 12:30pmJared Speck, “Shock Formation in Solutions to the Compressible Euler Equations
      12:30pm – 2:00pmLunch
      2:00pm – 2:45pmLorenzo Sironi, “Electron Heating and Acceleration in the Vicinity of Supermassive Black Holes
      2:45pm – 3:30pmAlex Lupsasca, “Near Horizon Extreme Kerr Magnetospheres
      * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Workshop on Aspects on General Relativity“.
      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

      Organizers: Piotr T. Chruściel and Shing-Tung Yau

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Angular momentum in general relativity
      8:30 am-9:30 am
      12/01/2024

      Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

    • CMSA EVENT: F-Theory Conference
      8:30 am-3:00 pm
      12/01/2024-09/30/2018

      The CMSA will be hosting an F-Theory workshop September 29-30, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. 

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Click here for videos of the talks. 

      Organizers:

      Speakers:

    • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
      8:30 am-2:00 pm
      12/01/2024-10/24/2018

      In Fall 2018, the CMSA will host a Program on Mathematical Biology, which aims to describe recent mathematical advances in using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.

      The plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale, the   shapes seen in a garden at the scale of a pollen grain, a seed, a sapling, a root, a flower or leaf are so numerous that “it is enough to drive the sanest man mad,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively?

      In biology, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists, to understand how polymeric assemblies grow and shrink (in the cytoskeleton), and how cells divide, change size and shape, and move to organize tissues, change their topology and geometry, and link multiple scales and connect biochemical to mechanical aspects of these problems, all in a self-regulated setting.

      To understand these questions, we need to describe shape (biomathematics), predict shape (biophysics), and design shape (bioengineering).

      For example, in mathematics there are some beautiful links to Nash’s embedding theorem,  connections to quasi-conformal geometry, Ricci flows and geometric PDE, to Gromov’s h principle, to geometrical singularities and singular geometries, discrete and computational differential geometry, to stochastic geometry and shape characterization (a la Grenander, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor, Adler) to look for similarities and differences across species during development, and across evolution.

      In physics, there are questions of generalizing classical theories to include activity, break the usual Galilean invariance, as well as isotropy, frame indifference, homogeneity, and create both agent (cell)-based and continuum theories for ordered, active machines, linking statistical to continuum mechanics, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals, polar materials, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied.

      The CMSA will be hosting a Workshop on Morphometrics, Morphogenesis and Mathematics from October 22-24 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Videos of the talks

      Confirmed Speakers:

    • CMSA EVENT: Workshop on Foundations of Computational Science
      8:30 am-2:45 pm
      12/01/2024-08/31/2019
      AI-Poster-3

      On August 29-31, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on Foundations of Computational Science. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA This workshop is organized by David Xianfeng Gu.

      Please register here. 

      Speakers:

      Videos of the talks are contained in the Youtube playlist below. They can also be found through links in the schedule.

    • Quantum Matter
      8:30 am-10:00 am
      12/01/2024
    • CMSA EVENT: Morphogenesis: Geometry and Physics
      8:30 am-2:30 pm
      12/01/2024-12/05/2018

      Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book – a literary masterpiece – is a visionary synthesis of the geometric biology of form. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. So, how far are we from realizing the century-old vision that “Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed” ?

      To address this requires an appreciation of the enormous ‘morphospace’ in terms of the potential shapes and sizes that living forms take, using the language of mathematics. In parallel, we need to consider the biological processes that determine form in mathematical terms is based on understanding how instabilities and patterns in physical systems might be harnessed by evolution.

      In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.
      The first workshop will focus on the interface between Morphometrics and Mathematics, while the second will focus on the interface between Morphogenesis and Physics.The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

      As part of the program on Mathematical Biology a workshop on Morphogenesis: Geometry and Physics will take place on December 3-5, 2018.  The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Videos

      Please Register Here

      PDF of the Schedule

      Speakers:

    • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
      8:30 am-5:20 pm
      12/01/2024-08/20/2018
      Mumford-3

      David_Mumford-1

      On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center, Hall B.

       Saturday, August 18th:  A day of talks on Vision, AI and brain sciences
      Monday, August 20th: a day of talks on Math

      Speakers:

      Organizers:

       

      Publication:

      Pure and Applied Mathematics Quarterly

      Special Issue: In Honor of David Mumford

      Guest Editors: Ching-Li Chai, Amnon Neeman

       

    • Member Seminar
      8:45 am-10:15 am
      12/01/2024

      Speaker: Jörn Boehnke

      Title: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning

      Abstract:  In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.

    • CMSA EVENT: 2015 Conference on Big Data
      8:45 am-4:00 pm
      12/01/2024-10/26/2015
      1 Oxford Street, Cambridge MA 02138

      The Center of Mathematical Sciences and Applications will be having a conference on Big Data August 24-26, 2015, in Science Center Hall B at Harvard University.  This conference will feature many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      For more info, please contact Sarah LaBauve at slabauve@math.harvard.edu.

       

      Registration for the conference is now closed.

      Please click here for a downloadable version of this schedule.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found here.

      Monday, August 24

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amSendhil MullainathanPrediction Problems in Social Science: Applications of Machine Learning to Policy and Behavioral Economics
      9:45amMike LucaDesigning Disclosure for the Digital Age
      10:30Break
      10:45Jianqing FanBig Data Big Assumption: Spurious discoveries and endogeneity
      11:30amDaniel GoroffPrivacy and Reproducibility in Data Science
      12:15pmBreak for Lunch
      2:00pmRyan AdamsExact Markov Chain Monte Carlo with Large Data
      2:45pmDavid DunsonScalable Bayes: Simple algorithms with guarantees
      3:30pmBreak
      3:45pmMichael JordanComputational thinking, inferential thinking and Big Data
      4:30pmJoel TroppApplied Random Matrix Theory
      5:15pmDavid WoodruffInput Sparsity and Hardness for Robust Subspace Approximation

      Tuesday, August 25

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amGunnar CarlssonPersistent homology for qualitative analysis and feature generation
      9:45amAndrea MontanariSemidefinite Programming Relaxations for Graph and Matrix Estimation: Algorithms and Phase Transitions
      10:30amBreak
      10:45amSusan AtheyMachine Learning and Causal Inference for Policy Evaluation
      11:30amDenis NekipelovRobust Empirical Evaluation of Large Competitive Markets
      12:15pmBreak for Lunch
      2:00pmLucy ColwellUsing evolutionary sequence variation to make inferences about protein structure and function: Modeling with Random Matrix Theory
      2:45pmSimona CoccoInverse Statistical Physics approaches for the modeling of protein families
      3:30pmBreak
      3:45pmRemi MonassonInference of top components of correlation matrices with prior informations
      4:30pmSayan MukherjeeRandom walks on simplicial complexes and higher order notions of spectral clustering

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

      A Banquet from 7:00 – 8:30pm will follow Tuesday’s talks. This event is by invitation only.

       Wednesday, August 26 

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amAnkur MoitraBeyond Matrix Completion
      9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
      10:30amBreak
      10:45amPiotr IndykFast Algorithms for Structured Sparsity
      11:30amGuido ImbensExact p-values for network inference
      12:15pmBreak for lunch
      2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
      2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
      3:30pmBreak
      3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
      4:30pmJelani NelsonDimensionality reductions via sparse matrices
    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024
      Lecture_Fukaya-pdf

      Kenji Fukaya (Simons Center for Geometry and Physics)

      Title: Homological (homotopical) algebra and moduli spaces in Topological Field theories

      Abstract: Moduli spaces of various gauge theory equations and of various versions of (pseudo) holomorphic curve equations have played important role in geometry in these 40 years. Started with Floer’s work people start to obtain more sophisticated object such as groups, rings, or categories from (system of) moduli spaces. I would like to survey some of those works and the methods to study family of moduli spaces systematically.

      Talk chair: Peter Kronheimer

      Slides | Video

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Don Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics)

      Title: Quantum topology and new types of modularity

      Abstract: The talk concerns two fundamental themes of modern 3-dimensional topology and their unexpected connection with a theme coming from number theory. A deep insight of William Thurston in the mid-1970s is that the vast majority of complements of knots in the 3-sphere, or more generally of 3-manifolds, have a unique metric structure as hyperbolic manifolds of constant curvature -1, so that 3-dimensional topology is in some sense not really a branch of topology at all, but of differential geometry. In a different direction, the work of Vaughan Jones and Ed Witten in the late 1980s gave rise to the field of Quantum Topology, in which new types of invariants of knot complements and 3-manifolds are introduced that have their origins in ideas coming from quantum field theory. These two themes then became linked by Kashaev’s famous Volume Conjecture, now some 25 years old, which says that the Kashaev invariant _N of a hyperbolic knot K (this is a quantum invariant defined for each positive integer N and whose values are algebraic numbers) grows exponentially as N tends to infinity with an exponent proportional to the hyperbolic volume of the knot complement. About 10 years ago, I was led by numerical experiments to the discovery that Kashaev’s invariant could be upgraded to an invariant having rational numbers as its argument (with the original invariant being the value at 1/N) and that the Volume Conjecture then became part of a bigger story saying that the new invariant has some sort of strange transformation property under the action x -> (ax+b)/(cx+d) of the modular group SL(2,Z) on the argument. This turned out to be only the beginning of a fascinating and multi-faceted story relating quantum invariants, q-series, modularity, and many other topics. In the talk, which is intended for a general mathematical audience, I would like to recount some parts of this story, which is joint work with Stavros Garoufalidis (and of course involving contributions from many other authors). The “new types of modularity” in the title refer to a specific byproduct of these investigations, namely that there is a generalization of the classical notion of holomorphic modular form – which plays an absolutely central role in modern number theory – to a new class of holomorphic functions in the upper half-plane that no longer satisfy a transformation law under the action of the modular group, but a weaker extendability property instead. This new class, called “holomorphic quantum modular forms”, turns out to contain many other functions of a more number-theoretical nature as well as the original examples coming from quantum invariants.

      Talk chair: Mark Kisin

      Video

    • Combinatorics Physics and Probability
      9:00 am-10:00 am
      12/01/2024

      Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Liang Kong (Sustech)

      Title: Topological Wick Rotation and Holographic duality

      Abstract: I will explain a new type of holographic dualities between
      n+1D topological orders with a chosen boundary condition and nD
      (potentially gapless) quantum liquids. It is based on the idea of
      topological Wick rotation, a notion which was first used in
      arXiv:1705.01087 and was named, emphasized and generalized later in
      arXiv:1905.04924. Examples of these holographic dualities include the
      duality between 2+1D toric code model and 1+1D Ising chain and its
      finite-group generalizations (independently discovered by many
      others); those between 2+1D topological orders and 1+1D rational
      conformal field theories; and those between n+1D finite gauge theories
      with a gapped boundary and nD gapped quantum liquids. I will also
      briefly discuss some generalizations of this holographic duality and
      its relation to AdS/CFT duality.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: João Caetano (CERN)

      Title: Unorientable Quantum Field Theories: From crosscaps to holography

      Abstract: In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state.

      In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4-manifold. I will show how to do this in the example of N=4 Supersymmetric Yang-Mills, discuss its holographic description and present a new solvable setup of AdS/CFT.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Michele Del Zotto (Uppsala University)

      Title: On the six-dimensional origin of non-invertible symmetries

      Abstract: I will present a review about recent progress in charting non-invertible symmetries for four-dimensional quantum field theories that have a six-dimensional origin. These include in particular N=4 supersymmetric Yang-Mills theories, and also a large class of N=2 supersymmetric theories which are conformal and do not have a conventional Lagrangian description (the so-called theories of “class S”). Among the main results, I will explain criteria for identifying examples of systems with intrinsic and non-intrinsic non-invertible symmetries, as well as explore their higher dimensional origin. This seminar is based on joint works with Vladimir Bashmakov, Azeem Hasan, and Justin Kaidi.

       

      https://www.youtube.com/watch?v=0Tscbn9RhF8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=31

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 11.2.22

      Topological Quantum Matter Seminar

      Speaker: Junyeong Ahn (Harvard)

      Title: Optical axion electrodynamics

      Abstract: Electromagnetic fields in a magneto-electric medium behave in close analogy to photons coupled to the hypothetical elementary particle, the axion. This emergent axion electrodynamics is expected to provide novel ways to detect and control material properties with electromagnetic fields. Despite having been studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Formulating axion electrodynamics at general optical frequencies requires resolving the difficulty of calculating optical magneto-electric coupling in periodic systems and demands a proper generalization of the axion field. In this talk, I will introduce a theory of optical axion electrodynamics that allows for a simple quantitative analysis. Then, I will move on to discuss the issue of the Kerr effect in axion antiferromagnets, refuting the conventional wisdom that the Kerr effect is a measure of the net magnetic moment. Finally, I will apply our theory to a topological antiferromagnet MnBi2Te4.

      References:
      [1] Theory of Optical Axion Electrodynamics, J. Ahn, S.Y. Xu, A.Vishwanath, arXiv:2205.06843

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Ethan Lake (MIT)

      Title: Insulating BECs and other surprises in dipole-conserving systems

      Abstract: I will discuss recent work on bosonic models whose dynamics conserves both total charge and total dipole moment, a situation which can be engineered in strongly tilted optical lattices. Related models have received significant attention recently for their interesting out-of-equilibrium dynamics, but analytic and numeric studies reveal that they also possess rather unusual ground states. I will focus in particular on a dipole-conserving variant of the Bose-Hubbard model, which realizes an unusual phase of matter that possesses a Bose-Einstein condensate, but which is nevertheless insulating, and has zero superfluid weight. Time permitting, I will also describe the physics of a regime in which these models spontaneously fracture into an exotic type of glassy state.

       

      https://www.youtube.com/watch?v=Nad45apS8TE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=29

    • Quantum Matter
      9:00 am-4:00 pm
      12/01/2024
    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Daniel A. Spielman

      Dan Spielman (Yale University)

      Title: Discrepancy Theory and Randomized Controlled Trials

      Abstract: Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other.  By “surprisingly similar” we mean much more similar than a random partition. I will begin by surveying fundamental results in discrepancy theory, including Spencer’s famous existence proofs and Bansal’s recent algorithmic realizations of them. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar.  When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we know information about the experimental subjects, called covariates, we can combine the strengths of randomization with the promises of discrepancy theory. This should allow us to obtain more accurate estimates of the effectiveness of treatments, or to conduct trials with fewer experimental subjects. I will introduce the Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, which produces random solutions to discrepancy problems. I will then explain how Chris Harshaw, Fredrik Sävje, Peng Zhang, and I use this algorithm to improve the design of randomized controlled trials. Our Gram-Schmidt Walk Designs have increased accuracy when the experimental outcomes are correlated with linear functions of the covariates, and are comparable to uniform random assignments in the worst case.

      Talk chair: Salil Vadhan

      Video

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 10.26.22

      Topological Quantum Matter Seminar

      Speaker: Bruno Mera, Tohoku University
      Title: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
      Abstract: The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect, certain geometric constraints, associated with the holomorphic character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.
      References:
      [1] Tomoki Ozawa and Bruno Mera. Relations between topology and the quantum metric for Chern insulators. Phys. Rev. B, 104:045103, Jul 2021.
      [2] Bruno Mera and Tomoki Ozawa. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Phys. Rev. B, 104:045104, Jul 2021.
      [3] Bruno Mera and Tomoki Ozawa. Engineering geometrically flat Chern bands with Fubini-Study  Kähler structure. Phys. Rev. B, 104:115160, Sep 2021.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Francisco Machado  (Berkeley/Harvard)

      Title: Kardar-Parisi-Zhang dynamics in integrable quantum magnets

      Abstract: Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.

      In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.

      Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.

      [1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
      B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
      (PRL in press) – arXiv:2205.02853

      [2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
      D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
      Science (2022) — arXiv:2107.00038

       

      https://www.youtube.com/watch?v=65DjgbX30FU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=27

    • Math Science Literature Lecture Series
      9:00 am-12:13 pm
      12/01/2024

      Harry Shum (Tsinghua University)

      Title: From Deep Learning to Deep Understanding

      Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model,  and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike GPT or similar language models learnt from data, it is a multi-turn decision making system which takes user input, updates the belief state, retrieved from the database via symbolic reasoning, and decides how to complete the task with grounded response.

      Talk chair: Shing-Tung Yau

      Video

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      10/12/2021 Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      Title: On counting algebraically defined graphs

      Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

    • Program
      9:00 am-5:00 pm
      12/01/2024-05/13/2022

      Please visit the Swampland Initiative for current events.

      The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.

       


      During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”

      The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology,  which has led to a great deal of activity in the field in the last few years.

      The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.

      This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.

      Seminars

      Swampland Seminar Series & Group Meetings

      Program Visitors

      • Pieter Bomans, Princeton, 10/30/21 – 11/02/21
      • Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
      • Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
      • Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
      • Timo Weigand, 03/21/22 – 03/28/22
      • Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
      • Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
      • Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
      • Sergio Cecotti, 05/08/22 – 05/21/22
      • Tom Rudelius, 05/09/22 – 05/13/22

      https://sites.harvard.edu/swampland-initiative/

    • Math Science Literature Lecture Series
      9:00 am-9:06 am
      12/01/2024

      Claire Voisin (Collège de France)

      Title: Hodge structures and the topology of algebraic varieties

      Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results  we will discuss  rely on Hodge theory, which  has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization,  is missing in the general Kaehler context. We will also discuss some results and problems related to algebraic cycles and motives.

      Talk chair: Joe Harris

      Video | Slides | Article

    • Conference
      9:00 am-5:30 pm
      12/01/2024-03/01/2023
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Poster_GeometryStatistics_8.5x11.final

      On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

      Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

      This conference will be held in person. Directions and Recommended Lodging

      Registration is required.

      Register here to attend in-person.

      Organizing Committee:
      Stephan Huckemann (Georg-August-Universität Göttingen)
      Ezra Miller (Duke University)
      Zhigang Yao (Harvard CMSA and Committee Chair)

      Scientific Advisors:
      Horng-Tzer Yau (Harvard CMSA)
      Shing-Tung Yau (Harvard CMSA)

      Speakers:

      • Tamara Broderick (MIT)
      • David Donoho (Stanford)
      • Ian Dryden (Florida International University in Miami)
      • David Dunson (Duke)
      • Charles Fefferman (Princeton)
      • Stefanie Jegelka (MIT)
      • Sebastian Kurtek (OSU)
      • Lizhen Lin (Notre Dame)
      • Steve Marron (U North Carolina)
      • Ezra Miller (Duke)
      • Hans-Georg Mueller (UC Davis)
      • Nicolai Reshetikhin (UC Berkeley)
      • Wolfgang Polonik (UC Davis)
      • Amit Singer (Princeton)
      • Zhigang Yao (Harvard CMSA)
      • Bin Yu (Berkeley)

      Moderator: Michael Simkin (Harvard CMSA)

       

      SCHEDULE

      Monday, Feb. 27, 2023 (Eastern Time)

      8:30 amBreakfast
      8:45–8:55 amZhigang YaoWelcome Remarks
      8:55–9:00 amShing-Tung Yau*Remarks
      Morning Session Chair: Zhigang Yao
      9:00–10:00 amDavid DonohoTitle: ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise

      Abstract: Truncation of the singular value decomposition is a true scientific workhorse. But where to Truncate?

      For 55 years the answer, for many scientists, has been to eyeball the scree plot, an approach which still generates hundreds of papers per year.

      I will describe ScreeNOT, a mathematically solid alternative deriving from the many advances in Random Matrix Theory over those 55 years. Assuming a model of low-rank signal plus possibly correlated noise, and adopting an asymptotic viewpoint with number of rows proportional to the number of columns, we show that ScreeNOT has a surprising oracle property.

      It typically achieves exactly, in large finite samples, the lowest possible MSE for matrix recovery, on each given problem instance – i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure.

      The talk is based on joint work with Matan Gavish and Elad Romanov, Hebrew University.

      10:00–10:10 amBreak
      10:10–11:10 amSteve MarronTitle: Modes of Variation in Non-Euclidean Spaces

      Abstract: Modes of Variation provide an intuitive means of understanding variation in populations, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts, including shapes as data objects, vectors of directional data, amplitude and phase variation and compositional data.

      11:10–11:20 amBreak
      11:20 am–12:20 pmZhigang YaoTitle: Manifold fitting: an invitation to statistics

      Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference:https://arxiv.org/abs/1909.10228

       12:20–1:50 pm12:20 pm Group Photo

      followed by Lunch

      Afternoon Session Chair: Stephan Huckemann
      1:50–2:50 pmBin Yu*Title: Interpreting Deep Neural Networks towards Trustworthiness

      Abstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.

      2:50–3:00 pmBreak
      3:00-4:00 pmHans-Georg MuellerTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression

      Abstract: Random objects, i.e., random variables that take values in a separable metric space, pose many challenges for statistical analysis, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions, covariance matrices or surfaces, graph Laplacians to represent networks, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics, an emerging collection of statistical tools to characterize, infer and relate samples of random objects. Recent developments include depth profiles, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey, Y. Chen 2022).

      These distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.

      4:00-4:10 pmBreak
      4:10-5:10 pmStefanie JegelkaTitle: Some benefits of machine learning with invariances

      Abstract: In many applications, especially in the sciences, data and tasks have known invariances. Encoding such invariances directly into a machine learning model can improve learning outcomes, while it also poses challenges on efficient model design. In the first part of the talk, we will focus on the invariances relevant to eigenvectors and eigenspaces being inputs to a neural network. Such inputs are important, for instance, for graph representation learning. We will discuss targeted architectures that can universally express functions with the relevant invariances – sign flips and changes of basis – and their theoretical and empirical benefits.

      Second, we will take a broader, theoretical perspective. Empirically, it is known that encoding invariances into the machine learning model can reduce sample complexity. For the simplified setting of kernel ridge regression or random features, we will discuss new bounds that illustrate two ways in which invariances can reduce sample complexity. Our results hold for learning on manifolds and for invariances to (almost) any group action, and use tools from differential geometry.

      This is joint work with Derek Lim, Joshua Robinson, Behrooz Tahmasebi, Lingxiao Zhao, Tess Smidt, Suvrit Sra, and Haggai Maron.

       

       

       

      Tuesday, Feb. 28, 2023 (Eastern Time)

      8:30-9:00 amBreakfast
      Morning Session Chair: Zhigang Yao
      9:00-10:00 amCharles Fefferman*Title: Lipschitz Selection on Metric Spaces

      Abstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.

      10:00-10:10 amBreak
      10:10-11:10 amDavid DunsonTitle: Inferring manifolds from noisy data using Gaussian processes

      Abstract: In analyzing complex datasets, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm, we provide simulated and real data examples to illustrate the performance. Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478

      11:10-11:20 amBreak
      11:20 am-12:20 pmWolfgang PolonikTitle: Inference in topological data analysis

      Abstract: Topological data analysis has seen a huge increase in popularity finding applications in numerous scientific fields. This motivates the importance of developing a deeper understanding of benefits and limitations of such methods. Using this angle, we will present and discuss some recent results on large sample inference in topological data analysis, including bootstrap for Betti numbers and the Euler characteristics process.

      12:20–1:50 pmLunch
      Afternoon Session Chair: Stephan Huckemann
      1:50-2:50 pmEzra MillerTitle: Geometric central limit theorems on non-smooth spaces

      Abstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data, such as angles or phylogenetic trees, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures, correct analogues of Gaussian random variables, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers, starting with a review of the usual linear CLT and its generalization to smooth manifolds, viewed through a lens that casts the singular CLT as a natural outgrowth, and concluding with how this investigation opens gateways to further advances in geometric probability, topology, and statistics. Joint work with Jonathan Mattingly and Do Tran.

      2:50-3:00 pmBreak
      3:00-4:00 pmLizhen LinTitle: Statistical foundations of deep generative models

      Abstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in empirical performance, theoretical understanding of such models is largely lacking. We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates, and ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.

      4:00-4:10 pmBreak
      4:10-5:10 pmConversation session

       

       

       

      Wednesday, March 1, 2023 (Eastern Time)

      8:30-9:00 amBreakfast
      Morning Session Chair: Ezra Miller
      9:00-10:00 amAmit Singer*Title: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning

      Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.

      10:00-10:10 amBreak
      10:10-11:10 amIan DrydenTitle: Statistical shape analysis of molecule data

      Abstract: Molecular shape data arise in many applications, for example high dimension low sample size cryo-electron microscopy (cryo-EM) data and large temporal sequences of peptides from molecular dynamics simulations. In both applications it is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D sub-shape spaces and provide some practical fitting algorithms. The methodology is applied to cryo-EM data of a large sliding clamp multi-protein complex and to cluster analysis of peptides, where different states of the molecules can be identified. Further molecular modeling tasks include resolution matching, where coarse resolution models are back-mapped into high resolution (atomistic) structures. This is joint work with Kwang-Rae Kim, Charles Laughton and Huiling Le.

      11:10-11:20 amBreak
      11:20 am-12:20 pmTamara BroderickTitle: An Automatic Finite-Sample Robustness Metric: Can Dropping a Little Data Change Conclusions?

      Abstract: One hopes that data analyses will be used to make beneficial decisions regarding people’s health, finances, and well-being. But the data fed to an analysis may systematically differ from the data where these decisions are ultimately applied. For instance, suppose we analyze data in one country and conclude that microcredit is effective at alleviating poverty; based on this analysis, we decide to distribute microcredit in other locations and in future years. We might then ask: can we trust our conclusion to apply under new conditions? If we found that a very small percentage of the original data was instrumental in determining the original conclusion, we might not be confident in the stability of the conclusion under new conditions. So we propose a method to assess the sensitivity of data analyses to the removal of a very small fraction of the data set. Analyzing all possible data subsets of a certain size is computationally prohibitive, so we provide an approximation. We call our resulting method the Approximate Maximum Influence Perturbation. Our approximation is automatically computable, theoretically supported, and works for common estimators. We show that any non-robustness our method finds is conclusive. Empirics demonstrate that while some applications are robust, in others the sign of a treatment effect can be changed by dropping less than 0.1% of the data — even in simple models and even when standard errors are small.

       12:20-1:50 pmLunch
      Afternoon Session Chair: Ezra Miller
      1:50-2:50 pmNicolai Reshetikhin*Title: Random surfaces in exactly solvable models in statistical mechanics.

      Abstract: In the first part of the talk I will be an overview of a few models in statistical mechanics where a random variable is a geometric object such as a random surface or a random curve. The second part will be focused on the behavior of such random surfaces in the thermodynamic limit and on the formation of the so-called “limit shapes”.

      2:50-3:00 pmBreak
      3:00-4:00 pmSebastian KurtekTitle: Robust Persistent Homology Using Elastic Functional Data Analysis

      Abstract: Persistence landscapes are functional summaries of persistence diagrams designed to enable analysis of the diagrams using tools from functional data analysis. They comprise a collection of scalar functions such that birth and death times of topological features in persistence diagrams map to extrema of functions and intervals where they are non-zero. As a consequence, variation in persistence diagrams is encoded in both amplitude and phase components of persistence landscapes. Through functional data analysis of persistence landscapes, under an elastic Riemannian metric, we show how meaningful statistical summaries of persistence landscapes (e.g., mean, dominant directions of variation) can be obtained by decoupling their amplitude and phase variations. This decoupling is achieved via optimal alignment, with respect to the elastic metric, of the persistence landscapes. The estimated phase functions are tied to the resolution parameter that determines the filtration of simplicial complexes used to construct persistence diagrams. For a dataset obtained under geometric, scale and sampling variabilities, the phase function prescribes an optimal rate of increase of the resolution parameter for enhancing the topological signal in a persistence diagram. The proposed approach adds to the statistical analysis of data objects with rich structure compared to past studies. In particular, we focus on two sets of data that have been analyzed in the past, brain artery trees and images of prostate cancer cells, and show that separation of amplitude and phase of persistence landscapes is beneficial in both settings. This is joint work with Dr. James Matuk (Duke University) and Dr. Karthik Bharath (University of Nottingham).

      4:00-4:10 pmBreak
      4:10-5:10 pmConversation session
      5:10-5:20 pmStephan Huckemann, Ezra Miller, Zhigang YaoClosing Remarks

      * Virtual Presentation


       

    • Algebraic Geometry in String Theory Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 02.24.2023

      Algebraic Geometry in String Theory Seminar

      Speaker: Chao-Ming Lin (University of California, Irvine)

      Title: On the convexity of general inverse $\sigma_k$ equations and some applications

      Abstract: In this talk, I will show my recent work on general inverse $\sigma_k$ equations and the deformed Hermitian-Yang-Mills equation (hereinafter the dHYM equation). First, I will show my recent results. This result states that if a level set of a general inverse $\sigma_k$ equation (after translation if needed) is contained in the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the Monge-Ampère equation, the J-equation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special class of univariate polynomials and give a Positivstellensatz type result. These give a numerical criterion to verify whether the level set will be contained in the positive orthant. Last, as an application, I will prove one of the conjectures by Collins-Jacob-Yau when the dimension equals four. This conjecture states that under the supercritical phase assumption, if there exists a C-subsolution to the dHYM equation, then the dHYM equation is solvable.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Geodesics and minimal surfaces
      9:00 am-10:00 am
      12/01/2024
      20220209_Andre-Neves_poster

      Abstract: There are several properties of closed geodesics which are proven using its Hamiltonian formulation, which has no analogue for minimal surfaces. I will talk about some recent progress in proving some of these properties for minimal surfaces.

    • Colloquium
      9:00 am-10:00 am
      12/01/2024
    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Camillo De Lellis (IAS)

      Title: Area-minimizing integral currents and their regularity

      Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will also touch upon several fundamental open problems which still defy our understanding. 

      Talk Chair: William Minicozzi

      Video

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Rational Polypols
      9:00 am-10:00 am
      12/01/2024

      Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics, positive geometries are real semialgebraic sets together with a rational canonical form. We combine these two worlds by providing an explicit formula for the canonical form of a rational polypol in terms of defining equations of the adjoint curve and the facets of the polypol. For the special case of polygons, we show that the adjoint curve is hyperbolic and provide an explicit description of its nested ovals. Finally, we discuss the map that associates the adjoint curve to a given rational polypol, in particular the cases where this map is finite. For instance, using monodromy we find that a general quartic curve is the adjoint of 864 heptagons.

      This talk is based on joint work with R. Piene, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn,  M.-S. Sorea, and S. Telen.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Greedy maximal independent sets via local limits
      9:00 am-10:00 am
      12/01/2024

      Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge.

      In this talk, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs, such as paths and various random graphs, and by providing new results for other models such as random trees.

      If time allows, I will discuss a more delicate (and combinatorial) result, according to which, in expectation, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order.

      The talk is based on joint work with Michael Krivelevich, Tamás Mészáros and Clara Shikhelman.

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Theorems of Torelli type
      9:00 am-10:30 am
      12/01/2024
      Lecture_Looijenga-pdf

      Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University)

      Title: Theorems of Torelli type

      Abstract: Given a closed manifold of even dimension 2n, then Hodge showed around 1950 that a  kählerian complex structure on that manifold determines a decomposition of its complex cohomology. This decomposition, which can potentially vary continuously with the complex structure, extracts from a non-linear given,  linear data. It can contain a lot of information. When there is essentially no loss of data in this process, we say that the Torelli theorem holds.  We review the underlying theory and then survey some cases where this is the case. This will include the classical case n=1, but the emphasis will be on K3 manifolds (n=2) and more generally, on hyperkählerian manifolds. These cases stand out, since one can then also tell which decompositions occur.

      Talk chair: Gerard van der Geer

      Video 

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Yang Qi (Fudan)

      Title: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon

      Abstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon, leading to a significant broadening of the single-particle spectral functions. Quantitatively, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.

      https://www.youtube.com/watch?v=p1q0ots1X5s&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=20

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 10.12.22

      Topological Quantum Matter Seminar

      Speaker: Jennifer Cano (Stony Brook and Flatiron Institute)

      Title: Engineering topological phases with a superlattice potential
      Abstract: We propose an externally imposed superlattice potential as a platform for manipulating topological phases, which has both advantages and disadvantages compared to a moire superlattice. In the first example, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long sought-after goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example, we show that a superlattice potential applied to Bernal-stacked bilayer graphene can generate flat Chern bands, similar to in twisted bilayer graphene, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry, making it a promising alternative to achieve designer flat bands without a moire heterostructure.
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      10/5/2021 Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      Title: Geodesic Geometry on Graphs

      Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

      We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

      Joint work with Nati Linial.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Federico Bonetti (Oxford)

      Title: Non-Invertible Symmetries from Holography and Branes

      Abstract:  The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects, and of their action on extended operators of the 4d QFT.

      https://www.youtube.com/watch?v=opvlpWdTXr4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=21

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Junkai Dong (Harvard University)

      Title: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

      Abstract: Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

       

      https://www.youtube.com/watch?v=RfUKlzKs70o&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=23

    • Workshop
      9:00 am-3:30 pm
      12/01/2024-12/01/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Videos are available on the CMSA Youtube Playlist.

      On November 28 – Dec 1, 2022, the CMSA hosted a Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.

      Organizers: An Huang (Brandeis University) | Siu-Cheong Lau (Boston University) | Tsung-Ju Lee (CMSA, Harvard) | Andrew Linshaw (University of Denver)

      Scientific Advisor: Shing-Tung Yau (Harvard, Tsinghua)

      Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

      Directions and Recommended Lodging

      The conference was held in hybrid format, both in-person and online.

      The workshop was partially supported by Simons and NSF Grant DMS-2227199.

       

      Speakers: 

      • Tomoyuki Arakawa (Kyoto)
      • Thomas Creutzig (Edmonton)
      • Jonathan Mboyo Esole (Northeastern)
      • Fei Han (National University of Singapore)
      • Shinobu Hosono (Gakushuin University)
      • Flor Orosz Hunziker (Colorado)
      • Cuipo Jiang (Shanghai)
      • Shashank Kanade (Denver)
      • Matt Kerr (Washington University in St. Louis)
      • Carl Lian (Humboldt-Universität zu Berlin)
      • Nai-Chung Conan Leung (CUHK)
      • Ivan Loseu (Yale)
      • Robert McRae (Tsinghua University)
      • Anne Moreau (Université Paris-Saclay, Orsay)
      • Tony Pantev (University of Pennsylvania)
      • Mauricio Romo (Tsinghua University)
      • Bailin Song (USTC)
      • Cumrun Vafa (Harvard University)
      • Chin-Lung Wang (National Taiwan University)
      • Weiqiang Wang (Virginia)
      • Yaping Yang (University of Melbourne)
      • Shing-Tung Yau (Tsinghua University)
      • Chenglong Yu (Tsinghua University)
      • Gufang Zhao (University of Melbourne)

       

      Schedule (Eastern Time)

      Schedule (pdf)

      11/28 (Monday)

      08:30am – 08:55amRefreshments
      08:55am – 09:00amOpening remarks by Horng-Tzer Yau
      09:00am – 09:45amShing-Tung Yau*Title: The Hull-Strominger system through conifold transitions

      Abstract: In this talk I discuss the geometry of C-Y manifolds outside of the Kähler regime and especially describe the Hull-Strominger system through the conifold transitions.

      10:00am – 10:45amChenglong Yu*Title: Commensurabilities among Lattices in PU(1,n)

      Abstract: In joint work with Zhiwei Zheng, we study commensurabilities among certain subgroups in PU(1,n). Those groups arise from the monodromy of hypergeometric functions. Their discreteness and arithmeticity are classified by Deligne and Mostow. Thurston also obtained similar results via flat conic metrics. However, the classification of the lattices among them up to conjugation and finite index (commensurability) is not completed. When n=1, it is the commensurabilities of hyperbolic triangles. The cases of n=2 are almost resolved by Deligne-Mostow and Sauter’s commensurability pairs, and commensurability invariants by Kappes-Möller and McMullen. Our approach relies on the study of some higher dimensional Calabi-Yau type varieties instead of complex reflection groups. We obtain some relations and commensurability indices for higher n and also give new proofs for existing pairs in n=2.

      11:00am – 11:45amThomas Creutzig*Title: Shifted equivariant W-algebras

      Abstract: The CDO of a compact Lie group is a family of VOAs whose top level is the space of functions on the Lie group. Similar structures appear at the intersections of boundary conditions in 4-dimensional gauge theories, I will call these new families of VOAs shifted equivariant W-algebras. I will introduce these algebras, construct them and explain how they can be used to quickly prove the GKO-coset realization of principal W-algebras.

      11:45am – 1:30 pmLunch
      01:30pm – 02:15pmCumrun VafaTitle: Reflections on Mirror Symmetry

      Abstract: In this talk I review some of the motivations leading to the search and discovery of mirror symmetry as well as some of the applications it has had.

      02:30pm – 03:15pmJonathan Mboyo EsoleTitle: Algebraic topology and matter representations in F-theory

      Abstract: Recently, it was observed that representations appearing in geometric engineering in F-theory all satisfy a unique property: they correspond to characteristic representations of embedding of Dynkin index one between Lie algebras. However, the reason why that is the case is still being understood. In this talk, I will present new insights, giving a geometric explanation for this fact using K-theory and the topology of Lie groups and their classifying spaces. In physics, this will be interpreted as conditions on the charge of instantons and the classifications of Wess-Zumino-Witten terms.

      03:15pm – 03:45 pmBreak
      03:45pm – 04:30pmWeiqiang WangTitle: A Drinfeld presentation of affine i-quantum groups

      Abstract: A quantum symmetric pair of affine type (U, U^i) consists of a Drinfeld-Jimbo affine quantum group (a quantum deformation of a loop algebra) U and its coideal subalgebra U^i (called i-quantum group). A loop presentation for U was formulated by Drinfeld and proved by Beck. In this talk, we explain how i-quantum groups can be viewed as a generalization of quantum groups, and then we give a Drinfeld type presentation for the affine quasi-split i-quantum group U^i. This is based on joint work with Ming Lu (Sichuan) and Weinan Zhang (Virginia).

      04:45pm – 05:30pmTony PantevTitle: Decomposition, anomalies, and quantum symmetries

      Abstract: Decomposition is a phenomenon in quantum physics which converts quantum field theories with non-effectively acting gauge symmetries into equivalent more tractable theories in which the fields live on a disconnected space. I will explain the mathematical content of decomposition which turns out to be a higher categorical version of Pontryagin duality. I will examine how this duality interacts with quantum anomalies and secondary quantum symmetries and will show how the anomalies can be canceled by homotopy coherent actions of diagrams of groups. I will discuss in detail the case of 2-groupoids which plays a central role in anomaly cancellation, and will describe a new duality operation that yields decomposition in the presence of anomalies. The talk is based on joint works with Robbins, Sharpe, and Vandermeulen.

       

      11/29 (Tuesday)

       

      Refreshments
      09:00am – 09:45amRobert MacRae*Title: Rationality for a large class of affine W-algebras

      Abstract: One of the most important results in vertex operator algebras is Huang’s theorem that the representation category of a “strongly rational” vertex operator algebra is a semisimple modular tensor category. Conversely, it has been conjectured that every (unitary) modular tensor category is the representation category of a strongly rational (unitary) vertex operator algebra. In this talk, I will describe my results on strong rationality for a large class of affine W-algebras at admissible levels. This yields a large family of modular tensor categories which generalize those associated to affine Lie algebras at positive integer levels, as well as those associated to the Virasoro algebra.

      10:00am – 10:45amBailin Song*Title: The global sections of chiral de Rham complexes on compact Calabi-Yau manifolds

      Abstract: Chiral de Rham complex is a sheaf of vertex algebras on a complex manifold. We will describe the space of global sections of the chiral de Rham complexes on compact Calabi-Yau manifolds.

      11:00am – 11:45amCarl Lian*Title: Curve-counting with fixed domain

      Abstract: The fixed-domain curve-counting problem asks for the number of pointed curves of fixed (general) complex structure in a target variety X subject to incidence conditions at the marked points. The question comes in two flavors: one can ask for a virtual count coming from Gromov-Witten theory, in which case the answer can be computed (in principle) from the quantum cohomology of X, or one can ask for the “honest” geometric count, which tends to be more subtle. The answers are conjectured to agree in the presence of sufficient positivity, but do not always. I will give an overview of some recent results and open directions. Some of this work is joint with Alessio Cela, Gavril Farkas, and Rahul Pandharipande.

      11:45am – 01:30pmLunch
      01:30pm – 02:15pmChin-Lung WangTitle: A blowup formula in quantum cohomology

      Abstract: We study analytic continuations of quantum cohomology $QH(Y)$ under a blowup $\phi: Y \to X$ of complex projective manifolds along the extremal ray variable $q^{\ell}$. Under $H(Y) = \phi^* H(X) plus K$ where $K = \ker \phi_*$, we show that (i) the restriction of quantum product along the $\phi^*H(X)$ direction, denoted by $QH(Y)_X$, is meromorphic in $x := 1/q^\ell$, (ii) $K$ deforms uniquely to a quantum ideal $\widetilde K$ in $QH(Y)_X$, (iii) the quotient ring $QH(Y)_X/\widetilde K$ is regular over $x$, and its restriction to $x = 0$ is isomorphic to $QH(X)$. This is a joint work (in progress) with Y.-P. Lee and H.-W. Lin.

      02:30pm – 03:15pmIvan LoseuTitle: Quantizations of nilpotent orbits and their Lagrangian subvarieties

      Abstract: I’ll report on some recent progress on classifying quantizations of the algebras of regular functions of nilpotent orbits (and their covers) in semisimple Lie algebras, as well as the classification of quantizations of certain Lagrangian subvarieties. An ultimate goal here is to understand the classification of unitary representations of real semisimple Lie groups.

      03:15pm – 03:45pmBreak
      03:45pm – 04:30pmMatt Kerr*Title: $K_2$ and quantum curves

      Abstract: The basic objects for this talk are motives consisting of a curve together with a $K_2$ class, and their mixed Hodge-theoretic invariants.

      My main objective will be to explain a connection (recently proved in joint work with C. Doran and S. Sinha Babu) between (i) Hodge-theoretically distinguished points in the moduli of such motives and (ii) eigenvalues of operators on L^2(R) obtained by quantizing the equations of the curves.

      By local mirror symmetry, this gives evidence for a conjecture in topological string theory (due to M. Marino, A. Grassi, and others) relating enumerative invariants of toric CY 3-folds to spectra of quantum curves.

      04:45pm – 05:30pmFlor Orosz HunzikerTitle: Tensor structures associated to the N=1 super Virasoro algebra

      Abstract:  We have recently shown that there is a natural category of representations associated to the N=1 super Virasoro vertex operator algebras that have braided tensor structure. We will describe this category and discuss the problem of establishing its rigidity at particular central charges. This talk is based on joint work in progress with Thomas Creutzig, Robert McRae and Jinwei Yang.

       

       

       

      11/30 (Wednesday)

      08:30am – 09:00amRefreshments
      09:00am – 09:45amTomoyuki ArakawaTitle: 4D/2D duality and representation theory

      Abstract: This talk is about the 4D/2D duality discovered by Beem et al. rather recently in physics. It associates a vertex operator algebra (VOA) to any 4-dimensional superconformal field theory, which is expected to be a complete invariant of thl theory. The VOAs appearing in this manner may be regarded as chiralization of various symplectic singularities and their representations are expected to be closely related with the Coulomb branch of the 4D theory. I will talk about this remarkable 4D/2D duality from a representation theoretic perspective.

      10:00am – 10:45amShashank KanadeTitle: Combinatorics of principal W-algebras of type A

      Abstract: The combinatorics of principal W_r(p,p’) algebras of type A is controlled by cylindric partitions. However, very little seems to be known in general about fermionic expressions for the corresponding characters. Welsh’s work explains the case of Virasoro minimal models W_2(p,p’). Andrews, Schilling and Warnaar invented and used an A_2 version of the usual (A_1) Bailey machinery to give fermionic characters (up to a factor of (q)_\infty) of some, but not all, W_3(3,p’) modules. In a recent joint work with Russell, we have given a complete set of conjectures encompassing all of the remaining modules for W_3(3,p’), and proved our conjectures for small values of p’. In another direction, characters of W_r(p,p’) algebras also arise as appropriate limits of certain sl_r coloured Jones invariants of torus knots T(p,p’), and we expect this to provide further insights on the underlying combinatorics.

      11:00am – 11:45amGufang ZhaoTitle: Quasimaps to quivers with potentials

      Abstract: This talk concerns non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of the potential. The construction borrows ideas from the theory of gauged linear sigma models as well as recent development in shifted symplectic geometry and Donaldson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual counts arising from quivers with potentials are discussed. This is based on work in progress, in collaboration with Yalong Cao.

      11:45am – 01:30pmGroup Photo, Lunch
      01:30pm – 02:15pmYaping YangTitle: Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

      Abstract: Let X be a smooth local toric Calabi-Yau 3-fold. On the cohomology of the moduli spaces of certain sheaves on X, there is an action of the cohomological Hall algebra (COHA) of Kontsevich and Soibelman via “raising operators”. I will discuss the “double” of the COHA that acts on the cohomology of the moduli space by adding the “lowering operators”. We associate a root system to X. The double COHA is expected to be the shifted Yangian of this root system. We also give a prediction for the shift in terms of an intersection pairing. We provide evidence of the aforementioned expectation in various examples. This is based on my joint work with M. Rapcak, Y. Soibelman, and G. Zhao

      02:30pm – 03:15pmFei HanTitle: Graded T-duality with H-flux for 2d sigma models

      Abstract: T-duality in string theory can be realised as a transformation acting on the worldsheet fields in the two-dimensional nonlinear sigma model. Bouwknegt-Evslin-Mathai established the T-duality in a background flux for the first time upon compactifying spacetime in one direction to a principal circle by constructing the T-dual maps transforming the twisted cohomology of the dual spacetimes. In this talk, we will describe our recent work on how to promote the T-duality maps of Bouwknegt-Evslin-Mathai in two aspects. More precisely, we will introduce (1) graded T-duality, concerning the graded T-duality maps of all levels of twistings; (2) the 2-dimensional sigma model picture, concerning the double loop space of spacetimes. This represents our joint work with Mathai.

      03:15pm – 3:45pmBreak
      03:45pm – 04:30pmMauricio RomoTitle: Networks and BPS Counting: A-branes view point

      Abstract: I will review the countings of BPS invariants via exponential/spectral networks and present an interpretation of this counting as a count of certain points in the moduli space of A-branes corresponding to degenerate Lagrangians.

      04:45pm – 05:30pmShinobu HosonoTitle: Mirror symmetry of abelian fibered Calabi-Yau manifolds with ρ = 2

      Abstract: I will describe mirror symmetry of Calabi-Yau manifolds fibered by (1,8)-polarized abelian surfaces, which have Picard number two. Finding a mirror family over a toric variety explicitly, I  observe that mirror symmetry of all related Calabi-Yau manifods arises from the corresponding boundary points, which are not necessarily toric boundary points.  Calculating Gromov-Witten invariants up to genus 2, I find that the generating functions are expressed elliptic (quasi-)modular forms, which reminds us the modular anomaly equation found for elliptic surfaces. This talk is based on a published work with Hiromichi Takaki (arXiv:2103.08150).

      06:00pmBanquet @ Royal East Restaurant, 782 Main St, Cambridge, MA 02139

       

      12/1 (Thursday)

      08:30am – 09:00amRefreshments
      09:00am – 09:45amConan Nai Chung Leung*Title: Quantization of Kahler manifolds

      Abstract: I will explain my recent work on relationships among geometric quantization, deformation quantization, Berezin-Toeplitz quantization and brane quantization.

      10:00am – 10:45amCuipo Jiang*Title: Cohomological varieties associated to vertex operator algebras

      Abstract: We define and examine the cohomological variety of a vertex algebra, a notion cohomologically dual to that of the associated variety, which measures the smoothness of the associated scheme at the vertex point.  We study its basic properties. As examples, we construct a closed subvariety of the cohomological variety for rational affine vertex operator algebras constructed from finite dimensional simple Lie algebras. We also determine the cohomological varieties of the simple Virasoro vertex operator algebras. These examples indicate that, although the associated variety for a rational $C_2$-cofinite vertex operator algebra is always a simple point, the cohomological variety can have as large a dimension as possible. This talk is based on joint work with Antoine Caradot and Zongzhu Lin.

      11:00am – 11:45amAnne Moreau*Title: Action of the automorphism group on the Jacobian of Klein’s quartic curve

      Abstract: In a joint work with Dimitri Markouchevitch, we prove that the quotient variety of the 3-dimensional Jacobian of the plane Klein quartic curve by its full automorphism group of order 336 is isomorphic to the 3-dimensional weighted projective space with weights 1,2,4,7.

      The latter isomorphism is a particular case of the general conjecture of Bernstein and Schwarzman suggesting that a quotient of the n-dimensional complex space by the action of an irreducible complex crystallographic group generated by reflections is a weighted projective space.

      In this talk, I will explain this conjecture and the proof of our result. An important ingredient is the computation of the Hilbert function of the algebra of invariant theta-functions on the Jacobian.

      11:45am – 11:50amClosing remarks
      11:50amFree discussions and departure

      * = Online speaker

      CMSA COVID-19 Policies

       

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 11.23.22

      Topological Quantum Matter Seminar

      Speaker: Jian Kang, School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

      Title: Continuum field theory of graphene bilayer system

      Abstract: The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the magic-angle twisted bilayer graphene (MATBG), and nowadays is a starting point for most theoretical works. In this talk, I will briefly review the BM model and then present a continuum field theory [1] for graphene bilayer system allowing any smooth lattice deformation including the small twist angle. With the gradient expansion to the second order, the continuum theory for MATBG [2] produces the spectrum that almost perfectly matches the spectrum of the microscopic model, suggesting the validity of this theory. In the presence of the lattice deformation, the inclusion of the pseudo-vector potential does not destroy but shift the flat band chiral limit to a smaller twist angle. Furthermore, the continuum theory contains another important interlayer tunneling term that was overlooked in all previous works. This term non-negligibly breaks the particle-hole symmetry of the narrow bands and may be related with the experimentally observed particle-hole asymmetry.

      1. O. Vafek and JK, arXiv: 2208.05933.
      2. JK and O. Vafek, arXiv: 2208.05953.

       

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Sungwoo Hong (U Chicago & KAIST)

      Title: Neutrino Masses from Generalized Symmetry Breaking

      Abstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

       

      https://www.youtube.com/watch?v=4eZa06kiPCs&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=22

    • Program
      9:00 am-5:00 pm
      12/01/2024-05/24/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Mathematical Aspects of Scattering Amplitudes Program

      To receive email updates and program announcements, visit this link to sign up for the CMSA Mathematical Aspects of Scattering Amplitudes Program mailing list.

      Dates: April 15 – May 24, 2024

      Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138

      Organizers:

      Participants:

      This program will feature a weekly seminar series.
      Further Details TBA.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Justin Kulp (Perimeter Institute)

      Title: Holomorphic Twists and Confinement in N=1 SYM

      Abstract: Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

    • Workshop
      9:00 am-5:00 pm
      12/01/2024-05/05/2022
      GR Workshop Poster

      General Relativity Workshop on scalar curvature, minimal surfaces, and initial data sets

      Dates: May 2–5, 2022

      Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138 and via Zoom webinar.
      Advanced registration for in-person components is required.

      Organizers: Dan Lee (CMSA/CUNY), Martin Lesourd (CMSA/BHI), and Lan-Hsuan Huang (University of Connecticut).

      Speakers:

      • Zhongshan An, University of Connecticut
      • Paula Burkhardt-Guim, NYU
      • Hyun Chul Jang, University of Miami
      • Chao Li, NYU
      • Christos Mantoulidis, Rice University
      • Robin Neumayer, Carnegie Mellon University
      • Andre Neves, University of Chicago
      • Tristan Ozuch, MIT
      • Annachiara Piubello, University of Miami
      • Antoine Song, UC Berkeley
      • Tin-Yau Tsang, UC Irvine
      • Ryan Unger, Princeton
      • Zhizhang Xie, Texas A & M
      • Xin Zhou, Cornell University
      • Jonathan Zhu, Princeton University

      Schedule

      Download PDF

      Monday, May 2, 2022

      9:30–10:30 amHyun Chul JangTitle: Mass rigidity for asymptotically locally hyperbolic manifolds with boundary

      Abstract: Asymptotically locally hyperbolic (ALH) manifolds are a class of manifolds whose sectional curvature converges to −1 at infinity. If a given ALH manifold is asymptotic to a static reference manifold, the Wang-Chruściel-Herzlich mass integrals are well-defined, which is a geometric invariant that essentially measure the difference from the reference manifold. In this talk, I will present the result that an ALH manifold which minimize the mass integrals admits a static potential. To show this, we proved the scalar curvature map is locally surjective when it is defined on (1) the space of ALH metrics that coincide exponentially toward the boundary or (2) the space of ALH metrics with arbitrarily prescribed nearby Bartnik boundary data. And then, we establish the rigidity of the known positive mass theorems by studying the static uniqueness. This talk is based on joint work with L.-H. Huang.

      10:40–11:40 amAnnachiara PiubelloTitle: Estimates on the Bartnik mass and their geometric implications.

      Abstract: In this talk, we will discuss some recent estimates on the Bartnik mass for data with non-negative Gauss curvature and positive mean curvature. In particular, if the metric is round the estimate reduces to an estimate found by Miao and if the total mean curvature approaches 0, the estimate tends to 1/2 the area radius, which is the bound found by Mantoulidis and Schoen in the blackhole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.

      LUNCH BREAK
      1:30–2:30 pmRyan UngerTitle: Density and positive mass theorems for black holes and incomplete manifolds

      Abstract: We generalize the density theorems for the Einstein constraint equations of Corvino-Schoen and Eichmair-Huang-Lee-Schoen to allow for marginally outer trapped boundaries (which correspond physically to apparent horizons). As an application, we resolve the spacetime positive mass theorem in the presence of MOTS boundary in the non-spin case. This also has a surprising application to the Riemannian setting, including a non-filling result for manifolds with negative mass. This is joint work with Martin Lesourd and Dan Lee.

      2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications I

      Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

      TEA BREAK
      4:10–5:10 pmAntoine Song (virtual)Title: The spherical Plateau problem

      Abstract: For any closed oriented manifold with fundamental group G, or more generally any group homology class for a group G, I will discuss an infinite codimension Plateau problem in a Hilbert classifying space for G. For instance, for a closed oriented 3-manifold M, the intrinsic geometry of any Plateau solution is given by the hyperbolic part of M.

      Tuesday, May 3, 2022

      9:30–10:30 amChao LiTitle: Stable minimal hypersurfaces in 4-manifolds

      Abstract: There have been a classical theory for complete minimal surfaces in 3-manifolds, including the stable Bernstein conjecture in R^3 and rigidity results in 3-manifolds with positive Ricci curvature. In this talk, I will discuss how one may extend these results in four dimensions. This leads to new comparison theorems for positively curved 4-manifolds.

      10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds I

      Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

      LUNCH BREAK
      1:30–2:30 pmZhongshan AnTitle: Local existence and uniqueness of static vacuum extensions of Bartnik boundary data

      Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data — the induced metric and mean curvature of the boundary — is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang.

      2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications II

      Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

      TEA BREAK
      4:10–5:10 pmTin-Yau TsangTitle: Dihedral rigidity, fill-in and spacetime positive mass theorem

      Abstract: For compact manifolds with boundary, to characterise the relation between scalar curvature and boundary geometry, Gromov proposed dihedral rigidity conjecture and fill-in conjecture. In this talk, we will see the role of spacetime positive mass theorem in answering the corresponding questions for initial data sets.

      Speakers Banquet

      Wednesday, May 4, 2022

      9:30–10:30 amTristan OzuchTitle: Weighted versions of scalar curvature, mass and spin geometry for Ricci flows

      Abstract: With A. Deruelle, we define a Perelman-like functional for ALE metrics which lets us study the (in)stability of Ricci-flat ALE metrics. With J. Baldauf, we extend some classical objects and formulas from the study of scalar curvature, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.

      10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds II

      Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

      LUNCH BREAK
      1:30–2:30 pmChristos MantoulidisTitle: Metrics with lambda_1(-Delta+kR) > 0 and applications to the Riemannian Penrose Inequality

      Abstract: On a closed n-dimensional manifold, consider the space of all Riemannian metrics for which -Delta+kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally, for different values of k, in the study of scalar curvature in dimension n + 1 via minimal surfaces, the Yamabe problem in dimension n, and Perelman’s surgery for Ricci flow in dimension n = 3. We study these spaces in unison and generalize, as appropriate, scalar curvature results that we eventually apply to k = 1/2, where the space above models apparent horizons in time-symmetric initial data sets to the Einstein equations and whose flexibility properties are intimately tied with the instability of the Riemannian Penrose Inequality. This is joint work with Chao Li.

      2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications III

      Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

      TEA BREAK
      4:10–5:10 pmXin Zhou
      (Virtual)
      Title: Min-max minimal hypersurfaces with higher multiplicity

      Abstract: It is well known that minimal hypersurfaces produced by the Almgren-Pitts min-max theory are counted with integer multiplicities. For bumpy metrics (which form a generic set), the multiplicities are one thanks to the resolution of the Marques-Neves Multiplicity One Conjecture. In this talk, we will exhibit a set of non-bumpy metrics on the standard (n+1)-sphere, in which the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere. Such non-bumpy metrics form the first set of examples where the min-max theory must produce higher multiplicity minimal hypersurfaces. The talk is based on a joint work with Zhichao Wang (UBC).

      May 5, 2022

      9:00–10:00 amAndre NevesTitle: Metrics on spheres where all the equators are minimal

      Abstract: I will talk about joint work with Lucas Ambrozio and Fernando Marques where we study the space of metrics where all the equators are minimal.

      10:10–11:10 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds III

      Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

      11:20–12:20 pmPaula Burkhardt-GuimTitle: Lower scalar curvature bounds for C^0 metrics: a Ricci flow approach

      Abstract: We describe some recent work that has been done to generalize the notion of lower scalar curvature bounds to C^0 metrics, including a localized Ricci flow approach. In particular, we show the following: that there is a Ricci flow definition which is stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C^0 initial data.

      LUNCH BREAK
      1:30–2:30 pmJonathan ZhuTitle: Widths, minimal submanifolds and symplectic embeddings

      Abstract: Width or waist inequalities measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels.

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.26.2022-1583x2048-1

      Abstract: In spatial population genetics, it is important to understand the probability of extinction in multi-species interactions such as growing bacterial colonies, cancer tumor evolution and human migration. This is because extinction probabilities are instrumental in determining the probability of coexistence and the genealogies of populations. A key challenge is the complication due to spatial effect and different sources of stochasticity. In this talk, I will discuss about methods to compute the probability of extinction and other long-time behaviors for stochastic reaction-diffusion equations on metric graphs that flexibly parametrizes the underlying space. Based on recent joint work with Adrian Gonzalez-Casanova and Yifan (Johnny) Yang.

    • Colloquium
      Colloquium Colloquia & Seminar
      Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a seminar on Combinatorics, Physics and Probability, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu).

      The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/25/2022
      *note special time 9:00–10:00 AM ET
      Jacob Bourjaily (Penn State University, Eberly College of ScienceTitle: Adventures in Perturbation Theory

      Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

      2/3/2022Ran Tessler
      (Weizmann Institute of Science)
      Title: The Amplituhedron BCFW Triangulation

      Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

      2/8/2022Anna Seigal (Harvard)Title: Invariant theory for maximum likelihood estimation

      Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

      2/15/2022Igor Balla, Hebrew University of JerusalemTitle: Equiangular lines and regular graphs

      Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

      Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
      the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/21/2021Nima Arkani-Hamed
      IAS (Institute for Advanced Study), School of Natural Sciences
      Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes
      9/28/2021Melissa Sherman-Bennett
      University of Michigan, Department of Mathematics
      Title: The hypersimplex and the m=2 amplituhedron

      Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

      10/5/2021Daniel Cizma, Hebrew UniversityTitle: Geodesic Geometry on Graphs

      Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

      We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

      Joint work with Nati Linial.

      10/12/2021Lisa Sauermann, MITTitle: On counting algebraically defined graphs

      Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

      10/19/2021Pavel Galashin
      UCLA, Department of Mathematics
      Title: Ising model, total positivity, and criticality

      Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
      The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
      I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model.

      10/26/2021Candida Bowtell, University of OxfordTitle: The n-queens problem

      Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

      In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

      This is joint work with Peter Keevash.

      11/9/2021Steven Karp
      Universite du Quebec a Montreal, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)
      Title: Gradient flows on totally nonnegative flag varieties

      Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.
      11/16/2021
      *note special time 12:30–1:30 ET*
      Yinon Spinka (University of British Columbia)Title: A tale of two balloons

      Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
      Joint work with Omer Angel and Gourab Ray.

      11/23/2021Lutz Warnke (UC San Diego)Title: Prague dimension of random graphs

      Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

      11/30/2021Karel Devriendt (University of Oxford)Title: Resistance curvature – a new discrete curvature on graphs

      Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
      In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
      Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
      This work was done in collaboration with Renaud Lambiotte.

      12/7/2021Matthew Jenssen (University of Birmingham)Title: The singularity probability of random symmetric matrices

      Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

      12/14/2021Stefan Glock (ETH Zurich)Title: The longest induced path in a sparse random graph

      Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

      12/21/2021
      01/25/2022Jacob Bourjaily
      Penn State University, Department of Physics
    • Program
      9:00 am-5:00 pm
      12/01/2024-06/12/2022
      CMSA-2-600x338

      The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

      Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

      In this course, we will start with an introduction to computer programming, algorithms, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, and differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

      The program hopes to provide several research mentors from various disciplines who will give some of the course lectures. Students will have the opportunity to work with one of the research mentors offered by the program.

      Prerequisites: Basic coding ability in some programming language (C/Python/Matlab or CS50 experience). Some background in calculus and linear algebra is needed too. If you wish to work with a research mentor on differential geometry, more background in geometry such as from Math 132 or 136 will be useful. If you wish to work with a research mentor on computer science, coding experience mentioned above will be very useful. If you wish to work with a medical scientist, some background in life science or basic organic chemistry is recommended.

      The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

      This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard-related perks (such as a place to live if you are in Boston over the summer.)

      However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third-year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

      If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited, so don’t wait too long to apply.

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.19.22-1583x2048-1

      Abstract: Conditional independence (CI) is an important tool instatistical modeling, as, for example, it gives a statistical interpretation to graphical models. In general, given a list of dependencies among random variables, it is difficult to say which constraints are implied by them. Moreover, it is important to know what constraints on the random variables are caused by hidden variables. On the other hand, such constraints are corresponding to some determinantal conditions on the tensor of joint probabilities of the observed random variables. Hence, the inference question in statistics relates to understanding the algebraic and geometric properties of determinantal varieties such as their irreducible decompositions or determining their defining equations. I will explain some recent progress that arises by uncovering the link to point configurations in matroid theory and incidence geometry. This connection, in particular, leads to effective computational approaches for (1) giving a decomposition for each CI variety; (2) identifying each component in the decomposition as a matroid variety; (3) determining whether the variety has a real point or equivalently there is a statistical model satisfying a given collection of dependencies. The talk is based on joint works with Oliver Clarke, Kevin Grace, and Harshit Motwani.

      The papers are available on arxiv: https://arxiv.org/pdf/2011.02450
      and https://arxiv.org/pdf/2103.16550.pdf

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/22/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Conference
      9:00 am-6:00 pm
      12/01/2024
      150 Western Ave, Allston, MA 02134
      SMaSH_2022-2

      SMaSH: Symposium for Mathematical Sciences at Harvard

      On Tuesday, May 17, 2022, from 9:00 am – 5:30 pm, the Harvard John A Paulson School of Engineering and Applied Sciences (SEAS) and the Harvard Center of Mathematical Sciences and Applications (CMSA) held a Symposium for Mathematical Sciences for the mathematical sciences community at Harvard.

      Organizing Committee

      • Michael Brenner, Applied Mathematics (SEAS)
      • Michael Desai, Organismic and Evolutionary Biology (FAS)
      • Sam Gershman, Psychology (FAS)
      • Michael Hopkins, Mathematics (FAS)
      • Gary King, Government (FAS)
      • Peter Koellner, Philosophy (FAS)
      • Scott Kominers, Economics (FAS) & Entrepreneurial Management (HBS)
      • Xihong Lin, Biostatistics (HSPH) & Statistics (FAS)
      • Yue Lu, Electrical Engineering (SEAS)
      • Susan Murphy, Statistics (FAS) & Computer Science (SEAS)
      • Lisa Randall, Physics (SEAS)
      • Eugene Shakhnovich, Chemistry (FAS)
      • Salil Vadhan, Computer Science (SEAS)
      • Horng-Tzer Yau, Mathematics (FAS)

      This event was held in-person at the Science and Engineering Complex (SEC) at 150 Western Ave, Allston, MA 02134, and streamed on Zoom.

      Harvard graduate students and postdocs presented Poster Sessions.


      Venue: Science and Engineering Complex (SEC)


      Speakers

      • Anurag Anshu, Computer Science (SEAS)
      • Morgane Austern, Statistics (FAS)
      • Demba Ba, Electrical Engineering & Bioengineering (SEAS)
      • Michael Brenner, Applied Mathematics (SEAS)
      • Rui Duan, Biostatistics (HSPH)
      • Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)
      • Kosuke Imai, Government & Statistics (FAS)
      • Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)
      • Seth Neel, Technology & Operations Management (HBS)
      • Melanie Matchett Wood, Mathematics (FAS)

      Schedule PDF

      Schedule

      9:00–9:30 amCoffee and Breakfast
      West Atrium (ground floor of the SEC)
      9:30–10:30 amFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumKosuke Imai, Government & Statistics (FAS): Use of Simulation Algorithms for Legislative Redistricting Analysis and EvaluationYannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS): The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization
      10:30–11:00 amCoffee Break
      West Atrium (ground floor of the SEC)
      11:00–12:00 pmFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumSeth Neel, Technology & Operations Management (HBS): “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy LawDemba Ba, Electrical Engineering & Bioengineering (SEAS): Geometry, AI, and the Brain
      12:00–1:00 pmLunch Break
      Engineering Yard Tent
      1:00–2:30 pmFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMelanie Matchett Wood, Mathematics (FAS): Understanding distributions of algebraic structures through their momentsMorgane Austern, Statistics (FAS): Limit theorems for structured random objectsAnurag Anshu, Computer Science (SEAS): Operator-valued polynomial approximations and their use.
      2:30–3:00 pmCoffee Break
      West Atrium (ground floor of the SEC)
      3:00–4:30 pmFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMichael Brenner, Applied Mathematics (SEAS): Towards living synthetic materialsRui Duan, Biostatistics (HSPH): Federated and transfer learning for healthcare data integrationSham M. Kakade, Computer Science (SEAS) & Statistics (FAS): What is the Statistical Complexity of Reinforcement Learning?
      4:30–5:30 pmReception with Jazz musicians
      & Poster Session
      Engineering Yard Tent

      Faculty Talks

      SpeakerTitle / Abstract / Bio
      Anurag Anshu, Computer Science (SEAS)Title: Operator-valued polynomial approximations and their use.

      Abstract: Approximation of complicated functions with low degree polynomials is an indispensable tool in mathematics. This becomes particularly relevant in computer science, where the complexity of interesting functions is often captured by the degree of the approximating polynomials. This talk concerns the approximation of operator-valued functions (such as the exponential of a hermitian matrix, or the intersection of two projectors) with low-degree operator-valued polynomials. We will highlight the challenges that arise in achieving similarly good approximations as real-valued functions, as well as recent methods to overcome them. We will discuss applications to the ground states in physics and quantum complexity theory: correlation lengths, area laws and concentration bounds.

      Bio: Anurag Anshu is an Assistant Professor of computer science at Harvard University. He spends a lot of time exploring the rich structure of quantum many-body systems from the viewpoint of quantum complexity theory, quantum learning theory and quantum information theory. He held postdoctoral positions at University of California, Berkeley and University of Waterloo and received his PhD from National University of Singapore, focusing on quantum communication complexity.

      Morgane Austern, Statistics (FAS)Title: Limit theorems for structured random objects

      Abstract: Statistical inference relies on numerous tools from probability theory to study the properties of estimators. Some of the most central ones are the central limit theorem and the free central limit theorem. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting. We consider distributionally “structured’ and dependent random object i.e random objects whose distribution is invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory.

      Bio: Morgane Austern is an assistant professor in the Statistics Department of Harvard University. Broadly, she is interested in developing probability tools for modern machine learning and in establishing the properties of learning algorithms in structured and dependent data contexts. She graduated with a PhD in statistics from Columbia University in 2019 where she worked in collaboration with Peter Orbanz and Arian Maleki on limit theorems for dependent and structured data. She was a postdoctoral researcher at Microsoft Research New England from 2019 to 2021.

      Demba Ba, Electrical Engineering & Bioengineering (SEAS)Title: Geometry, AI, and the Brain

      Abstract: A large body of experiments suggests that neural computations reflect, in some sense, the geometry of “the world”. How do artificial and neural systems learn representations of “the world” that reflect its geometry? How, for instance, do we, as humans, learn representations of objects, e.g. fruits, that reflect the geometry of object space? Developing artificial systems that can capture/understand the geometry of the data they process may enable them to learn representations useful in many different contexts and tasks. My talk will describe an artificial neural-network architecture that, starting from a simple union-of-manifold model of data comprising objects from different categories, mimics some aspects of how primates learn, organize, and retrieve concepts, in a manner that respects the geometry of object space.

      Bio: Demba Ba serves as an Associate Professor of electrical engineering and bioengineering in Harvard University’s School of Engineering and Applied Sciences, where he directs the CRISP group. Recently, he has taken a keen interest in the connection between artificial neural networks and sparse signal processing. His group leverages this connection to solve data-driven unsupervised learning problems in neuroscience, to understand the principles of hierarchical representations of sensory signals in the brain, and to develop explainable AI. In 2016, he received a Research Fellowship in Neuroscience from the Alfred P. Sloan Foundation. In 2021, Harvard’s Faculty of Arts and Sciences awarded him the Roslyn Abramson award for outstanding undergraduate teaching.

      Michael Brenner, Applied Mathematics (SEAS)Title: Towards living synthetic materials

      Abstract: Biological materials are much more complicated and functional than synthetic ones. Over the past several years we have been trying to figure out why. A sensible hypothesis is that biological materials are programmable. But we are very far from being able to program materials we create with this level of sophistication.  I will discuss our (largely unsuccessful) efforts to bridge this gap, though as of today I’m somewhat optimistic that we are arriving at a set of theoretical models that is rich enough to produce relevant emergent behavior.

      Bio: I’ve been at Harvard for a long time. My favorite part of Harvard is the students.

      Rui Duan, Biostatistics (HSPH)Title: Federated and transfer learning for healthcare data integration

      Abstract: The growth of availability and variety of healthcare data sources has provided unique opportunities for data integration and evidence synthesis, which can potentially accelerate knowledge discovery and improve clinical decision-making. However, many practical and technical challenges, such as data privacy, high dimensionality, and heterogeneity across different datasets, remain to be addressed. In this talk, I will introduce several methods for the effective and efficient integration of multiple healthcare datasets in order to train statistical or machine learning models with improved generalizability and transferability. Specifically, we develop communication-efficient federated learning algorithms for jointly analyzing multiple datasets without the need of sharing patient-level data, as well as transfer learning approaches that leverage shared knowledge learned across multiple datasets to improve the performance of statistical models in target populations of interest. We will discuss both the theoretical properties and examples of implementation of our methods in real-world research networks and data consortia.

      Bio: Rui Duan is an Assistant Professor of Biostatistics at the Harvard T.H. Chan School of Public Health. She received her Ph.D. in Biostatistics in May 2020 from the University of Pennsylvania. Her research interests focus on developing statistical, machine learning, and informatics tools for (1) efficient data integration in biomedical research, (2) understanding and accounting for the heterogeneity of biomedical data, and improving the generalizability and transferability of models across populations (3) advancing precision medicine research on rare diseases and underrepresented populations.

      Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)Title: The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization

      Abstract: We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε > 0, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples.

      Our fully nonparametric approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that are not necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art.

      Joint work with S. Matthew Weinberg

      Bio: Yannai A. Gonczarowski is an Assistant Professor of Economics and of Computer Science at Harvard University—the first faculty member at Harvard to have been appointed to both of these departments. Interested in both economic theory and theoretical computer science, Yannai explores computer-science-inspired economics: he harnesses approaches, aesthetics, and techniques traditionally originating in computer science to derive economically meaningful insights. Yannai received his PhD from the Departments of Math and CS, and the Center for the Study of Rationality, at the Hebrew University of Jerusalem, where he was advised by Sergiu Hart and Noam Nisan. Yannai is also a professionally-trained opera singer, having acquired a bachelor’s degree and a master’s degree in Classical Singing at the Jerusalem Academy of Music and Dance. Yannai’s doctoral dissertation was recognized with several awards, including the 2018 Michael B. Maschler Prize of the Israeli Chapter of the Game Theory Society, and the ACM SIGecom Doctoral Dissertation Award for 2018. For the design and implementation of the National Matching System for Gap-Year Programs in Israel, he was awarded the Best Paper Award at MATCH-UP’19 and the inaugural INFORMS AMD Michael H. Rothkopf Junior Researcher Paper Prize (first place) for 2020. Yannai is also the recipient of the inaugural ACM SIGecom Award for Best Presentation by a Student or Postdoctoral Researcher at EC’18. His first textbook, “Mathematical Logic through Python” (Gonczarowski and Nisan), which introduces a new approach to teaching the material of a basic Logic course to Computer Science students, tailored to the unique intuitions and strengths of this cohort of students, is forthcoming in Cambridge University Press.

      Kosuke Imai, Government & Statistics (FAS)Title: Use of Simulation Algorithms for Legislative Redistricting Analysis and Evaluation

      Abstract: After the 2020 Census, many states have been redrawing the boundaries of Congressional and state legislative districts. To evaluate the partisan and racial bias of redistricting plans, scholars have developed Monte Carlo simulation algorithms. The idea is to generate a representative sample of redistricting plans under a specified set of criteria and conduct a statistical hypothesis test by comparing a proposed plan with these simulated plans. I will give a brief overview of these redistricting simulation algorithms and discuss how they are used in real-world court cases.

      Bio: Kosuke Imai is Professor in the Department of Government and Department of Statistics at Harvard University. Before moving to Harvard in 2018, Imai taught at Princeton University for 15 years where he was the founding director of the Program in Statistics and Machine Learning. Imai specializes in the development of statistical methods and machine learning algorithms and their applications to social science research. His areas of expertise include causal inference, computational social science, program evaluation, and survey methodology.

      Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)Title: What is the Statistical Complexity of Reinforcement Learning?

      Abstract: This talk will highlight much of the recent progress on the following fundamental question in the theory of reinforcement learning: what (representational or structural) conditions govern our ability to generalize and avoid the curse of dimensionality?  With regards to supervised learning, these questions are reasonably well understood, both practically and theoretically: practically, we have overwhelming evidence on the value of representational learning (say through modern deep networks) as a means for sample efficient learning, and, theoretically, there are well-known complexity measures (e.g. the VC dimension and Rademacher complexity) that govern the statistical complexity of learning.  Providing an analogous theory for reinforcement learning is far more challenging, where even characterizing structural conditions which support sample efficient generalization has been far less well understood, until recently.

      This talk will survey recent advances towards characterizing when generalization is possible in RL, focusing on both necessary and sufficient conditions. In particular, we will introduce a new complexity measure, the Decision-Estimation Coefficient, that is proven to be necessary (and, essentially, sufficient) for sample-efficient interactive learning.

      Bio: Sham Kakade is a professor at Harvard University and a co-director of the Kempner Institute for the Study of Artificial and Natural Intelligence.  He works on the mathematical foundations of machine learning and AI. Sham’s thesis helped lay the statistical foundations of reinforcement learning. With his collaborators, his additional contributions include foundational results on: policy gradient methods in reinforcement learning; regret bounds for linear bandit and Gaussian process bandit models; the tensor and spectral methods for latent variable models; and a number of convergence analyses for convex and non-convex algorithms.  He is the recipient of the ICML Test of Time Award, the IBM Pat Goldberg best paper award, and INFORMS Revenue Management and Pricing Prize. He has been program chair for COLT 2011.

      Sham was an undergraduate at Caltech, where he studied physics and worked under the guidance of John Preskill in quantum computing. He completed his Ph.D. with Peter Dayan in computational neuroscience at the Gatsby Computational Neuroscience Unit. He was a postdoc with Michael Kearns at the University of Pennsylvania.

      Seth Neel, Technology & Operations Management (HBS)Title: “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy Law

      Abstract:  Businesses like Facebook and Google depend on training sophisticated models on user data. Increasingly—in part because of regulations like the European Union’s General Data Protection Act and the California Consumer Privacy Act—these organizations are receiving requests to delete the data of particular users. But what should that mean? It is straightforward to delete a customer’s data from a database and stop using it to train future models. But what about models that have already been trained using an individual’s data? These are not necessarily safe; it is known that individual training data can be exfiltrated from models trained in standard ways via model inversion attacks. In a series of papers we help formalize a rigorous notion of data-deletion and propose algorithms to efficiently delete user data from trained models with provable guarantees in both convex and non-convex settings.

      Bio: Seth Neel is a first-year Assistant Professor in the TOM Unit at Harvard Business School, and Co-PI of the SAFR ML Lab in the D3 Institute, which develops methodology to incorporate privacy and fairness guarantees into techniques for machine learning and data analysis, while balancing other critical considerations like accuracy, efficiency, and interpretability. He obtained his Ph.D. from the University of Pennsylvania in 2020 where he was an NSF graduate fellow. His work has focused primarily on differential privacy, notions of fairness in a variety of machine learning settings, and adaptive data analysis.

      Melanie Matchett Wood, Mathematics (FAS)Title: Understanding distributions of algebraic structures through their moments

      Abstract: A classical tool of probability and analysis is to use the moments (mean, variance, etc.) of a distribution to recognize an unknown distribution of real numbers.  In recent work, we are interested in distributions of algebraic structures that can’t be captured in a single number.  We will explain one example, the fundamental group, that captures something about the shapes of possibly complicated or high dimensional spaces.  We are developing a new theory of the moment problem for random algebraic structures which helps to to identify distributions of such, such as fundamental groups of random three dimensional spaces.  This talk is based partly on joint work with Will Sawin.

      Bio: Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study.  Her work spans number theory, algebraic geometry, algebraic topology, additive combinatorics, and probability. Wood has been awarded a CAREER grant, a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, and the AWM-Microsoft Research Prize in Algebra and Number Theory, and she is a Fellow of the American Mathematical Society. In 2021, Wood received the National Science Foundation’s Alan T. Waterman Award, the nation’s highest honor for early-career scientists and engineers.


    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Frances Kirwan (University of Oxford)

      TitleMoment maps and the Yang-Mills functional

      Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led.

      This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

      Talk chair: Peter Kronheimer

      Video

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/29/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Conference in Memory of Professor Masatake Kuranishi
      9:00 am-12:30 pm
      12/01/2024-05/12/2022
      150 Western Ave, Allston, MA 02134
      Kuranishi_Harvard_10x12-2

      On May 9–12, 2022, the CMSA hosted the conference Deformations of structures and moduli in geometry and analysis: A Memorial in honor of Professor Masatake Kuranishi.

      Organizers:  Tristan Collins (MIT) and Shing-Tung Yau (Harvard and Tsinghua)

      Videos are available on the conference playlist.

       

      Speakers:

      Charles Fefferman (Princeton University)

      Teng Fei (Rutgers University)

      Robert Friedman (Columbia University)

      Kenji Fukaya (Simons Center, Stony Brook)

      Akito Futaki (Tsinghua University)

      Victor Guillemin (Massachusetts Institute of Technology)

      Nigel Hitchin (Oxford University)

      Blaine Lawson (Stony Brook University)

      Yu-Shen Lin (Boston University)

      Melissa C.C. Liu (Columbia University)

      Takeo Ohsawa (Nagoya University)

      Duong H. Phong (Columbia University)

      Sebastien Picard (University of British Columbia)

      Paul Seidel (Massachusetts Institute of Technology)

      Gabor Szekelyhidi (University of Notre Dame)

      Claire Voisin (Institut de Mathematiques, Jussieu, France)

      Shing-Tung Yau (Harvard University)

       

      Schedule (download pdf)


      Monday, May 9, 2022

      8:15 amLight breakfast & coffee/tea
      8:45–9:00 amOpening Remarks
      9:00–10:00 amKenji FukayaTitle: Gromov Hausdorff convergence of filtered A infinity category

      Abstract: In mirror symmetry a mirror to a symplectic manifold is actually believed to be a family of complex manifold parametrized by a disk (of radius 0). The coordinate ring of the parameter space is a kind of formal power series ring the Novikov ring. Novikov ring is a coefficient ring of Floer homology. Most of the works on homological Mirror symmetry so far studies A infinity category over Novikov field, which corresponds to the study of generic fiber. The study of A infinity category over Novikov ring is related to several interesting phenomenon of Hamiltonian dynamics. In this talk I will explain a notion which I believe is useful to study mirror symmetry.

      Video

      10:15–11:15 amNigel Hitchin (Zoom)Title: Deformations: A personal perspective

      Abstract: The talk, largely historical, will focus on different deformation complexes I have encountered in my work, starting with instantons on 4-manifolds, but also monopoles, Higgs bundles and generalized complex structures. I will also discuss some speculative ideas related to surfaces of negative curvature.

      Video

      11:30–12:30 pmH. Blaine LawsonTitle: Projective Hulls, Projective Linking, and Boundaries of Varieties

      Abstract: In 1958 John Wermer proved that the polynomial hull of a compact real analytic curve γ ⊂ Cn was a 1-dim’l complex subvariety of Cn − γ. This result engendered much subsequent activity, and was related to Gelfand’s spectrum of a Banach algebra. In the early 2000’s Reese Harvey and I found a projective analogue of these concepts and wondered whether Wermer’s Theorem could be generalized to the projective setting. This question turned out to be more subtle and quite intriguing, with unexpected consequences. We now know a great deal, a highpoint of which s a result with Harvey and Wermer. It led to conjectures (for Cω-curves in P2C) which imply several results. One says, roughly, that a (2p − 1)-cycle Γ in Pn bounds a positive holomorphic p-chain of mass ≤ Λ ⇐⇒ its normalized linking number with all positive (n − p)-cycles in Pn − |Γ| is ≥ −Λ. Another says that a class τ ∈ H2p(Pn,|Γ|;Z) with ∂τ = Γ contains a positive holomorphic p-chain ⇐⇒ τ•[Z]≥0 for all positive holomorphic (n−p)-cycles Z in Pn−|Γ|

      Video

      12:30–2:30 pmLunch Break
      2:30–3:30 pmGabor SzekelyhidiTitle: Singularities along the Lagrangian mean curvature flow.

      Abstract: We study singularity formation along the Lagrangian mean curvature flow of surfaces. On the one hand we show that if a tangent flow at a singularity is the special Lagrangian union of two transverse planes, then the flow undergoes a “neck pinch”, and can be continued past the flow. This can be related to the Thomas-Yau conjecture on stability conditions along the Lagrangian mean curvature flow. In a different direction we show that ancient solutions of the flow, whose blow-down is given by two planes meeting along a line, must be translators. These are joint works with Jason Lotay and Felix Schulze.

      Video

      3:30–4:00 pmCoffee Break 
      4:00–5:00 pmTakeo OhsawaTitle: Glimpses of embeddings and deformations of CR manifolds

      Abstract: Basic results on the embeddings and the deformations of CR manifolds will be reviewed with emphasis on the reminiscences of impressive moments with Kuranishi since his visit to Kyoto in 1975.

      Video

       

       

       

      Tuesday, May 10, 2022

       

      8:15 amLight breakfast & coffee/tea
      9:00–10:00 amCharles Fefferman (Zoom)Title: Interpolation of Data by Smooth Functions

      Abstract: Let X be your favorite Banach space of continuous functions on R^n. Given an (arbitrary) set E in R^n and an arbitrary function f:E->R, we ask: How can we tell whether f extends to a function F \in X? If such an F exists, then how small can we take its norm? What can we say about its derivatives (assuming functions in X have derivatives)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F as above with norm nearly as small as possible? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few data points (x, f(x)) as “outliers”? Which points should we discard?

      The results were obtained jointly with A. Israel, B. Klartag, G.K. Luli and P. Shvartsman over many years.

      Video

      10:15–11:15 amClaire VoisinTitle: Deformations of K-trivial manifolds and applications to hyper-Kähler geometry

      Summary: I will explain the Ran approach via the T^1-lifting principle to the BTT theorem stating that deformations of K-trivial compact Kähler manifolds are unobstructed. I will explain a similar unobstructedness result for Lagrangian submanifolds of hyper-Kähler manifolds and I will describe important consequences on the topology and geometry of hyper-Kähler manifolds.

      Video

      11:30– 2:30 pmVictor GuilleminTitle: Semi-Classical Functions of Isotropic Type

      Abstract: The world of semiclassical analysis is populated by objects of “Lagrangian type.” The topic of this talk however will be objects in semi-classical analysis that live instead on isotropic submanifolds. I will describe in my talk a lot of interesting examples of such objects.

      Video

      12:30–2:30 pmLunch Break
      2:30–3:30 pmTeng FeiTitle: Symplectic deformations and the Type IIA flow

      Abstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong, Picard and Zhang.

      Video

      Speakers Banquet

       

       

       

      Wednesday, May 11, 2022

       

      8:15 amLight breakfast & coffee/tea
      9:00–10:00 amShing-Tung Yau (Zoom)Title: Canonical metrics and stability in mirror symmetry

      Abstract: I will discuss the deformed Hermitian-Yang-Mills equation, its role in mirror symmetry and its connections to notions of stability.  I will review what is known, and pose some questions for the future.

      Video

      10:15–11:15 amDuong H. PhongTitle: $L^\infty$ estimates for the Monge-Ampere and other fully non-linear equations in complex geometry

      Abstract: A priori estimates are essential for the understanding of partial differential equations, and of these, $L^\infty$ estimates are particularly important as they are also needed for other estimates. The key $L^\infty$ estimates were obtained by S.T. Yau in 1976 for the Monge-Ampere equation for the Calabi conjecture, and sharp estimates obtained later in 1998 by Kolodziej using pluripotential theory. It had been a long-standing question whether a PDE proof of these estimates was possible. We provide a positive answer to this question, and derive as a consequence sharp estimates for general classes of fully non-linear equations. This is joint work with B. Guo and F. Tong.

      Video

      11:30–2:30 pmPaul SeidelTitle: The quantum connection: familiar yet puzzling

      Abstract: The small quantum connection on a Fano variety is possibly the most basic piece of enumerative geometry. In spite of being really easy to write down, it is the subject of far-reaching conjectures (Dubrovin, Galkin, Iritani), which challenge our understanding of mirror symmetry. I will give a gentle introduction to the simplest of these questions.

      Video

      12:30–2:30 pmLunch Break
      2:30–3:30 pmMelissa C.C. LiuTitle: Higgs-Coulumb correspondence for abelian gauged linear sigma models

      Abstract: The underlying geometry of a gauged linear sigma model (GLSM) consists of a GIT quotient of a complex vector space by the linear action of a reductive algebraic group G (the gauge group) and a polynomial function (the superpotential) on the GIT quotient. The Higgs-Coulomb correspondence relates (1) GLSM invariants which are virtual counts of curves in the critical locus of the superpotential (Higgs branch), and (2) Mellin-Barnes type integrals on the Lie algebra of G (Coulomb branch). In this talk, I will describe the correspondence when G is an algebraic torus, and explain how to use the correspondence to study dependence of GLSM invariants on the stability condition. This is based on joint work with Konstantin Aleshkin.

      Video

      3:30–4:00 pmCoffee Break 
      4:00–5:00 pmSebastien PicardTitle: Topological Transitions of Calabi-Yau Threefolds

      Abstract: Conifold transitions were proposed in the works of Clemens, Reid and Friedman as a way to travel in the parameter space of Calabi-Yau threefolds with different Hodge numbers. This process may deform a Kahler Calabi-Yau threefold into a non-Kahler complex manifold with trivial canonical bundle. We will discuss the propagation of differential geometric structures such as balanced hermitian metrics, Yang-Mills connections, and special submanifolds through conifold transitions. This is joint work with T. Collins, S. Gukov and S.-T. Yau.

      Video

       

       

       

      Thursday, May 12, 2022

       

      8:15 amLight breakfast & coffee/tea
      9:00 am–10:00 amAkito Futaki (Zoom)Title: Transverse coupled Kähler-Einstein metrics and volume minimization

      Abstract:
      We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kählercone, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.Video
      10:15 am–11:15 amYu-Shen LinTitle: SYZ Mirror Symmetry of Log Calabi-Yau Surfaces

      Abstract: Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admits special Lagrangian fibrations. The conjecture serves as one of the guiding principles in mirror symmetry. In this talk, I will explain the existence of the special Lagrangian fibrations in some log Calabi-Yau surfaces and their dual fibrations in their expected mirrors. The journey leads us to the study of the moduli space of Ricci-flat metrics with certain asymptotics on these geometries and the discovery of new semi-flat metrics. If time permits, I will explain the application to the Torelli theorem of ALH^* gravitational instantons. The talk is based on joint works with T. Collins and A. Jacob.

      Video

      11:30 am – 12:30 pmRobert FriedmanTitle: Deformations of singular Fano and Calabi-Yau varieties

      Abstract: This talk will describe recent joint work with Radu Laza on deformations of generalized Fano and Calabi-Yau varieties, i.e. compact analytic spaces whose dualizing sheaves are either duals of ample line bundles or are trivial. Under the assumption of isolated hypersurface canonical singularities, we extend results of Namikawa and Steenbrink in dimension three and discuss various generalizations to higher dimensions.

      Video

      12:30 pmConcluding Remarks

       

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/6/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Symposium on Foundations of Responsible Computing (FORC)
      9:00 am-5:00 pm
      12/01/2024-06/08/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Screen-Shot-2020-03-05-at-11.54.28-AM-600x338

      On June 6-8, 2022, the CMSA hosted the 3rd annual Symposium on Foundations of Responsible Computing (FORC).

      The Symposium on Foundations of Responsible Computing (FORC) is a forum for mathematical research in computation and society writ large.  The Symposium aims to catalyze the formation of a community supportive of the application of theoretical computer science, statistics, economics and other relevant analytical fields to problems of pressing and anticipated societal concern.

      Organizers: Cynthia Dwork, Harvard SEAS | Omer Reingold, Stanford | Elisa Celis, Yale

      Schedule

      DOWNLOAD PDF

      June 6, 2022

      9:15 am–10:15 amOpening Remarks

      Keynote Speaker: Caroline Nobo, Yale University

      Title: From Theory to Impact: Why Better Data Systems are Necessary for Criminal Legal Reform

      Abstract: This talk will dive into the messy, archaic, and siloed world of local criminal justice data in America. We will start with a 30,000 foot discussion about the current state of criminal legal data systems, then transition to the challenges of this broken paradigm, and conclude with a call to measure new things – and to measure them better! This talk will leave you with an understanding of criminal justice data infrastructure and transparency in the US, and will discuss how expensive case management software and other technology are built on outdated normative values which impede efforts to reform the system. The result is an infuriating paradox: an abundance of tech products built without theoretical grounding, in a space rich with research and evidence.

      10:15 am–10:45 amCoffee Break
      10:45 am–12:15 pmPaper Session 1Session Chair: Ruth Urner
      Georgy Noarov, University of PennsylvaniaTitle: Online Minimax Multiobjective Optimization

      Abstract: We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. The learner’s objective is to minimize the maximum cumulative loss over all coordinates. We give a simple algorithm that lets the learner do almost as well as if she knew the adversary’s actions in advance. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains, ranging from multicalibration to a large set of no-regret algorithms, to a variant of Blackwell’s approachability theorem for polytopes with fast convergence rates. As a new application, we show how to “(multi)calibeat” an arbitrary collection of forecasters — achieving an exponentially improved dependence on the number of models we are competing against, compared to prior work.

      Matthew Eichhorn, Cornell UniversityTitle: Mind your Ps and Qs: Allocation with Priorities and Quotas

      Abstract: In many settings, such as university admissions, the rationing of medical supplies, and the assignment of public housing, decision-makers use normative criteria (ethical, financial, legal, etc.) to justify who gets an allocation. These criteria can often be translated into quotas for the number of units available to particular demographics and priorities over agents who qualify in each demographic. Each agent may qualify in multiple categories at different priority levels, so many allocations may conform to a given set of quotas and priorities. Which of these allocations should be chosen? In this talk, I’ll formalize this reserve allocation problem and motivate Pareto efficiency as a natural desideratum. I’ll present an algorithm to locate efficient allocations that conform to the quota and priority constraints. This algorithm relies on beautiful techniques from integer and linear programming, and it is both faster and more straightforward than existing techniques in this space. Moreover, its clean formulation allows for further refinement, such as the secondary optimization of some heuristics for fairness.

      Haewon Jeong, Harvard UniversityTitle: Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values

      Abstract: We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature, most of them require a complete training set as input. In practice, data can have missing values, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead, we train a tree with missing incorporated as attribute (MIA), which does not require explicit imputation, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset, through several experiments on real-world datasets.

      Emily Diana, University of PennsylvaniaTitle: Multiaccurate Proxies for Downstream Fairness

      Abstract: We study the problem of training a model that must obey demographic fairness conditions when the sensitive features are not available at training time — in other words, how can we train a model to be fair by race when we don’t have data about race? We adopt a fairness pipeline perspective, in which an “upstream” learner that does have access to the sensitive features will learn a proxy model for these features from the other attributes. The goal of the proxy is to allow a general “downstream” learner — with minimal assumptions on their prediction task — to be able to use the proxy to train a model that is fair with respect to the true sensitive features. We show that obeying multiaccuracy constraints with respect to the downstream model class suffices for this purpose, provide sample- and oracle efficient-algorithms and generalization bounds for learning such proxies, and conduct an experimental evaluation. In general, multiaccuracy is much easier to satisfy than classification accuracy, and can be satisfied even when the sensitive features are hard to predict.

      12:15 pm–1:45 pmLunch Break
      1:45–3:15 pmPaper Session 2Session Chair: Guy Rothblum
      Elbert Du, Harvard UniversityTitle: Improved Generalization Guarantees in Restricted Data Models

      Abstract: Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis — even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that, under this assumption, it is possible to “re-use” privacy budget on different portions of the data, significantly improving accuracy without increasing the risk of overfitting.

      Ruth Urner, York UniversityTitle: Robustness Should not be at Odds with Accuracy

      Abstract: The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability and trustworthiness: in many instances an imperceptible perturbation can falsely flip a neural network’s prediction. Applied research in this area has mostly focused on developing novel adversarial attack strategies or building better defenses against such. It has repeatedly been pointed out that adversarial robustness may be in conflict with requirements for high accuracy. In this work, we take a more principled look at modeling the phenomenon of adversarial examples. We argue that deciding whether a model’s label change under a small perturbation is justified, should be done in compliance with the underlying data-generating process. Through a series of formal constructions, systematically analyzing the the relation between standard Bayes classifiers and robust-Bayes classifiers, we make the case for adversarial robustness as a locally adaptive measure. We propose a novel way defining such a locally adaptive robust loss, show that it has a natural empirical counterpart, and develop resulting algorithmic guidance in form of data-informed adaptive robustness radius. We prove that our adaptive robust data-augmentation maintains consistency of 1-nearest neighbor classification under deterministic labels and thereby argue that robustness should not be at odds with accuracy.

      Sushant Agarwal, University of WaterlooTitle: Towards the Unification and Robustness of Perturbation and Gradient Based Explanations

      Abstract: As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method, and a variant of LIME which is a perturbation based method. More specifically, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation, i.e., when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties, such as robustness and linearity, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally, we empirically validate our theory using extensive experimentation on both synthetic and real world datasets.

      Tijana Zrnic, University of California, BerkeleyTitle: Regret Minimization with Performative Feedback

      Abstract: In performative prediction, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time, the learner needs to deploy a model to get feedback about the distribution it induces. We study the problem of finding near-optimal models under performativity while maintaining low regret. On the surface, this problem might seem equivalent to a bandit problem. However, it exhibits a fundamentally richer feedback structure that we refer to as performative feedback: after every deployment, the learner receives samples from the shifted distribution rather than only bandit feedback about the reward. Our main contribution is regret bounds that scale only with the complexity of the distribution shifts and not that of the reward function. The key algorithmic idea is careful exploration of the distribution shifts that informs a novel construction of confidence bounds on the risk of unexplored models. The construction only relies on smoothness of the shifts and does not assume convexity. More broadly, our work establishes a conceptual approach for leveraging tools from the bandits literature for the purpose of regret minimization with performative feedback.

      3:15 pm–3:45 pmCoffee Break
      3:45 pm–5:00 pmPanel DiscussionTitle: What is Responsible Computing?

      Panelists: Jiahao Chen, Cynthia Dwork, Kobbi Nissim, Ruth Urner

      Moderator: Elisa Celis

       

      June 7, 2022

      9:15 am–10:15 amKeynote Speaker: Isaac Kohane, Harvard Medical SchoolTitle: What’s in a label? The case for and against monolithic group/ethnic/race labeling for machine learning

      Abstract: Populations and group labels have been used and abused for thousands of years. The scale at which AI can incorporate such labels into its models and the ways in which such models can be misused are cause for significant concern. I will describe, with examples drawn from experiments in precision medicine, the task dependence of how underserved and oppressed populations can be both harmed and helped by the use of group labels. The source of the labels and the utility models underlying their use will be particularly emphasized.

      10:15 am–10:45 amCoffee Break
      10:45 am–12:15 pmPaper Session 3Session Chair: Ruth Urner
      Rojin Rezvan, University of Texas at AustinTitle: Individually-Fair Auctions for Multi-Slot Sponsored Search

      Abstract: We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from Chawla and Jagadeesan.

      Judy Hanwen Shen, StanfordTitle: Leximax Approximations and Representative Cohort Selection

      Abstract: Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency, exploiting significant utility improvements, and robustness to noise. Among other definitional contributions, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.

      Jiayuan Ye,
      National University of Singapore
      Title: Differentially Private Learning Needs Hidden State (or Much Faster Convergence)

      Abstract: Differential privacy analysis of randomized learning algorithms typically relies on composition theorems, where the implicit assumption is that the internal state of the iterative algorithm is revealed to the adversary. However, by assuming hidden states for DP algorithms (when only the last-iterate is observable), recent works prove a converging privacy bound for noisy gradient descent (on strongly convex smooth loss function) that is significantly smaller than composition bounds after a few epochs. In this talk, we extend this hidden-state analysis to various stochastic minibatch gradient descent schemes (such as under “shuffle and partition” and “sample without replacement”), by deriving novel bounds for the privacy amplification by random post-processing and subsampling. We prove that, in these settings, our privacy bound is much smaller than composition for training with a large number of iterations (which is the case for learning from high-dimensional data). Our converging privacy analysis, thus, shows that differentially private learning, with a tight bound, needs hidden state privacy analysis or a fast convergence. To complement our theoretical results, we present experiments for training classification models on MNIST, FMNIST and CIFAR-10 datasets, and observe a better accuracy given fixed privacy budgets, under the hidden-state analysis.

      Mahbod Majid, University of WaterlooTitle: Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism

      Abstract: We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution from O(d) independent samples (up to logarithmic factors) subject to pure differential privacy.

      Our main technique is a new approach to use the powerful Sum of Squares method (SoS) to design differentially private algorithms. SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics – estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees. We demonstrate a similar proofs to private algorithms phenomenon: instances of the workhorse exponential mechanism which apparently require exponential time but which can be analyzed with low-degree SoS proofs can be automatically turned into polynomial-time differentially private algorithms. We prove a meta-theorem capturing this phenomenon, which we expect to be of broad use in private algorithm design.

      12:15 pm–1:45 pmLunch Break
      1:45–3:15 pmPaper Session 4Session Chair: Kunal Talwar
      Kunal Talwar,
      Apple
      Title: Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

      Abstract: Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation (SMC) protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected.
      In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.

      Giuseppe Vietri, University of MinnesotaTitle: Improved Regret for Differentially Private Exploration in Linear MDP

      Abstract: We study privacy-preserving exploration in sequential decision-making for environments that rely on sensitive data such as medical records. In particular, we focus on solving the problem of reinforcement learning (RL) subject to the constraint of (joint) differential privacy in the linear MDP setting, where both dynamics and rewards are given by linear functions. Prior work on this problem due to Luyo et al. (2021) achieves a regret rate that has a dependence of O(K^{3/5}) on the number of episodes K. We provide a private algorithm with an improved regret rate with an optimal dependence of O(K^{1/2}) on the number of episodes. The key recipe for our stronger regret guarantee is the adaptivity in the policy update schedule, in which an update only occurs when sufficient changes in the data are detected. As a result, our algorithm benefits from low switching cost and only performs O(log(K)) updates, which greatly reduces the amount of privacy noise. Finally, in the most prevalent privacy regimes where the privacy parameter ? is a constant, our algorithm incurs negligible privacy cost — in comparison with the existing non-private regret bounds, the additional regret due to privacy appears in lower-order terms.

      Mingxun Zhou,
      Carnegie Mellon University
      Title: The Power of the Differentially Oblivious Shuffle in Distributed Privacy MechanismsAbstract: The shuffle model has been extensively investigated in the distributed differential privacy (DP) literature. For a class of useful computational tasks, the shuffle model allows us to achieve privacy-utility tradeoff similar to those in the central model, while shifting the trust from a central data curator to a “trusted shuffle” which can be implemented through either trusted hardware or cryptography. Very recently, several works explored cryptographic instantiations of a new type of shuffle with relaxed security, called differentially oblivious (DO) shuffles. These works demonstrate that by relaxing the shuffler’s security from simulation-style secrecy to differential privacy, we can achieve asymptotical efficiency improvements. A natural question arises, can we replace the shuffler in distributed DP mechanisms with a DO-shuffle while retaining a similar privacy-utility tradeoff?
      In this paper, we prove an optimal privacy amplification theorem by composing any locally differentially private (LDP) mechanism with a DO-shuffler, achieving parameters that tightly match the shuffle model. Moreover, we explore multi-message protocols in the DO-shuffle model, and construct mechanisms for the real summation and histograph problems. Our error bounds approximate the best known results in the multi-message shuffle-model up to sub-logarithmic factors. Our results also suggest that just like in the shuffle model, allowing each client to send multiple messages is fundamentally more powerful than restricting to a single message.
      Badih Ghazi,
      Google Research
      Title: Differentially Private Ad Conversion Measurement

      Abstract: In this work, we study conversion measurement, a central functionality in the digital advertising space, where an advertiser seeks to estimate advertiser site conversions attributed to ad impressions that users have interacted with on various publisher sites. We consider differential privacy (DP), a notion that has gained in popularity due to its strong and rigorous guarantees, and suggest a formal framework for DP conversion measurement, uncovering a subtle interplay between attribution and privacy. We define the notion of an operationally valid configuration of the attribution logic, DP adjacency relation, privacy
      budget scope and enforcement point, and provide, for a natural space of configurations, a complete characterization.

      3:15 pm–3:45 pmCoffee Break
      3:45 pm–5:00 pmOpen Poster Session

       

      June 8, 2022

      9:15 am–10:15 amKeynote Speaker: Nuria Oliver, Data-Pop AllianceTitle: Data Science against COVID-19

      Abstract: In my talk, I will describe the work that I have been doing since March 2020, leading a multi-disciplinary team of 20+ volunteer scientists working very closely with the Presidency of the Valencian Government in Spain on 4 large areas: (1) human mobility modeling; (2) computational epidemiological models (both metapopulation, individual and LSTM-based models); (3) predictive models; and (4) citizen surveys via the COVID19impactsurvey with over 600,000 answers worldwide.

      I will describe the results that we have produced in each of these areas, including winning the 500K XPRIZE Pandemic Response Challenge and best paper award at ECML-PKDD 2021. I will share the lessons learned in this very special initiative of collaboration between the civil society at large (through the survey), the scientific community (through the Expert Group) and a public administration (through the Commissioner at the Presidency level). WIRED magazine just published an article describing our story.

      10:15 am–10:45 amCoffee Break
      10:45 am–12:15 pmPaper Session 5Session Chair: Kunal Talwar
      Shengyuan Hu, Carnegie Mellon UniversityTitle: Private Multi-Task Learning: Formulation and Applications to Federated Learning

      Abstract: Many problems in machine learning rely on multi-task learning (MTL), in which the goal is to solve multiple related machine learning tasks simultaneously. MTL is particularly relevant for privacy-sensitive applications in areas such as healthcare, finance, and IoT computing, where sensitive data from multiple, varied sources are shared for the purpose of learning. In this work, we formalize notions of task-level privacy for MTL via joint differential privacy (JDP), a relaxation of differential privacy for mechanism design and distributed optimization. We then propose an algorithm for mean-regularized MTL, an objective commonly used for applications in personalized federated learning, subject to JDP. We analyze our objective and solver, providing certifiable guarantees on both privacy and utility. Empirically, our method allows for improved privacy/utility trade-offs relative to global baselines across common federated learning benchmarks

      Christina Yu,
      Cornell University
      Title: Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve

      Abstract: We consider the problem of dividing limited resources to individuals arriving over T rounds with a goal of achieving fairness across individuals. In general there may be multiple resources and multiple types of individuals with different utilities. A standard definition of `fairness’ requires an allocation to simultaneously satisfy envy-freeness and Pareto efficiency. However, in the online sequential setting, the social planner must decide on a current allocation before the downstream demand is realized, such that no policy can guarantee these desiderata simultaneously with probability 1, requiring a modified metric of measuring fairness for online policies. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to L_T necessarily suffers an efficiency loss of at least 1 / L_T. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. Our result is the first to provide guarantees for fair online resource allocation with high probability for multiple resource and multiple type settings. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.

      Hedyeh Beyhaghi, Carnegie Mellon UniversityTitle: On classification of strategic agents who can both game and improve

      Abstract: In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

      Keegan Harris, Carnegie Mellon UniversityTitle: Bayesian Persuasion for Algorithmic Recourse

      Abstract: When subjected to automated decision-making, decision subjects may strategically modify their observable features in ways they believe will maximize their chances of receiving a favorable decision. In many practical situations, the underlying assessment rule is deliberately kept secret to avoid gaming and maintain competitive advantage. The resulting opacity forces the decision subjects to rely on incomplete information when making strategic feature modifications. We capture such settings as a game of Bayesian persuasion, in which the decision maker offers a form of recourse to the decision subject by providing them with an action recommendation (or signal) to incentivize them to modify their features in desirable ways. We show that when using persuasion, both the decision maker and decision subject are never worse off in expectation, while the decision maker can be significantly better off. While the decision maker’s problem of finding the optimal Bayesian incentive-compatible (BIC) signaling policy takes the form of optimization over infinitely-many variables, we show that this optimization can be cast as a linear program over finitely-many regions of the space of possible assessment rules. While this reformulation simplifies the problem dramatically, solving the linear program requires reasoning about exponentially-many variables, even under relatively simple settings. Motivated by this observation, we provide a polynomial-time approximation scheme that recovers a near-optimal signaling policy. Finally, our numerical simulations on semi-synthetic data empirically illustrate the benefits of using persuasion in the algorithmic recourse setting.

      12:15 pm–1:45 pmLunch Break
      1:45–3:15 pmPaper Session 6Session Chair: Elisa Celis
      Mark Bun, Boston UniversityTitle: Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling

      Abstract: Sampling schemes are fundamental tools in statistics, survey design, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However, in practice, sampling designs are often more complex than the simple, data-independent sampling schemes that are addressed in prior work. In this work, we extend the study of privacy amplification results to more complex, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms, as well as provide some insight into the study of more general sampling designs.

      Samson Zhou, Carnegie Mellon UniversityTitle: Private Data Stream Analysis for Universal Symmetric Norm Estimation

      Abstract: We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular, we focus on releasing the family of symmetric norms, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include L_p norms, k-support norms, top-k norms, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the “heavy” coordinates in important levels and releases approximate level sizes for the “light” coordinates in important levels. Surprisingly, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover, our mechanism permits (1+\alpha)-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.

      Aloni Cohen, University of ChicagoTitle: Attacks on Deidentification’s Defenses

      Abstract: Quasi-identifier-based deidentification techniques (QI-deidentification) are widely used in practice, including k-anonymity, ?-diversity, and t-closeness. We present three new attacks on QI-deidentification: two theoretical attacks and one practical attack on a real dataset. In contrast to prior work, our theoretical attacks work even if every attribute is a quasi-identifier. Hence, they apply to k-anonymity, ?-diversity, t-closeness, and most other QI-deidentification techniques.
      First, we introduce a new class of privacy attacks called downcoding attacks, and prove that every QI-deidentification scheme is vulnerable to downcoding attacks if it is minimal and hierarchical. Second, we convert the downcoding attacks into powerful predicate singling-out (PSO) attacks, which were recently proposed as a way to demonstrate that a privacy mechanism fails to legally anonymize under Europe’s General Data Protection Regulation. Third, we use LinkedIn.com to reidentify 3 students in a k-anonymized dataset published by EdX (and show thousands are potentially vulnerable), undermining EdX’s claimed compliance with the Family Educational Rights and Privacy Act.

      The significance of this work is both scientific and political. Our theoretical attacks demonstrate that QI-deidentification may offer no protection even if every attribute is treated as a quasi-identifier. Our practical attack demonstrates that even deidentification experts acting in accordance with strict privacy regulations fail to prevent real-world reidentification. Together, they rebut a foundational tenet of QI-deidentification and challenge the actual arguments made to justify the continued use of k-anonymity and other QI-deidentification techniques.

      Steven Wu,
      Carnegie Mellon University
      Title: Fully Adaptive Composition in Differential Privacy

      Abstract: Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. The authors introduce two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the tightness of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. We also construct several general families of odometers. These odometers can match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging recent advances in time-uniform martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss, and conjecture that our results are essentially not improvable (even in constants) in general.

      3:15 pm–3:45 pmFORC Reception
      3:45 pm–5:00 pmSocial Hour
    • Workshop
      9:00 am-5:00 pm
      12/01/2024-04/29/2022
      Blockchain,Network,Concept,,,Distributed,Ledger,,Computer,Connection,Technology,,Matrix

      On April 27–29, 2022, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics.

      Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

      In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

      Speakers:

      • Federico Ardila (San Francisco State)
      • Nima Arkani-Hamed (IAS)
      • Madeline Brandt (Brown)
      • Nick Early (Max Planck Institute)
      • Chris Eur (Harvard)
      • Claudia Fevola (Max Planck Institute)
      • Christian Gaetz (Harvard)
      • Yuji Kodama (Ohio State University)
      • Yelena Mandelshtam (Berkeley)
      • Sebastian Mizera (IAS)
      • Matteo Parisi (Harvard CMSA)
      • Emma Previato (Boston University)
      • Anna Seigal (Harvard)
      • Melissa Sherman-Bennett (University of Michigan)
      • Simon Telen (Max Planck Institute)
      • Charles Wang (Harvard)

      Schedule

      Schedule PDF

      Wednesday, April 27, 2022

      9:30 am–10:30 amFederico ArdilaTitle: Nonlinear spaces from linear spaces

      Abstract: Matroid theory provides a combinatorial model for linearity, but it plays useful roles beyond linearity. In the classical setup, a linear subspace V of an n-dimensional vector space gives rise to a matroid M(V) on {1,…,n}. However, the matroid M(V) also knows about some nonlinear geometric spaces related to V. Conversely, those nonlinear spaces teach us things we didn’t know about matroids. My talk will discuss some examples.

      10:30 am–11:00 amCOFFEE BREAK
      11:00 am–11:45 amChris EurTitle: Tautological classes of matroids

      Abstract: Algebraic geometry has furnished fruitful tools for studying matroids, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (K-classes) on permutohedral varieties, which we call “tautological bundles (classes)” of matroids, as a new framework that unifies, recovers, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget, Hunter Spink, and Dennis Tseng.

      11:45 am–2:00 pmLUNCH BREAK
      2:00 pm–2:45 pmNick EarlyTitle: Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes

      Abstract: The associahedron is known to encapsulate physical properties such as the notion of tree-level factorization for one of the simplest Quantum Field Theories, the biadjoint scalar, which has only cubic interactions.  I will discuss novel instances of the associahedron and the biadjoint scalar in a class of generalized amplitudes, discovered by Cachazo, Early, Guevara and Mizera, by taking certain limits thereof. This connection leads to a simple proof of a new realization of the associahedron involving a Minkowski sum of certain positroid polytopes in the second hypersimplex.

      2:45 pm–3:30 pmAnna SeigalTitle: Invariant theory for maximum likelihood estimation

      Abstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

      3:30 pm–4:00 pmCOFFEE BREAK
      4:00 pm–4:45 pmMatteo ParisiTitle: Amplituhedra, Scattering Amplitudes, and Triangulations

      Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – introduced by physicists to encode interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory.
      Triangulations of polygons are encoded in the associahedron, studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes, constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. I will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between Amplituhedra of “m=2” type and a seemingly unrelated object – the Hypersimplex. The latter is a polytope which appears in many contexts, from matroid theory to tropical geometry.
      Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski.

      4:45 pm–5:30 pmMelissa Sherman-BennettTitle: The hypersimplex and the m=2 amplituhedron

      Abstract: In this talk, I’ll continue where Matteo left off. I’ll give some more details about the curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). The hypersimplex decompositions are closely related to matroidal subdivisions. Along the way, we prove a nice description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers, inspired by an analogous triangulation of the hypersimplex into Eulerian-number-many simplices.

       

      Thursday, April 28, 2022

      9:30 am–10:30 amClaudia FevolaTitle: Nonlinear Algebra meets Feynman integrals

      Abstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. They form a finite-dimensional vector space and the elements of a basis are named “master integrals” in the physics literature. The number of master integrals has been interpreted in different ways: it equals the dimension of a twisted de Rham cohomology group, the Euler characteristic of a very affine variety, and the holonomic rank of a D-module. In this talk, we are interested in a more general family of integrals that contains Feynman integrals as a special case. We explore this setting using tools coming from nonlinear algebra. This is an ongoing project with Daniele Agostini, Anna-Laura Sattelberger, and Simon Telen.

      10:30 am–11:00 amCOFFEE BREAK
      11:00 am–11:45 amSimon TelenTitle: Landau discriminants

      Abstract: The Landau discriminant is a projective variety containing kinematic parameters for which a Feynman integral can have singularities. We present a definition and geometric properties. We discuss how to compute Landau discriminants using symbolic and numerical methods. Our methods can be used, for instance, to compute the Landau discriminant of the pentabox diagram, which is a degree 12 hypersurface in 6-space. This is joint work with Sebastian Mizera.

      11:45 am–2:00 pmLUNCH BREAK
      2:00 pm–2:45 pmChristian GaetzTitle: 1-skeleton posets of Bruhat interval polytopes

      Abstract: Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes, despite not being simple, have interesting h-vectors. In a special case, work of Williams shows that Bruhat interval polytopes are isomorphic to bridge polytopes, so that chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs.

      2:45 pm–3:30 pmMadeleine BrandtTitle: Top Weight Cohomology of $A_g$

      Abstract: I will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of $A_g$. Thus, it can be computed combinatorially. This is joint work with Juliette Bruce, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.

      3:30 pm–4:00 pmCOFFEE BREAK
      4:00 pm–5:00 pmEmma PreviatoTitle: Sigma function on curves with non-symmetric semigroup

      Abstract: We start with an overview of the correspondence between spectral curves and commutative rings of differential operators, integrable hierarchies of non-linear PDEs and Jacobian vector fields. The coefficients of the operators can be written explicitly in terms of the Kleinian sigma function: Weierstrass’ sigma function was generalized to genus greater than one by Klein, and is a ubiquitous tool in integrability. The most accessible case is the sigma function of telescopic curves. In joint work with J. Komeda and S. Matsutani, we construct a curve with non-symmetric Weierstrass semigroup (equivalently, Young tableau), consequently non-telescopic, and its sigma function. We conclude with possible applications to commutative rings of differential operators.

      6:00 pmDinner Banquet, Gran Gusto Trattoria

       

      Friday, April 29, 2022

      9:00 am–10:00 amYuji KodamaTitle: KP solitons and algebraic curves

      Abstract: It is well-known that soliton solutions of the KdV hierarchy are obtained by singular limits of hyper-elliptic curves. However, there is no general results for soliton solutions of the KP hierarchy, KP solitons. In this talk, I will show that some of the KP solitons are related to the singular space curves associated with certain class of numerical semigroups.

      10:00 am–10:30 amCOFFEE BREAK
      10:30 am–11:15 amYelena MandelshtamTitle: Curves, degenerations, and Hirota varieties

      Abstract: The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases, Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This talk is based on joint work with Daniele Agostini, Claudia Fevola, and Bernd Sturmfels.

      11:15 am–12:00 pmCharles WangTitle: Differential Algebra of Commuting Operators

      Abstract: In this talk, we will give an overview of the problem of finding the centralizer of a fixed differential operator in a ring of differential operators, along with connections to integrable hierarchies and soliton solutions to e.g. the KdV or KP equations. Given these interesting connections, it is important to be able to compute centralizers of differential operators, and we discuss how to use techniques from differential algebra to approach this question, as well as how having these computational tools can help in understanding the structure of soliton solutions to these equations.

      12:00 pm–2:00 pmLUNCH BREAK
      2:00 pm–3:00 pmSebastian MizeraTitle: Feynman Polytopes

      Abstract: I will give an introduction to a class of polytopes that recently emerged in the study of scattering amplitudes in quantum field theory.

      3:00 pm–3:30 pmCOFFEE BREAK
      3:30 pm–4:30 pmNima Arkani-HamedTitle: Spacetime, Quantum Mechanics and Combinatorial Geometries at Infinity

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Algebraic Statistics with a View towards Physics
      9:00 am-10:00 am
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.

      **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

      All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

      LINK TO FORM

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/13/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.21.22-1583x2048-1

      Abstract:
      Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure, the adoption of MPC in real industry is still very much limited as of today, the biggest obstacle of which boils down to its efficiency.

      My research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal, my research spans both theoretical and applied cryptography. In theory, I develop new techniques for achieving general MPC with the optimal complexity, bringing theory closer to practice. In practice, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice.

      Biography:
      Peihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC, she received her Ph.D. from the University of California, Berkeley in 2019 and had brief stints at Google, Facebook, Microsoft Research, and Visa Research. Her research interests lie broadly in cryptography, theory, and security, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/20/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Workshop
      9:00 am-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series.

      Location: Room G10, 20 Garden Street, Cambridge, MA 02138.

      Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).

      Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory, algebraic geometry, and representation theory.

      At this workshop, we will bring together mathematicians, theoretical physicists, and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.

      Speakers:

      • James Halverson, Northeastern University Dept. of Physics and IAIFI
      • Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI
      • Andrew Sutherland, MIT Department of Mathematics

       

      https://youtu.be/qseSPgHHFtQ

       

       

      https://youtu.be/JN3mVazeP2E

       

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.14.22-1583x2048

      Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.

    • Member Seminar
      9:00 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Farzan Vafa

      Title: Diffusive growth sourced by topological defects

      Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time, and predict that in the presence of a positive defect, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature, we exploit the fact that for axisymmetric surfaces, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry, for polar order and small bending modulus, is a deformed football.
      We apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/27/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      6/3/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: The Atiyah-Singer Index Theorem
      9:00 am-10:30 am
      12/01/2024

      Dan Freed (The University of Texas at Austin)

      Title: The Atiyah-Singer Index Theorem

      Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator.

      This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

      Talk chair: Cumrun Vafa

      Video

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Interdisciplinary Science Seminar
      Speaker: Jianfeng Lu, Duke UniversityTitle: Surface hopping algorithms for non-adiabatic quantum systems

      Abstract: Surface hopping algorithm is widely used in chemistry for mixed quantum-classical dynamics. In this talk, we will discuss some of our recent works in mathematical understanding and algorithm development for surface hopping methods. These methods are based on stochastic approximations of semiclassical path-integral representation to the solution of multi-level Schrodinger equations; such methodology also extends to other high-dimensional transport systems.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      7/8/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Big Data Conference 2022
      9:00 am-1:00 pm
      12/01/2024
      Big Data 2022_web

      On August 26, 2022 the CMSA hosted our eighth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The 2022 Big Data Conference took place virtually on Zoom.

      Organizers:

      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
      • Sergiy Verstyuk, CMSA, Harvard University

      Speakers:

      Schedule

      9:00 amConference OrganizersIntroduction and Welcome
      9:10 am – 9:55 amXiaohong ChenTitle: On ANN optimal estimation and inference for policy functionals of nonparametric conditional moment restrictions

      Abstract:  Many causal/policy parameters of interest are expectation functionals of unknown infinite-dimensional structural functions identified via conditional moment restrictions. Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional covariates more effectively than linear sieves. In this talk we present ANN optimal estimation and inference on  policy functionals, such as average elasticities or value functions, of unknown structural functions of endogenous covariates. We provide ANN efficient estimation and optimal t based confidence interval for regular policy functionals such as average derivatives in nonparametric instrumental variables regressions. We also present ANN quasi likelihood ratio based inference for possibly irregular policy functionals of general nonparametric conditional moment restrictions (such as quantile instrumental variables models or Bellman equations) for time series data. We conduct intensive Monte Carlo studies to investigate computational issues with ANN based optimal estimation and inference in economic structural models with endogeneity. For economic data sets that do not have very high signal to noise ratios, there are current gaps between theoretical advantage of ANN approximation theory vs inferential performance in finite samples.
      Some of the results are applied to efficient estimation and optimal inference for average price elasticity in consumer demand and BLP type demand.

      The talk is based on two co-authored papers:
      (1) Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators
      (Authors: Jiafeng Chen, Xiaohong Chen and Elie Tamer)
      https://arxiv.org/abs/2110.06763

      (2) Neural network Inference on Nonparametric conditional moment restrictions with weakly dependent data
      (Authors: Xiaohong Chen, Yuan Liao and Weichen Wang).

      View/Download Lecture Slides (pdf)

      10:00 am – 10:45 amJessica JeffersTitle: Labor Reactions to Credit Deterioration: Evidence from LinkedIn Activity

      Abstract: We analyze worker reactions to their firms’ credit deterioration. Using weekly networking activity on LinkedIn, we show workers initiate more connections immediately following a negative credit event, even at firms far from bankruptcy. Our results suggest that workers are driven by concerns about both unemployment and future prospects at their firm. Heightened networking activity is associated with contemporaneous and future departures, especially at financially healthy firms. Other negative events like missed earnings and equity downgrades do not trigger similar reactions. Overall, our results indicate that the build-up of connections triggered by credit deterioration represents a source of fragility for firms.

      10:50 am – 11:35 amMiles CranmerTitle: Interpretable Machine Learning for Physics

      Abstract: Would Kepler have discovered his laws if machine learning had been around in 1609? Or would he have been satisfied with the accuracy of some black box regression model, leaving Newton without the inspiration to discover the law of gravitation? In this talk I will explore the compatibility of industry-oriented machine learning algorithms with discovery in the natural sciences. I will describe recent approaches developed with collaborators for addressing this, based on a strategy of “translating” neural networks into symbolic models via evolutionary algorithms. I will discuss the inner workings of the open-source symbolic regression library PySR (github.com/MilesCranmer/PySR), which forms a central part of this interpretable learning toolkit. Finally, I will present examples of how these methods have been used in the past two years in scientific discovery, and outline some current efforts.

      View/Download Lecture Slides (pdf) 

      11:40 am – 12:25 pmDan RobertsTitle: A Statistical Model of Neural Scaling Laws

      Abstract: Large language models of a huge number of parameters and trained on near internet-sized number of tokens have been empirically shown to obey “neural scaling laws” for which their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model — a joint generative data model and random feature model — that captures this neural scaling phenomenology. By solving this model using tools from random matrix theory, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws (ii) how nonlinear feature maps, i.e the role played by the deep neural network, enable scaling laws when trained on these datasets, and (iii) how such scaling laws can break down, and what their behavior is when they do. A key feature is the manner in which the power laws that occur in the statistics of natural datasets are translated into power law scalings of the test loss, and how the finite extent of such power laws leads to both bottlenecks and breakdowns.

      View/Download Lecture Slides (pdf)

       

      12:30 pmConference OrganizersClosing Remarks

       

      Information about last year’s conference can be found here.

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 09.28.22

      Topological Quantum Matter Seminar

      Speaker: Ruihua Fan, Harvard University

      Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow
      Abstract: One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024
      CMSA QMMP Seminar 09.26.22

      Quantum Matter in Mathematics and Physics

      Speaker: Avner Karasik (University of Cambridge, UK)

      Title: Candidates for Non-Supersymmetric Dualities

      Abstract: In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

       

    • Math Science Literature Lecture Series
      9:00 am-10:30 pm
      12/01/2024

      Maxim Kontsevich  (IHÉS)

      Title: On the History of quantum cohomology and homological mirror symmetry

      Abstract: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry.  First, the usual cup-product on the cohomology of a complex projective variety admits a canonical multi-parameter deformation to so-called quantum product, satisfying a nice system of differential equations (WDVV equations).  The second discovery, even more striking,  is Mirror Symmetry, a duality between families of Calabi-Yau varieties acting as a mirror reflection on the Hodge diamond.

      Later it was realized that the quantum product belongs to the realm of symplectic geometry, and a half of mirror symmetry (called Homological Mirror Symmetry) is a duality between complex algebraic and symplectic varieties. The search of correct definitions and possible generalizations lead to great advances in many domains, giving mathematicians new glasses, through which they can see familiar objects in a completely new way.

      I will review the history of major mathematical advances in the subject of HMS, and the swirl of ideas around it.

      Talk chair: Paul Seidel

      Video

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      4/1/2021 Strongly Correlated Quantum Materials
      9:00 am-10:30 am
      12/01/2024
    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 09.21.22
      Topological Quantum Matter Seminar

      Speaker: Semyon Klevtsov, University of Strasbourg

      Title: Geometric test for topological states of matter

      Abstract: We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the

      degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille).

       

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024-04/27/2021

      In 2021, the CMSA hosted a lecture series on the literature of the mathematical sciences. This series highlights significant accomplishments in the intersection between mathematics and the sciences. Speakers include Edward Witten, Lydia Bieri, Simon Donaldson, Michael Freedman, Dan Freed, and many more.

      Videos of these talks can be found in this Youtube playlist.

      https://youtu.be/vb_JEhUW9t4

      In the Spring 2021 semester, the CMSA hosted a sub-program on this series titled A Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Below is the schedule for talks in that subprogram

      April 6, 2021 | 9:00 – 10:30am ET

      Edward Witten (IAS)

      TitleIsadore Singer’s Work on Analytic Torsion


      April 13, 2021 | 9:00 – 10:30am ET

      Claire Voisin (College de France)

      Title: K-theory and characteristic classes in topology and complex geometry  (a tribute to Atiyah and Hirzebruch)


      April 20, 2021 | 9:00 – 10:30am ET

      Dan Freed (the University of Texas at Austin)

      TitleThe Atiyah-Singer Index Theorem


      April 27, 2021 | 9:00 – 10:30am ET

      Frances Kirwan (University of Oxford)

      TitleMoment maps and the Yang-Mills functional

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Edward Witten (IAS)

      TitleIsadore Singer’s Work on Analytic Torsion

      Abstract:  I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory.

      This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and Singer.

      Talk chair: Cumrun Vafa

      Slides | Video

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Equiangular lines and regular graphs
      9:00 am-10:00 am
      12/01/2024

      Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

      Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
      the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA QMMP Seminar

      Quantum Matter in Mathematics and Physics Seminar

      Speaker: Zhengyan Darius Shi (MIT)
      Title: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
      Abstract: Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity \sigma(mega) \sim mega^{-2/z} (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result \sigma(mega) \sim mega^{-2(z-2)/z}  due to Kim et al. is incorrect for inversion-odd order parameters.
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      7/1/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Interdisciplinary Science Seminar

      Speaker: Yue M. Lu, Harvard University

      Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning

      Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
      In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.

      Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007.  He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.

    • CMSA EVENT: Joint BHI/CMSA Conference on Flat Holography
      9:00 am-5:00 pm
      12/01/2024-06/24/2022

      On June 21–24, 2022, the Harvard Black Hole Initiative and the CMSA hosted the Joint BHI/CMSA Conference on Flat Holography (and related topics).

      The recent discovery of infinitely-many soft symmetries for all quantum theories of gravity in asymptotically flat space has provided a promising starting point for a bottom-up construction of a holographic dual for the real world. Recent developments have brought together previously disparate studies of soft theorems, asymptotic symmetries, twistor theory, asymptotically flat black holes and their microscopic duals, self-dual gravity, and celestial scattering amplitudes, and link directly to AdS/CFT.

      The conference was held in room G10 of the CMSA, 20 Garden Street, Cambridge, MA.

      Organizers:

      • Daniel Kapec, CMSA
      • Andrew Strominger, BHI
      • Shing-Tung Yau, Harvard & Tsinghua

      Confirmed Speakers:

      • Nima Arkani-Hamed, IAS
      • Shamik Banerjee, Bhubaneswar, Inst. Phys.
      • Miguel Campiglia, Republica U., Montevido
      • Geoffrey Compere, Brussels
      • Laura Donnay, Vienna
      • Netta Engelhardt, MIT
      • Laurent Freidel, Perimeter
      • Alex Lupsasca, Princeton
      • Juan Maldacena, IAS
      • Lionel Mason, Oxford
      • Natalie Paquette, U. Washington
      • Sabrina Pasterski, Princeton/Perimeter
      • Andrea Puhm, Ecole Polytechnique
      • Ana-Maria Raclariu, Perimeter
      • Marcus Spradlin, Brown
      • Tomasz Taylor, Northeastern
      • Herman Verlinde, Princeton
      • Anastasia Volovich, Brown
      • Bin Zhu, Northeastern

      Short talks by: Gonçalo Araujo-Regado (Cambridge), Adam Ball (Harvard), Eduardo Casali (Harvard), Jordan Cotler (Harvard), Erin Crawley (Harvard), Stéphane Detournay (Brussels), Alfredo Guevara (Harvard), Temple He (UC Davis), Elizabeth Himwich (Harvard), Yangrui Hu (Brown), Daniel Kapec (Harvard), Rifath Khan (Cambridge), Albert Law (Harvard), Luke Lippstreu (Brown), Noah Miller (Harvard), Sruthi Narayanan (Harvard), Lecheng Ren (Brown), Francisco Rojas (UAI), Romain Ruzziconi (Vienna), Andrew Strominger (Harvard), Adam Tropper (Harvard), Tianli Wang (Harvard), Walker Melton (Harvard)

      Schedule

      Monday, June 20, 2022

      Arrival
      7:00–9:00 pmWelcome Reception at Andy’s residence

       

      Tuesday, June 21, 2022

      9:00–9:30 amBreakfastlight breakfast provided
      Morning SessionChair: Dan Kapec
      9:30–10:00 amHerman VerlindeTitle: Comments on Celestial Dynamics
      10:00–10:30 amJuan MaldacenaTitle: What happens when you spend too much time looking at supersymmetric
      black holes?
      10:30–11:00Coffee break
      11:00–11:30 amMiguel CampigliaTitle: Asymptotic symmetries and loop corrections to soft theorems
      11:30–12:00 pmGeoffrey CompereTitle: Metric reconstruction from $Lw_{1+\infty}$ multipoles

      Abstract: The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be exchanged under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely determined by a set of conserved celestial charges, which uniquely label transitions among non-radiative regions caused by radiative processes. The algebra of the conserved celestial charges is derived from the real $Lw_{1+\infty}$ algebra. The celestial charges are expressed in terms of multipole moments, which allows to holographically reconstruct the metric in de Donder, Newman-Unti or Bondi gauge outside of sources.

      12:00–2:00 pmLunch break
      Afternoon SessionChair: Eduardo Casali
      2:00–2:30 pmNatalie PaquetteTitle: New thoughts on old gauge amplitudes
      2:30–3:00 pmLionel MasonTitle: An open sigma model for celestial gravity

      Abstract: A global twistor construction for conformally self-dual split signature metrics on $S2\times S2$  was developed 15 years ago by Claude LeBrun and the speaker.  This encodes the conformal metric into the location of a finite deformation of the real twistor space inside the flat complex twistor space, $\mathbb{CP}3$. This talk adapts the construction to construct global SD Einstein metrics from conformal boundary data and perturbations around the self-dual sector.  The construction entails determining a family of holomorphic discs in $\mathbb{CP}3$ whose boundaries lie on the deformed real slice and the (chiral) sigma model controls these discs in the Einstein case and provides amplitude formulae.

      3:00–3:30 pmCoffee break
      3:30–4:30 pmShort TalksDaniel Kapec: Soft Scalars and the Geometry of the Space of Celestial CFTs

      Albert Law: Soft Scalars and the Geometry of the Space of Celestial CFTs

      Sruthi Narayanan: Soft Scalars and the Geometry of the Space of Celestial CFTs

      Stéphane Detournay: Non-conformal symmetries and near-extremal black holes

      Francisco Rojas: Celestial string amplitudes beyond tree level

      Temple He: An effective description of energy transport from holography

      4:30–5:00 pmNima Arkani-Hamed(Dual) surfacehedra and flow particles know about strings

       

      Wednesday, June 22, 2022

      9:00–9:30 amBreakfastlight breakfast provided
      Morning SessionChair: Alfredo Guevara
      9:30–10:00 amLaurent FreidelTitle: Higher spin symmetry in gravity

      Abstract: In this talk, I will review how the gravitational conservation laws at infinity reveal a tower of symmetry charges in an asymptotically flat spacetime.
      I will show how the conservation laws, at spacelike infinity, give a tower of soft theorems that connect to the ones revealed by celestial holography.
      I’ll present the expression for the symmetry charges in the radiative phase space, which opens the way to reveal the structure of the algebra beyond the positive helicity sector. Then, if time permits I’ll browse through many questions that these results raise:
      such as the nature of the spacetime symmetry these charges represent, the nature of the relationship with multipole moments, and the insights their presence provides for quantum gravity.

      10:00–10:30 amAna-Maria RaclariuTitle: Eikonal approximation in celestial CFT
      10:30–11:00 amCoffee break
      11:00–11:30 amAnastasia VolovichTitle: Effective Field Theories with Celestial Duals
      11:30–12:00 pmMarcus SpradlinTitle: Loop level gluon OPE’s in celestial holography
      12:00–2:00 pmLunch break
      Afternoon SessionChair: Chiara Toldo
      2:00–2:30 pmNetta EngelhardtTitle: Wormholes from entanglement: true or false?
      2:30–3:00 pmShort TalksLuke Lippstreu: Loop corrections to the OPE of celestial gluons

      Yangrui Hu: Light transforms of celestial amplitudes

      Lecheng Ren: All-order OPE expansion of celestial gluon and graviton primaries from MHV amplitudes

      3:00–3:30 pmCoffee break
      3:30–4:30 pmShort TalksNoah Miller: C Metric Thermodynamics

      Erin Crawley: Kleinian black holes

      Rifath Khan: Cauchy Slice Holography: A New AdS/CFT Dictionary

      Gonçalo Araujo-Regado: Cauchy Slice Holography: A New AdS/CFT Dictionary

      Tianli Wang: Soft Theorem in the BFSS Matrix Model

      Adam Tropper: Soft Theorem in the BFSS Matrix Model

      7:00–9:00 pmBanquetMaharaja Restaurant, 57 JFK Street, Cambridge, MA

       

      Thursday, June 23, 2022

      9:00–9:30 amBreakfastlight breakfast provided
      Morning SessionChair: Jordan Cotler
      9:30–10:00 amLaura DonnayTitle: A Carrollian road to flat space holography
      10:00–10:30 amAndrea PuhmTitle: Celestial wave scattering on Kerr-Schild backgrounds
      10:30–11:00 amCoffee break
      11:00–11:30 amSabrina PasterskiTitle: Mining Celestial Symmetries

      Abstract: The aim of this talk is to delve into the common thread that ties together recent work with H. Verlinde, L. Donnay, A. Puhm, and S. Banerjee exploring, explaining, and exploiting the symmetries encoded in the conformally soft sector.

      Come prepared to debate the central charge, loop corrections, contour prescriptions, and orders of limits!

      11:30–12:00 pmShamik BanerjeeTitle: Virasoro and other symmetries in CCFT

      Abstract:  In this talk I will briefly describe my ongoing work with Sabrina Pasterski. In this work we revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton.  In its original formulation, we find that there is an obstruction to reproducing the expected $TT$ OPE in the double soft limit. This obstruction is related to the existence of the $SL_2$ current algebra symmetry of the CCFT. We propose a modification to the definition of the stress tensor which circumvents this obstruction and also discuss its implications for the existence of other current algebra (w_{1+\infty}) symmetries in CCFT.

      12:00–2:00 pmLunch break
      Afternoon SessionChair: Albert Law
      2:00–2:30 pmTomasz TaylorTitle: Celestial Yang-Mills amplitudes and D=4 conformal blocks
      2:30–3:00 pmBin ZhuTitle:  Single-valued correlators and Banerjee-Ghosh equations

      Abstract:  Low-point celestial amplitudes are plagued with singularities resulting from spacetime translation. We consider a marginal deformation of the celestial CFT which is realized by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators.

      3:00–3:30 pmCoffee break
      3:30–4:00 pmAlex LupsascaTitle: Holography of the Photon Ring
      4:00–5:30 pmShort TalksElizabeth Himwich: Celestial OPEs and w(1+infinity) symmetry of massless and massive amplitudes

      Adam Ball: Perturbatively exact $w_{1+\infty}$ asymptotic symmetry of quantum self-dual gravity

      Romain Ruzziconi: A Carrollian Perspective on Celestial Holography

      Jordan Cotler: Soft Gravitons in 3D

      Alfredo Guevara: Comments on w_1+\inf

      Andrew Strominger: Top-down celestial holograms

      Eduardo Casali: Celestial amplitudes as AdS-Witten diagrams

      Walker Melton: Top-down celestial holograms

       

      Friday, June 24, 2022

      9:00–9:30 amBreakfast
      9:30–12:30 pmOpen Discussion
      12:30–2:30 pmLunch provided at the BHI
      Departure

       

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      Interdisciplinary Science Seminar
      Title: Recent Advances on Maximum Flows and Minimum-Cost Flows

      Abstract: We survey recent advances on computing flows in graphs, culminating in an almost linear time algorithm for solving minimum-cost flow and several other problems to high accuracy on directed graphs. Along the way, we will discuss intuitions from linear programming, graph theory, and data structures that influence these works, and the resulting natural open problems.

      Bio: Yang P. Liu is a final-year graduate student at Stanford University. He is broadly interested in the efficient design of algorithms, particularly flows, convex optimization, and online algorithms. For his work, he has been awarded STOC and ITCS best student papers.

    • Workshop
      9:00 am-5:00 pm
      12/01/2024-08/05/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Phase Transitions_Poster

      On August 2–5, the CMSA hosted a workshop on Phase Transitions and Topological Defects in the Early Universe.

      The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA and online via Zoom webinar.

      The next decade will see a wealth of new cosmological data, which can lead to new insights into fundamental physics. Upcoming facilities (such as LISA) will be able to probe signals of fascinating phenomena in the early universe. These include signals from “Phase Transitions and Topological Defects,” which are ubiquitously given rise to in well-motivated UV models. In-depth studies of such signals requires cross-talks between experts from a wide spectrum of fields.

      The workshop aims to provide a platform for efficient exchange of new ideas related to these topics. It will start with an overview of some of the past and future experimental efforts. Next, there will be a substantial number of talks probing different aspects of phenomenology of phase transitions and topological defects in the early universe. It will finally close with discussions on recent formal development in the field.

      Scientific Advisory: Julian B. Muñoz, Lisa Randall, Matthew Reece, Tracy Slatyer, Shing-Tung Yau

      Organizers:
      Harvard: Nick DePorzio, Katie Fraser, Sam Homiller, Rashmish Mishra, & Aditya Parikh
      MIT: Pouya Asadi, Marianne Moore, & Yitian Sun

      Schedule/Format
      There will be 20+ 10 minute talks, ample discussion time, and lightning chalkboard talks.

      Speakers:

      • Nancy Aggarwal (Northwestern)
      • Jae Hyeok Chang (UMD – JHU)
      • Yanou Cui (UC Riverside)
      • David Dunsky (UC Berkeley)
      • Isabel Garcia-Garcia (KITP – UCSB)
      • Oliver Gould (Nottingham)
      • Yann Gouttenoire (Tel Aviv)
      • Eleanor Hall (UC Berkeley)
      • Sungwoo Hong (Chicago)
      • Anson Hook (UMD)
      • Jessica Howard (UC Irvine)
      • Seth Koren (Chicago)
      • Mrunal Korwar (Wisconsin)
      • Soubhik Kumar (UC Berkeley)
      • Vuk Mandic (Minnesota)
      • Yuto Minami (Osaka)
      • Michael Nee (Oxford)
      • Kai Schmitz (CERN)
      • Stephen R. Taylor (Vanderbilt)
      • Ofri Telem (UC Berkeley)
      • Juven Wang (Harvard)
      • Yikun Wang (Caltech)

      Participants:

      • Manuel Buen Abad (UMD)
      • Pouya Asadi (MIT)
      • Sean Benevedes (MIT)
      • Sandipan Bhattacherjee (Birla Institute of Technology Mesra Ranchi India)
      • Xingang Chen (Harvard University)
      • Nicholas DePorzio (Harvard University)
      • Peizhi Du (Stony Brook University)
      • Nicolas Fernandez (University of Illinois Urbana-Champaign)
      • Joshua Foster (MIT)
      • Katherine Fraser (Harvard University)
      • Sarah Geller (MIT)
      • Aurora Ireland (University of Chicago)
      • Marius Kongsore (New York University)
      • Ho Tat Lam (Massachusetts Institute of Technology)
      • Lingfeng Li (Brown University)
      • Yingying Li (Fermilab)
      • Gustavo Marques-Tavares (UMD)
      • Rashmish Mishra (Harvard University)
      • Siddharth Mishra-Sharma (MIT/Harvard University)
      • Toby Opferkuch (UC Berkeley)
      • Tong Ou (University of Chicago)
      • Aditya Parikh (Harvard University)
      • Yitian Sun (MIT)
      • Juan Sebastian Valbuena-Bermudez (Ludwig Maximilian University of Munich and Max Planck Institute for Physics)
      • Isaac Wang (Rutgers)
      • Wei Xue (University of Florida)
      • Winston Yin (UC Berkeley)
      • Quratulain Zahoor (The Islamia University of Bahwalpur Punjab (Pakistan)

      Schedule

      Tuesday, August 2, 2022

      9:00–9:20 amBreakfast
      9:20–9:30 amRashmish MishraOpening Remarks
      9:30–10:00 amVuk MandicTitle: Searching for the Stochastic Gravitational Wave Background with LISA

      Abstract: The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) will open a window into the milliHertz band of the gravitational wave spectrum. Among the many sources in this band is the stochastic gravitational wave background (SGWB), arising as an incoherent superposition of many uncorrelated gravitational wave sources. The SGWB could be of cosmological origin, carrying unique information about the physical processes that took place within the first minute after the big bang, including possible phase transitions and topological defects. LISA therefore has the potential to illuminate particle physics at very high energy scales that may be inaccessible in laboratories. I will discuss how LISA can be used to search for the SGWB, highlighting a new pipeline developed for this purpose as well as several challenges and limitations that such a search will encounter.

      10:00–10:30 amNancy AggarwalTitle: Gravitational waves at frequencies above 10 kHz

      Abstract: Gravitational waves (GWs) at frequencies higher than the LIGO band can bring us completely new information about the universe. Besides being the most-interesting frequency region for looking at cosmological phenomena, they can also convey signatures of ultralight bosons through blackhole superradiance and light primordial blackholes (PBHs). I will introduce a new global initiative to study GW sources and detectors at ultra-high-frequencies (MHz-GHz), as well as a new experiment at Northwestern University to look for GWs in the frequency band of 10 kHz to 300 kHz using levitated optomechanical sensors. I will summarize the design, the current experimental progress, as well as a path forward for future improvements.

      10:30–11:00 amYuto MinamiTitle: New measurements of the cosmic birefringence

      Abstract: Polarised light of the cosmic microwave background, the remnant light of the Big Bang, is sensitive to parity-violating physics, cosmic birefringence. In this presentation I report on a new measurement of cosmic birefringence from polarisation data of the European Space Agency (ESA)’s Planck satellite released in 2018. The statistical significance of the measured signal is 2.4 sigma. Recently, we found a signal with 3.3 sigma statistical significance when we use the latest Planck data and consider an effect of polarised foreground emission. If confirmed with higher statistical significance in future, it would have important implications for the elusive nature of dark matter and dark energy.

      11:00–1:30 pmBreak
      1:30–3:00 pmLighting Talks 1Lingfeng Li
      Winston Yin
      Marius Kongsore
      Nick DePorzio
      3:00–3:30 pmJae Hyeok ChangTitle: Correlating gravitational wave and gamma-ray signals from primordial black holes

      Abstract: Asteroid-mass primordial black holes (PBHs) can explain the observed dark matter abundance while being consistent with the current indirect detection constraints. These PBHs can produce gamma-ray signals from Hawking radiation that are within the sensitivity of future measurements by the AMEGO and e-ASTROGAM experiments. PBHs which give rise to such observable gamma-ray signals have a cosmic origin from large primordial curvature fluctuations. There must then be a companion, stochastic gravitational wave (GW) background produced by the same curvature fluctuations. I will demonstrate that the resulting GW signals will be well within the sensitivity of future detectors such as LISA, DECIGO, BBO, and the Einstein Telescope. The multimessenger signal from the observed gamma-rays and GWs will allow a precise measurement of the primordial curvature perturbation that produces the PBH. I will also argue that the resulting correlation between the two types of observations can provide a smoking-gun signal of PBHs.

      3:30–4:00 pmAnson Hook
      (Virtual via Zoom)
      Title: Early Universe Cosmology from Stochastic Gravitational Waves

      Abstract:  The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure gstar and beta functions as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the 10^-3 level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to O(1) deviations of gstar and the QCD beta function from their Standard Model value at temperatures ~ 10^5 GeV. In this case, many motivated models such as split SUSY and other solutions to the Electroweak Hierarchy problem would be tested. Future detectors, such as DECIGO, would be 100 times more sensitive than LISA to these effects and be capable of testing other motivated scenarios such as WIMPs and axions. The amazing prospect of using precision gravitational wave measurements to test such well motivated theories provides a benchmark to aim for when developing a precise understanding of the gravitational wave spectrum both experimentally and theoretically.

       

      Wednesday, August 3, 2022

      9:00–9:30 amBreakfast
      9:30–10:00 amKai Schmitz
      (Virtual via Zoom)
      Title: Gravitational waves from metastable cosmic strings

      Abstract: Cosmic strings are predicted by many Standard Model extensions involving the cosmological breaking of an Abelian symmetry and represent a potential source of primordial gravitational waves (GWs). In many Grand Unified Theories (GUTs), cosmic strings especially turn out to be metastable, as the nucleation of GUT monopoles along strings after a finite lifetime eventually leads to the collapse of the entire string network. In this talk, I will discuss the theoretical description of such a network and its individual components as well as the consequences for the emitted GW spectrum. Remarkably, the GW signal from metastable strings may well explain the common-spectrum process recently observed in pulsar timing data, while at the same time and in contrast to stable cosmic strings predicting a signal at higher frequencies that is still within the reach of current-generation ground-based interferometers. On their way to design sensitivity, existing GW experiments will thus have a realistic chance to probe particle physics processes at energies close to the GUT scale via the observation of GWs from metastable strings. This talk is based on 2107.04578 in collaboration with Wilfried Buchmüller and Valerie Domcke.

      10:00–10:30 amOliver Gould
      (Virtual via Zoom)
      Title: Effective field theory for cosmological phase transitions

      Abstract: Phase transitions are driven by thermal loop fluctuations, which modify background fields at leading order. This breaks the loop expansion and leads to large theoretical uncertainties in typical calculations, especially for gravitational wave predictions. I will give an overview of our present understanding of these uncertainties, and of the tools that have been developed to overcome them. Effective field theory has been at the forefront of this development, and I will outline how it can be used to solve a number of decades-long-standing theoretical problems.

      10:30–11:00 amIsabel Garcia-GarciaTitle: The Rocket Science of Expanding Bubbles

      11:00–1:30 pmBreak
      1:30–3:00 pmLightning Talks 2Sarah Geller
      Peizhi Du
      Tong Ou
      Isaac Wang
      Katie Fraser
      3:00–3:30 pmDavid Dunsky
      (Virtual via Zoom)
      Title: Gravitational Wave Gastronomy

      Abstract: The symmetry breaking of grand unified gauge groups in the early universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable and can leave behind unique gravitational wave fingerprints. In this talk, I will discuss the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and “eat” the strings, 2) the collapse and decay of a monopole-string network by strings that “eat” the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and “eat” the wall, and 4) the collapse and decay of a string-bounded wall network by walls that “eat” the strings. We call the gravitational wave signals produced from the “eating” of one topological defect by another “gravitational wave gastronomy”. The gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO(10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects.

      3:30–4:00 pmYanou Cui
      (Virtual via Zoom)
      Title: Cosmic Archaeology with gravitational waves from (axion) cosmic strings

      Abstract: In this talk I will discuss important aspects of cosmology and particle physics that can be probed with GW signals from cosmic strings: probing the pre-BBN primordial dark age and axion physics.  Gravitational waves (GWs) originating from the dynamics of a cosmic string network have the ability to probe many otherwise inaccessible properties of the early universe. In particular, I will discuss how the frequency spectrum of a stochastic GW background (SGWB) from a cosmic string network can be used to probe Hubble expansion rate of the early universe prior to Big Bang Nucleosynthesis (BBN), during the “primordial dark age”. Furthermore I will show that in contrast to the standard expectation, cosmic strings formed before inflation could regrow back into the horizon and leave imprints, with GW bursts potentially being the leading signal. In relation to axion physics I will also demonstrate the detection prospect for SGWB from global/axion strings which may provide a new probe for axion-like dark matter models, considering various scenarios of cosmic history.

      4:00–4:30 pmMichael NeeTitle: The Boring Monopole

      Abstract: First order phase transitions play an important role in the cosmology of many theories of BSM physics. In this talk I will discuss how a population of magnetic monopoles present in the early universe can seed first order phase transitions, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, thus requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. Our results show that monopole-catalysed tunnelling can dominate over the homogeneous decay for a wide range of parameters.

       

      Thursday, August 4, 2022

      9:00–9:30 amBreakfast
      9:30–10:00 amYikun WangTitle: A New Approach to Electroweak Symmetry Non-Restoration

      Abstract: Electroweak symmetry non-restoration up to high temperatures well above the electroweak scale has intriguing implications for (electroweak) baryogenesis and early universe thermal histories. In this talk, I will discuss such a possible fate of the electroweak symmetry in the early universe and a new approach to realize it, via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. Examples of benchmark scenarios that allow for electroweak symmetry non-restoration all the way up to hundreds of TeV temperatures, at the same time featuring suppressed sphaleron washout factors down to the electroweak scale, will be presented. Renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures, have been implemented calculating the thermal history. This method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

      10:00–10:30 amSoubhik KumarTitle: Probing primordial fluctuations through stochastic gravitational wave background anisotropies

      Abstract: Stochastic gravitational wave backgrounds are expected to be anisotropic. While such anisotropies can be of astrophysical origin, a cosmological component of such anisotropies can carry rich information about primordial perturbations. Focusing on the case of a cosmological phase transition, I will talk about how such anisotropies can give us a powerful probe of primordial non-Gaussianities, complementary to current and future CMB and LSS searches. In the scenario where astrophysical foregrounds are also present, I will then discuss some strategies using which we can extract the cosmological signal, focusing on the case of LISA, Taiji and BBO, in particular.

      10:30–11:00 amJessica Howard
      (Virtual via Zoom)
      Title: Dark Matter Freeze-out during SU(2)_L Confinement

      Abstract: We explore the possibility that dark matter is a pair of SU(2)_L doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This phase of confinement causes the Standard Model doublets and dark matter to confine into pion-like objects. Before the weak sector deconfines, the dark pions freezeout and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the observed relic density. We determine which regions of this parameter space evade direct detection and collider bounds.

      11:00–11:30 amJuven WangTitle: Quantum Matter Adventure to Beyond the Standard Model Prediction

      Abstract: Ideas developed from the quantum matter and quantum field theory frontier may guide us to explore new physics beyond the 4d Standard Model. I propose a few such ideas. First, new physics for neutrinos: right-handed neutrinos carry a Z_{16} class mixed gauge-gravitational global anomaly index, which could be replaced by 4d or 5d topological quantum field theory, or 4d interacting conformal field theory. These theories provide possible new neutrino mass mechanisms [arXiv:2012.15860]. Second, deconfined quantum criticality between Grand Unified Theories: dictated by a Z_2 class global anomaly, a gapless quantum critical region can happen between Georgi-Glashow and Pati-Salam models as deformation of the Standard Model, where Beyond the Standard Model physics and Dark Gauge sector occur as neighbor phases [arXiv:2106.16248, arXiv:2112.14765, arXiv:2204.08393]. Third, the Strong CP problem can be solved by a new solution involving Symmetric Mass Generation [arXiv:2204.14271].

      11:30–1:30 pmBreak
      1:30–4:00 pmStephen R. TaylorTitle: Pulsar Timing Arrays: The Next Window onto the Low-frequency Gravitational-wave Universe

      Abstract: The nanohertz-frequency band of gravitational waves should be awash with signals from supermassive black-hole binaries, as well as cosmological signatures of phase transitions, cosmic strings, and other relics of the early Universe. Pulsar-timing arrays (PTAs) like the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and the International Pulsar Timing Array are poised to chart this new frontier of gravitational wave discovery within the next several years. I will present exciting new results from recent cutting-edge searches, discuss some milestones on the road to the next decade of PTA discovery, and take workshop attendees through a guided tutorial of how the broader community can use our production-level analysis pipeline to extract new science with ease.

       

      Friday, August 5, 2022

      9:00–9:30 amBreakfast
      9:30–10:00 amOfri TelemTitle: Charge-Monopole Pairwise Phases from Dressed Quantum States

      10:00–10:30 amSungwoo HongTitle: Coupling a Cosmic String to a TQFT

      Abstract: In the last few years, the notion of symmetry has been enlarged to “generalized symmetry” or “higher-form symmetry” and these more generalized symmetries have played a critical role in deepening our understanding of QFT, notably IR phases of QFT. In this talk, I will discuss a various ways of coupling the axion-Maxwell theory to a topological field theory (TQFT). Contrary to a common wisdom, I will show that such topological modifications can lead to direct changes in the local physics with possible observable consequences. This surprise can be realized by a dimensional reduction, namely, a coupling to a TQFT in 4d leads to a non-trivial and local impact on the 2d string world-sheet QFT. There also exists a topological modification of the theory, i.e. gauging a discrete subgroup of 0-form shift symmetry, and this time it results in a alteration of spectrum of cosmic strings. If time permits, I will also discuss generalized symmetries and associated higher-groups of these theories.

      10:30–11:00 amEleanor Hall
      (Virtual via Zoom)
      Title: Non-perturbative methods for false vacuum decay

      Abstract: Gravitational waves from phase transitions in the early universe are one of our most promising signal channels of BSM physics; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present the quasi-stationary effective action, a new non-perturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. This method opens the door to reliable calculation of gravitational wave signals and false vacuum decay rates for strongly-interacting theories. I will also discuss recent developments and ongoing extensions of the QSEA.

      11:00–1:30 pmBreak
      1:30–2:00 pmMrunal KorwarTitle: Electroweak Symmetric Balls

      Abstract: Electroweak symmetric balls are macroscopic objects with electroweak symmetry restored inside. Such an object can arise in models where dark sectors contain monopole or non-topological soliton with a Higgs portal interaction to the Standard Model. It could be produced in the early universe via phase transition or parametric resonance, accounting for all dark matter. In a scenario where the balls are allowed to evaporate, the observed baryon asymmetry in our universe could be explained by a mechanism of “catalyzed baryogenesis.” In this mechanism, the motion of a ball-like catalyst provides the necessary out-of-equilibrium condition, its outer wall has CP-violating interactions with the Standard Model particles, and its interior has baryon number violating interactions via electroweak Sphaleron. Because of electroweak symmetric cores, such objects have a large geometric cross-section off a nucleus, generating a multi-hit signature in large volume detectors. These objects could radiatively capture a nucleus and release GeV-scale energy for each interaction. The IceCube detector can probe dark matter balls with masses up to a gram.

      2:00–2:30 pmSeth KorenTitle: Discrete Gauged Baryon Minus Lepton Number and the Cosmological Lithium Problem

      Abstract: We study the baryon minus lepton number gauge theory broken by a scalar with charge six. The infrared discrete vestige of the gauge symmetry demands the existence of cosmic string solutions, and their production as dynamical objects in the early universe is guaranteed by causality. These topological defects can support interactions which convert three protons into three positrons, and we argue an `electric’-`magnetic’ interplay can lead to an amplified, strong-scale cross-section in an analogue of the Callan-Rubakov effect.
      The cosmological lithium problem—that theory predicts a primordial abundance thrice as high as that observed—has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We suggest cosmic strings have disintegrated O(1) of the primordial lithium nuclei and estimate the rate in a benchmark scenario. To our knowledge this is the first new physics mechanism with microphysical justification for the abundance of lithium uniquely to be modified after Big Bang Nucleosynthesis.

      2:30–3:00 pmYann GouttenoireTitle: Supercool Composite Dark Matter beyond 100 TeV

       

      Phase-Transitions_Poster

    • CMSA EVENT: Advances in Mathematical Physics
      9:00 am-1:45 pm
      12/01/2024-08/01/2022
      1 Oxford Street, Cambridge MA 02138
      Elliott-Lieb-conference-2022_banner-2-1536x734

      A Conference in Honor of Elliott H. Lieb on his 90th Birthday

      On July 30 – Aug 1, 2022 the Harvard Mathematics Department and the CMSA co-hosted a birthday conference in honor of Elliott Lieb.

      This meeting highlights Elliott’s vast contribution to math and physics. Additionally, this meeting features Prof. Lieb’s more recent impact in strong subadditivity of entropy and integrable systems (ice model, Temperley-Lieb algebra etc.).

      Venue:

      July 30–31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
      August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138

      Schedule (pdf)

      Organizers:
      Michael Aizenman, Princeton University
      Joel Lebowitz, Rutgers University
      Ruedi Seiler, Technische Universität Berlin
      Herbert Spohn, Technical University of Munich
      Horng-Tzer Yau, Harvard University
      Shing-Tung Yau, Harvard University
      Jakob Yngvason, University of Vienna

      SPEAKERS:
      Rafael Benguria, Pontificia Universidad Catolica de Chile
      Eric Carlen, Rutgers University
      Philippe Di Francesco, University of Illinois
      Hugo Duminil-Copin, IHES
      László Erdös, Institute of Science and Technology Austria
      Rupert Frank, Ludwig Maximilian University of Munich
      Jürg Fröhlich, ETH Zurich
      Alessandro Giuliani, Università degli Studi Roma Tre
      Bertrand Halperin, Harvard University
      Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
      Sabine Jansen, Ludwig Maximilian University of Munich
      Mathieu Lewin, Université Paris-Dauphine
      Bruno Nachtergaele, The University of California, Davis
      Yoshiko Ogata, University of Tokyo
      Ron Peled, Tel Aviv University
      Benjamin Schlein, University of Zurich
      Robert Seiringer, Institute of Science and Technology Austria
      Jan Philip Solovej, University of Copenhagen
      Hal Tasaki, Gakushuin University
      Simone Warzel, Technical University of Munich
      Jun Yin, The University of California, Los Angeles

       

      Elliott-Lieb-conference

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      CMSA Interdisciplinary Science Seminar

      Speaker: Sumit Sinha, Harvard University

      Title: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data (https://arxiv.org/abs/2202.10595)

      Abstract: Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.

      Bio: I am a postdoctoral fellow in Harvard SEAS (Applied Mathematics) and Dana Farber Cancer Institute (Data Science) beginning Feb 2022. I finished my PhD in Physics (Theoretical Biophysics) from UT Austin (Jan 2022) on “Theoretical and computational studies of growing tissue”.  I pursued my undergraduate degree in Physics from the Indian Institute of Technology, Kanpur in India (2015). Boradly, I am interested in developing theoretical models, inspired from many-body statistical physics, for biological processes at different length and time scales.

       

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024

      Abstract: The establishment of neural circuitry during early infancy is critical for developing visual, auditory, and motor functions. However, how cortical tissue develops postnatally is largely unknown. By combining T1 relaxation time from quantitative MRI and mean diffusivity (MD) from diffusion MRI, we tracked cortical tissue development in infants across three timepoints (newborn, 3 months, and 6 months). Lower T1 and MD indicate higher microstructural tissue density and more developed cortex. Our data reveal three main findings: First, primary sensory-motor areas (V1: visual, A1: auditory, S1: somatosensory, M1: motor) have lower Tand MD at birth than higher-level cortical areas. However, all primary areas show significant reductions in Tand MD in the first six months of life, illustrating profound tissue growth after birth. Second, significant reductions in Tand MD from newborns to 6-month-olds occur in all visual areas of the ventral and dorsal visual streams. Strikingly, this development was heterogenous across the visual hierarchies: Earlier areas are more developed with denser tissue at birth than higher-order areas, but higher-order areas had faster rates of development. Finally, analysis of transcriptomic gene data that compares gene expression in postnatal vs. prenatal tissue samples showed strong postnatal expression of genes associated with myelination, synaptic signaling, and dendritic processes. Our results indicate that these cellular processes may contribute to profound postnatal tissue growth in sensory cortices observed in our in-vivo measurements. We propose a novel principle of postnatal maturation of sensory systems: development of cortical tissue proceeds in a hierarchical manner, enabling the lower-level areas to develop first to provide scaffolding for higher-order areas, which begin to develop more rapidly following birth to perform complex computations for vision and audition.

      This work is published here: https://www.nature.com/articles/s42003-021-02706-w

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-07.14.22-1583x2048

      Abstract:  Introducing internal degrees of freedom in the description of crystalline insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses. Here, we present a semiclassical approach to transport and accumulation of general spinor degrees of freedom in adiabatically driven, weakly inhomogeneous crystals of dimensions one, two and three under external electromagnetic fields. Our approach shows that spatio-temporal modulations of the system induce a spinor current and density that is related to geometrical and topological objects — the spinor-Chern fluxes and numbers — defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates.

      The results are available here: https://arxiv.org/abs/2203.14902

      Bio: Ioannis Petrides is a postdoctoral fellow at the School of Engineering and Applied Sciences at Harvard University. He received his Ph.D. from the Institute for Theoretical Physics at ETH Zurich. His research focuses on the topological and geometrical aspects of condensed matter systems.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/15/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      Interdisciplinary Science Seminar
      Speaker: Fouad El Baidouri, Broad Institute

      Title: The phenotype of the last universal common ancestor and the evolution of complexity

      Abstract: A fundamental concept in evolutionary theory is the last universal common ancestor (LUCA) from which all living organisms originated. While some authors have suggested a relatively complex LUCA it is still widely assumed that LUCA must have been a very simple cell and that life has subsequently increased in complexity through time. However, while current thought does tend towards a general increase in complexity through time in Eukaryotes, there is increasing evidence that bacteria and archaea have undergone considerable genome reduction during their evolution. This raises the surprising possibility that LUCA, as the ancestor of bacteria and archaea may have been a considerably complex cell. While hypotheses regarding the phenotype of LUCA do exist, all are founded on gene presence/absence. Yet, despite recent attempts to link genes and phenotypic traits in prokaryotes, it is still inherently difficult to predict phenotype based on the presence or absence of genes alone. In response to this, we used Bayesian phylogenetic comparative methods to predict ancestral traits. Testing for robustness to horizontal gene transfer (HGT) we inferred the phenotypic traits of LUCA using two robust published phylogenetic trees and a dataset of 3,128 bacterial and archaeal species.

      Our results depict LUCA as a far more complex cell than has previously been proposed, challenging the evolutionary model of increased complexity through time in prokaryotes. Given current estimates for the emergence of LUCA we suggest that early life very rapidly evolved cellular complexity.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      6/24/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Some new algorithms in statistical genomics
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-06.23.2022-1583x2048-1

      Abstract: The statistical analysis of genomic data has incubated many innovations for computational method development. This talk will discuss some simple algorithms that may be useful in analyzing such data. Examples include algorithms for efficient resampling-based hypothesis testing, minimizing the sum of truncated convex functions, and fitting equality-constrained lasso problems. These algorithms have the potential to be used in other applications beyond statistical genomics.

      Bio: Hui Jiang is an Associate Professor in the Department of Biostatistics at the University of Michigan. He received his Ph.D. in Computational and Mathematical Engineering from Stanford University. Before joining the University of Michigan, he was a postdoc in the Department of Statistics and Stanford Genome Technology Center at Stanford University. He is interested in developing statistical and computational methods for analyzing large-scale biological data generated using modern high-throughput technologies.

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Peter Shor (MIT)

      TitleQuantum error correcting codes and fault tolerance

      Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field.

      Talk chair: Zhengwei Liu

      Video

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      The number of n-queens configurations
      9:00 am-10:00 am
      12/01/2024

      Speaker: Michael Simkin, Harvard CMSA

      Title: The number of n-queens configurations

      Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

      Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      6/10/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
      9:00 am-12:00 pm
      12/01/2024-01/13/2017
      banner-image-1

      The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

       

      Confirmed Participants:

    • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
      9:00 am-5:00 pm
      12/01/2024-05/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Organizers:

      D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

      Speakers:

      1. Netanel Blaier (MIT)
      2. Kwokwai Chan (CUHK)
      3. Bohan Fang (Peking University)
      4. Amanda Francis (BYU)
      5. Hansol Hong (CUHK)
      6. Heather Lee (Purdue University)
      7. Si Li (Tsinghua University)
      8. Yu-Shen Lin (Stanford University)
      9. Alex Perry (Harvard University)
      10. Hiro Tanaka (Harvard University)
      11. Sara Tukachinsky (HUJ)
      12. Michael Viscardi (MIT)
      13. Eric Zaslow (Northwestern University)
      14. Jingyu Zhao (Columbia University)

      Please click here for the conference Main Website.

      Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Schedule:

      May 6 – Day 1
      9:00amBreakfast
      9:35amOpening remarks
      9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
      10:45am – 11:15amBreak
      11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
      May 7 – Day 2
      9:00amBreakfast
      9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
      10:45am – 11:15amBreak
      11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
      May 8 – Day 3
      9:00amBreakfast
      9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
      10:45am – 11:15amBreak
      11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
      * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

      This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Adventures in Perturbation Theory
      9:00 am-10:00 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-01.25.2022-1

      Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The Amplituhedron BCFW Triangulation
      9:00 am-10:00 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-2.3.2022

      Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

    • CMSA EVENT: Workshop on Optimization in Image Processing
      9:00 am-12:30 pm
      12/01/2024-06/30/2016

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Speakers:

      1. Antonin Chambolle, CMAP, Ecole Polytechnique
      2. Raymond Chan, The Chinese University of Hong Kong
      3. Ke Chen, University of Liverpool
      4. Patrick Louis Combettes, Université Pierre et Marie Curie
      5. Mario Figueiredo, Instituto Superior Técnico
      6. Alfred Hero, University of Michigan
      7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
      8. Mila Nikolova, Ecole Normale Superieure Cachan
      9. Shoham Sabach, Israel Institute of Technology
      10. Martin Benning, University of Cambridge
      11. Jin Keun Seo, Yonsei University
      12. Fiorella Sgallari, University of Bologna
      13. Gabriele Steidl, Kaiserslautern University of Technology
      14. Joachim Weickert, Saarland University
      15. Isao Yamada, Tokyo Institute of Technology
      16. Wotao Yin, UCLA

      Please click Workshop Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

      Schedule:

      June 27 – Day 1
      9:00amBreakfast
      9:20amOpening remarks
      9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
      10:20am – 10:50amBreak
      10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
      11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
      12:30pm – 2:00pmLunch
      2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
      June 28 – Day 2
      9:00amBreakfast
      9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
      10:20am – 10:50amBreak
      10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
      11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 4:40pmDiscussions
      June 29 – Day 3
      9:00amBreakfast
      9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
      10:20am – 10:50amBreak
      10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
      11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
      June 30 – Day 4
      9:00amBreakfast
      9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
      10:20am – 10:50amBreak
      10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
      11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
      * This event is sponsored by CMSA Harvard University.

      Organizers: Raymond Chan and Shing-Tung Yau

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA/Tsinghua Math-Science Literature Lecture: Scott Kominers
      9:00 am-10:30 am
      12/01/2024

      CMSA/Tsinghua Math-Science Literature Lecture

      Prof. Scott Kominers will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

      Date: Monday, November 20, 2023

      Time: 9:00 – 10:30 am ET

      Location: Via Zoom Webinar

      Registration is required.

      Title: 60 Years of Matching: From Gale and Shapley to Trading Networks

      Abstract: Gale and Shapley’s 1962 American Mathematical Monthly paper, “College Admissions and the Stability of Marriage,” is by now one of the most cited articles in the journal’s history, having served as the foundation for an entire branch of the field of market design. This success owes in large part to the beautiful, applicable, and surprisingly general theory of matching mechanisms uncovered in Gale and Shapley’s work. This talk traces the history and evolution of matching theory from that paper forward to the present day, along the way touching on real-world applications to everything from medical residency matching to electricity markets.

      Moderator: Sergiy Verstyuk


      Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

       

      CMSA COVID-19 Policies

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      10/19/2021 Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      Title: Ising model, total positivity, and criticality

      Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
      The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
      I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model

    • Workshop
      9:00 am-5:00 pm
      12/01/2024-05/19/2023
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      GRAMSIAcover-600x338

      On May 16 – May 19, 2023 the CMSA hosted a four-day workshop on GRAMSIA: Graphical Models, Statistical Inference, and Algorithms. The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop was organized by David Gamarnik (MIT), Kavita Ramanan (Brown), and Prasad Tetali  (Carnegie Mellon).

      The purpose of this workshop is to highlight various mathematical questions and issues associated with graphical models and message-passing algorithms, and to bring together a group of researchers for discussion of the latest progress and challenges ahead. In addition to the substantial impact of graphical models on applied areas, they are also connected to various branches of the mathematical sciences. Rather than focusing on the applications, the primary goal is to highlight and deepen these mathematical connections.

      Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

       

      Speakers:
      • Jake Abernethy (Georgia Tech)
      • Guy Bresler (MIT)
      • Florent Krzakala (Ecole Polytechnique Federale de Lausanne)
      • Lester Mackey (Microsoft Research New England)
      • Theo McKenzie (Harvard)
      • Andrea Montanari (Stanford)
      • Elchanan Mossel (MIT)
      • Yury Polyanskiy (MIT)
      • Patrick Rebeschini (Oxford)
      • Subhabrata Sen (Harvard)
      • Devavrat Shah (MIT)
      • Pragya Sur (Harvard)
      • Alex Wein (UC Davis)
      • Yihong Wu (Yale)
      • Sarath Yasodharan (Brown)
      • Horng-Tzer Yau (Harvard)
      • Christina Lee Yu (Cornell)
      • Ilias Zadik (MIT)
      Schedule:

      Tuesday, May 16, 2023

      9:00 amBreakfast
      9:15 – 9:30 amIntroductory remarks by organizers
      9:30 – 10:20 amSubhabrata Sen (Harvard)

      Title: Mean-field approximations for high-dimensional Bayesian regression

      Abstract: Variational approximations provide an attractive computational alternative to MCMC-based strategies for approximating the posterior distribution in Bayesian inference. The Naive Mean-Field (NMF) approximation is the simplest version of this strategy—this approach approximates the posterior in KL divergence by a product distribution. There has been considerable progress recently in understanding the accuracy of NMF under structural constraints such as sparsity, but not much is known in the absence of such constraints. Moreover, in some high-dimensional settings, the NMF is expected to be grossly inaccurate, and advanced mean-field techniques (e.g. Bethe approximation) are expected to provide accurate approximations. We will present some recent work in understanding this duality in the context of high-dimensional regression. This is based on joint work with Sumit Mukherjee (Columbia) and Jiaze Qiu (Harvard University).

      10:30 – 11:00 amCoffee break 
      11:00 – 11:50 amElchanan Mossel (MIT)

      Title: Some modern perspectives on the Kesten-Stigum bound for reconstruction on trees.

      Abstract: The Kesten-Stigum bound is a fundamental spectral bound for reconstruction on trees. I will discuss some conjectures and recent progress on understanding when it is tight as well as some conjectures and recent progress on what it signifies even in cases where it is not tight.

      12:00 – 2:00 pmLunch
      2:00 – 2:50 pmChristina Lee Yu (Cornell)

      Title: Exploiting Neighborhood Interference with Low Order Interactions under Unit Randomized Design

      Abstract: Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in many real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we utilize knowledge of the network structure to provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. Central to our contribution is a new framework for balancing between model flexibility and statistical complexity as captured by this low order interactions structure.

      3:00 – 3:30 pmCoffee break
      3:30 – 4:20 pmTheo McKenzie (Harvard)

      Title: Spectral statistics for sparse random graphs

      Abstract: Understanding the eigenvectors and eigenvalues of the adjacency matrix of random graphs is fundamental to many algorithmic questions; moreover, it is related to longstanding questions in quantum physics. In this talk we focus on random models of sparse graphs, giving some properties that are unique to these sparse graphs, as well as some specific obstacles. Based on this, we show some new results on spectral statistics of sparse random graphs, as well as some conjectures.

      4:40 – 6:30 pmLightning talk session + welcome reception

       

      Wednesday, May 17, 2023

      9:00 amBreakfast
      9:30 – 10:20Ilias Zadik (MIT)

      Title: Revisiting Jerrum’s Metropolis Process for the Planted Clique Problem

      Abstract: Jerrum in 1992 (co-)introduced the planted clique model by proving the (worst-case initialization) failure of the Metropolis process to recover any o(sqrt(n))-sized clique planted in the Erdos-Renyi graph G(n,1/2). This result is classically cited in the literature of the problem, as the “first evidence” the o(sqrt(n))-sized planted clique recovery task is “algorithmically hard”.
      In this work, we show that the Metropolis process actually fails to work (under worst-case initialization) for any o(n)-sized planted clique, that is the failure applies well beyond the sqrt(n) “conjectured algorithmic threshold”. Moreover we also prove, for a large number of temperature values, that the Metropolis process fails also under “natural initialization”, resolving an open question posed by Jerrum in 1992.

      10:30 – 11:00Coffee break
      11:00 – 11:50Florent Krzakala (Ecole Polytechnique Federale de Lausanne)

      Title: Are Gaussian data all you need for machine learning theory?

      Abstract: Clearly, no! Nevertheless, the Gaussian assumption remains prevalent among theoreticians, particularly in high-dimensional statistics and physics, less so in traditional statistical learning circles. To what extent are Gaussian features merely a convenient choice for certain theoreticians, or genuinely an effective model for learning? In this talk, I will review recent progress on these questions, achieved using rigorous probabilistic approaches in high-dimension and techniques from mathematical statistical physics. I will demonstrate that, despite its apparent limitations, the Gaussian approach is sometimes much closer to reality than one might expect. In particular, I will discuss key findings from a series of recent papers that showcase the Gaussian equivalence of generative models, the universality of Gaussian mixtures, and the conditions under which a single Gaussian can characterize the error in high-dimensional estimation. These results illuminate the strengths and weaknesses of the Gaussian assumption, shedding light on its applicability and limitations in the realm of theoretical statistical learning.

      12:00 – 2:00 pmLunch
      2:00 – 2:50 pmAndrea Montanari (Stanford)

      Title: Dimension free ridge regression

      Abstract: Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we revisit ridge regression. We allow the feature vector to be high-dimensional, or even infinite-dimensional, in which case it belongs to a separable Hilbert space and assume it to satisfy a certain convex concentration property. Within this setting, we establish non-asymptotic bounds that approximate the bias and variance of ridge regression in terms of the bias and variance of an ‘equivalent’ sequence model (a regression model with diagonal design matrix). Previously, such an approximation result was known only in the proportional regime and only up to additive errors: in particular, it did not allow to characterize the behavior of the excess risk when this converges to 0. Our general theory recovers earlier results in the proportional regime (with better error rates). As a new application, we obtain a completely explicit and sharp characterization of ridge regression for Hilbert covariates with regularly varying spectrum. Finally, we analyze the overparametrized near-interpolation setting and obtain sharp ‘benign overfitting’ guarantees.

      [Based on joint work with Chen Cheng]

      3:00 – 3:50 pmYury Polyanskiy (MIT)

      Title: Recent results on broadcasting on trees and stochastic block model

      Abstract: I will survey recent results and open questions regarding the q-ary stochastic block model and its local version (broadcasting on trees, or BOT). For example, establishing uniqueness of non-trivial solution to distribution recursions (BP fixed point) implies a characterization for the limiting mutual information between the graph and community labels. For q=2 uniqueness holds in all regimes. For q>2 uniqueness is currently only proved above a certain threshold that is asymptotically (for large q) is close to Kesten-Stigum (KS) threshold. At the same time between the BOT reconstruction and KS we show that uniqueness does not hold, at least in the presence of (arbitrary small) vertex-level side information. I will also discuss extension of the robust reconstruction result of Janson-Mossel’2004.

      Based on joint works with Qian Yu (Princeton) and Yuzhou Gu (MIT).

      4:00 – 4:30 pmCoffee break
      4:30 – 5:20 pmAlex Wein (UC Davis)

      Title: Is Planted Coloring Easier than Planted Clique?

      Abstract: The task of finding a planted clique in the random graph G(n,1/2) is perhaps the canonical example of a statistical-computational gap: for some clique sizes, the task is statistically possible but believed to be computationally hard. Really, there are multiple well-studied tasks related to the planted clique model: detection, recovery, and refutation. While these are equally difficult in the case of planted clique, this need not be true in general. In the related planted coloring model, I will discuss the computational complexity of these three tasks and the interplay among them. Our computational hardness results are based on the low-degree polynomial model of computation.By taking the complement of the graph, the planted coloring model is analogous to the planted clique model but with many planted cliques. Here our conclusion is that adding more cliques makes the detection problem easier but not the recovery problem.

       

      Thursday, May 18, 2023

      9:00Breakfast
      9:30 – 10:20Guy Bresler (MIT)

      Title: Algorithmic Decorrelation and Planted Clique in Dependent Random Graphs

      Abstract: There is a growing collection of average-case reductions starting from Planted Clique (or Planted Dense Subgraph) and mapping to a variety of statistics problems, sharply characterizing their computational phase transitions. These reductions transform an instance of Planted Clique, a highly structured problem with its simple clique signal and independent noise, to problems with richer structure. In this talk we aim to make progress in the other direction: to what extent can these problems, which often have complicated dependent noise, be transformed back to Planted Clique? Such a bidirectional reduction between Planted Clique and another problem shows a strong computational equivalence between the two problems.  We develop a new general framework for reasoning about the validity of average-case reductions based on low sensitivity to perturbations. As a concrete instance of our general result, we consider the planted clique (or dense subgraph) problem in an ambient graph that has dependent edges induced by randomly adding triangles to the Erdos-Renyi graph G(n,p), and show how to successfully eliminate dependence by carefully removing the triangles while approximately preserving the clique (or dense subgraph). Joint work with Chenghao Guo and Yury Polyanskiy.

      10:30 – 11:00Coffee break 
      11:00 – 11:50Sarath Yasodharan (Brown)

      Title: A Sanov-type theorem for unimodular marked random graphs and its applications

      Abstract: We prove a Sanov-type large deviation principle for the component empirical measures of certain sequences of unimodular random graphs (including Erdos-Renyi and random regular graphs) whose vertices are marked with i.i.d. random variables. Specifically, we show that the rate function can be expressed in a fairly tractable form involving suitable relative entropy functionals. As a corollary, we establish a variational formula for the annealed pressure (or limiting log partition function) for various statistical physics models on sparse random graphs. This is joint work with I-Hsun Chen and Kavita Ramanan.

      12:00 – 12:15 pm

      12:15 – 2:00 pm

      Group Photo

      Lunch

      2:00 – 2:50 pmPatrick Rebeschini (Oxford)

      Title: Implicit regularization via uniform convergence

      Abstract: Uniform convergence is one of the main tools to analyze the complexity of learning algorithms based on explicit regularization, but it has shown limited applicability in the context of implicit regularization. In this talk, we investigate the statistical guarantees on the excess risk achieved by early-stopped mirror descent run on the unregularized empirical risk with the squared loss for linear models and kernel methods. We establish a direct link between the potential-based analysis of mirror descent from optimization theory and uniform learning. This link allows characterizing the statistical performance of the path traced by mirror descent directly in terms of localized Rademacher complexities of function classes depending on the choice of the mirror map, initialization point, step size, and the number of iterations. We will discuss other results along the way.

      3:00 – 3:50 pmPragya Sur (Harvard)

      Title: A New Central Limit Theorem for the Augmented IPW estimator in high dimensions

      Abstract: Estimating the average treatment effect (ATE) is a central problem in causal inference. Modern advances in the field studied estimation and inference for the ATE in high dimensions through a variety of approaches. Doubly robust estimators such as the augmented inverse probability weighting (AIPW) form a popular approach in this context. However, the high-dimensional literature surrounding these estimators relies on sparsity conditions, either on the outcome regression (OR) or the propensity score (PS) model. This talk will introduce a new central limit theorem for the classical AIPW estimator, that applies agnostic to such sparsity-type assumptions. Specifically, we will study properties of the cross-fit version of the estimator under well-specified OR and PS models, and the proportional asymptotics regime where the number of confounders and sample size diverge proportional to each other. Under assumptions on the covariate distribution, our CLT will uncover two crucial phenomena among others: (i) the cross-fit AIPW exhibits a substantial variance inflation that can be quantified in terms of the signal-to-noise ratio and other problem parameters, (ii) the asymptotic covariance between the estimators used while cross-fitting is non-negligible even on the root-n scale. These findings are strikingly different from their classical counterparts, and open a vista of possibilities for studying similar other high-dimensional effects. On the technical front, our work utilizes a novel interplay between three distinct tools—approximate message passing theory, the theory of deterministic equivalents, and the leave-one-out approach.

      4:00 – 4:30 pmCoffee break
      4:30 – 5:20 pmYihong Wu (Yale)

      Title: Random graph matching at Otter’s threshold via counting chandeliers

      Abstract: We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erdős–Rényi graphs G(n,q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nq\to\infty and the edge correlation coefficient ρ satisfies ρ^2>α≈0.338, where α is Otter’s tree-counting constant. Moreover, this almost exact matching can be made exact under an extra condition that is information-theoretically necessary. This is the first polynomial-time graph matching algorithm that succeeds at an explicit constant correlation and applies to both sparse and dense graphs. In comparison, previous methods either require ρ=1−o(1) or are restricted to sparse graphs. The crux of the algorithm is a carefully curated family of rooted trees called chandeliers, which allows effective extraction of the graph correlation from the counts of the same tree while suppressing the undesirable correlation between those of different trees. This is joint work with Cheng Mao, Jiaming Xu, and Sophie Yu, available at https://arxiv.org/abs/2209.12313

       

      Friday, May 19, 2023

      9:00Breakfast
      9:30 – 10:20Jake Abernethy (Georgia Tech)

      Title: Optimization, Learning, and Margin-maximization via Playing Games

      Abstract: A very popular trick for solving certain types of optimization problems is this: write your objective as the solution of a two-player zero-sum game, endow both players with an appropriate learning algorithm, watch how the opponents compete, and extract an (approximate) solution from the actions/decisions taken by the players throughout the process. This approach is very generic and provides a natural template to produce new and interesting algorithms. I will describe this framework and show how it applies in several scenarios, including optimization, learning, and margin-maximiation problems. Along the way we will encounter a number of novel tools and rediscover some classical ones as well.

      10:30 – 11:00Coffee break 
      11:00 – 11:50Devavrat Shah (MIT)

      Title: On counterfactual inference with unobserved confounding via exponential family

      Abstract: We are interested in the problem of unit-level counterfactual inference with unobserved confounders owing to the increasing importance of personalized decision-making in many domains: consider a recommender system interacting with a user over time where each user is provided recommendations based on observed demographics, prior engagement levels as well as certain unobserved factors. The system adapts its recommendations sequentially and differently for each user. Ideally, at each point in time, the system wants to infer each user’s unknown engagement if it were exposed to a different sequence of recommendations while everything else remained unchanged. This task is challenging since: (a) the unobserved factors could give rise to spurious associations, (b) the users could be heterogeneous, and (c) only a single trajectory per user is available.

      We model the underlying joint distribution through an exponential family. This reduces the task of unit-level counterfactual inference to simultaneously learning a collection of distributions of a given exponential family with different unknown parameters with single observation per distribution. We discuss a computationally efficient method for learning all of these parameters with estimation error scaling linearly with the metric entropy of the space of unknown parameters – if the parameters are an s-sparse linear combination of k known vectors in p dimension, the error scales as O(s log k/p).  En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality.

      Based on a joint work with Raaz Dwivedi, Abhin Shah and Greg Wornell (all at MIT) with manuscript available here: https://arxiv.org/abs/2211.08209

      12:00 – 2:00 pmLunch 
      2:00 – 2:50 pmLester Mackey  (Microsoft Research New England)

      Title: Advances in Distribution Compression

      Abstract: This talk will introduce two new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning:
      1. Given an initial n-point summary (for example, from independent sampling or a Markov chain), kernel thinning finds a subset of only square-root n-points with comparable worst-case integration error across a reproducing kernel Hilbert space.
      2. If the initial summary suffers from biases due to off-target sampling, tempering, or burn-in, Stein thinning simultaneously compresses the summary and improves the accuracy by correcting for these biases.
      These tools are especially well-suited for tasks that incur substantial downstream computation costs per summary point like organ and tissue modeling in which each simulation consumes 1000s of CPU hours.
      Based on joint work with Raaz Dwivedi, Marina Riabiz, Wilson Ye Chen, Jon Cockayne, Pawel Swietach, Steven A. Niederer, Chris. J. Oates, Abhishek Shetty, and Carles Domingo-Enrich.

      3:00 – 3:30 pmCoffee break
      3:30 – 4:20 pmHorng-Tzer Yau (Harvard)

      Title: On the spectral gap of mean-field spin glass models.

      Abstract: We will discuss recent progress regarding spectral gaps for the Glauber dynamics of spin glasses at high temperature. In addition, we will also report on estimating the operator norm  of the covariance matrix for the SK model.

       

      Moderators: Benjamin McKenna, Harvard CMSA & Changji Xu, Harvard CMSA


       

      CMSA COVID-19 Policies

       

    • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
      9:00 am-5:00 pm
      12/01/2024-12/04/2016

      The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

      The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

      Please click here to register for this event.

      Speakers:

      1. Cliff Taubes (Harvard University)
      2. Valentino Tosatti (Northwestern University)
      3. Pengfei Guan (McGill University)
      4. Jared Speck (MIT)

      Schedule:

      December 3rd – Day 1
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
      December 4th – Day 2
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

      Please click Mini-School Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • CMSA EVENT: Mirror symmetry, gauged linear sigma models, matrix factorizations, and related topics
      9:00 am-4:30 pm
      12/01/2024-03/06/2020
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Mirror-Symmetry-poster-1

      On March 4-6, 2020 the CMSA will be hosting a three-day workshop on Mirror symmetry, Gauged linear sigma models, Matrix factorizations, and related topics as part of the Simons Collaboration on Homological Mirror Symmetry. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      Speakers: 

      Schedule

      Videos from the workshop are available in the Youtube playlist.

    • CMSA EVENT: Quantum Matter Workshop
      9:00 am-5:00 pm
      12/01/2024-12/04/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Quantum Matter Workshop

      On December 2-4, 2019 the CMSA will be hosting a workshop on Quantum Matter as part of our program on Quantum Matter in Mathematics and Physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Pictures can be found here.

      Organizers: Juven Wang (CMSA), Xiao-Gang Wen (MIT), and Shing-Tung Yau (Harvard)

      Confirmed Speakers: 

       

    • CMSA EVENT: Workshop on Coding and Information Theory
      9:00 am-3:30 pm
      12/01/2024-04/13/2018

      The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

      Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      Click here for a list of registrants. 

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

    • Workshop
      9:00 am-6:00 pm
      12/01/2024-05/12/2023
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      The CMSA will be hosting a Workshop on Global Categorical Symmetries from May 7 – 12, 2023

      Participation in the workshop is by invitation.

      Public Lectures

      There will be three lectures on Thursday, May 11, 2023, which are open to the public.
      Location:  Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
      Note: The public lectures will be held in-person only.

      2:00 – 2:50 pm
      Speaker: Kantaro Ohmori (U Tokyo )
      Title: Fusion Surface Models: 2+1d Lattice Models from Higher Categories
      Abstract: Generalized symmetry in general dimensions is expected to be described by higher categories. Conversely, one might expect that, given a higher category with appropriate structures, there exist models that admit the category as its symmetry. In this talk I will explain a construction of such 2+1d lattice models for fusion 2-categories defined by Douglas and Reutter, generalizing the work of Aasen, Fendley and Mong on anyon chains. The construction is by decorating a boundary of a topological Freed-Teleman-Moore sandwich into a non-topological boundary. In particular we can construct a family of candidate lattice systems for chiral topological orders.

       

      3:00 – 3:50 pm
      Speaker: David Jordan (Edinburgh)
      Title: Langlands duality for 3-manifolds
      Abstract: Originating in number theory, and permeating representation theory, algebraic geometry, and quantum field theory, Langlands duality is a pattern of predictions relating pairs of mathematical objects which have no clear a priori mathematical relation. In this talk I’ll explain a new conjectural appearance of Langlands duality in the setting of 3-manifold topology, I’ll give some evidence in the form of special cases, and I’ll survey how the conjecture relates to both the arithmetic and geometric Langlands duality conjectures.

      3:50 – 4:30 pm
      Tea/Snack Break

      4:30 – 5:30 pm
      Speaker: Ken Intriligator (UCSD)
      Colloquium
      Title: QFT Aspects of Symmetry
      Abstract: Everything in the Universe, including the photons that we see and the quarks and electrons in our bodies, are actually ripples of quantum fields. Quantum field theory (QFT) is the underlying mathematical framework of Nature, and in the case of electrons and photons it is the most precisely tested theory in science. Strongly coupled aspects, e.g. the confinement of quarks and gluons at long distances, remain challenging. QFT also describes condensed matter systems, connects to string theory and quantum gravity, and describes cosmology. Symmetry has deep and powerful realizations and implications throughout physics, and this is especially so for the study of QFT. Symmetries play a helpful role in characterizing the phases of theories and their behavior under renormalization group flows (zooming out). Quantum field theory has also been an idea generating machine for mathematics, and there has been increasingly fruitful synergy in both directions. We are currently exploring the symmetry-based interconnections between QFT and mathematics in our Simons Collaboration on Global Categorical Symmetry, which is meeting here this week. I will try to provide an accessible, colloquium-level introduction to aspects of symmetries and QFT, both old and new.


    • CMSA EVENT: Big Data Conference 2023
      9:00 am-5:00 pm
      12/01/2024-09/01/2023
      1 Oxford Street, Cambridge MA 02138

      On August 31-Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      Location: Harvard University Science Center Hall D & via Zoom.

      Directions and Recommended Lodging

      Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

      Registration is required.

      Note: In-person registration is at capacity. Please sign up for the Zoom Webinar (registration link).

       

      Speakers:

       

      Organizers:

      • Michael Douglas, CMSA, Harvard University
      • Yannai Gonczarowski, Economics and Computer Science, Harvard University
      • Lucas Janson, Statistics and Computer Science, Harvard University
      • Tracy Ke, Statistics, Harvard University
      • Horng-Tzer Yau, Mathematics and CMSA, Harvard University
      • Yue Lu, Electrical Engineering and Applied Mathematics, Harvard University

      Schedule

      (PDF download)

      Thursday, August 31, 2023

      9:00 AMBreakfast
      9:30 AMIntroductions
      9:45–10:45 AMAlbert-László Barabási (Northeastern, Harvard)

      Title: From Network Medicine to the Foodome: The Dark Matter of Nutrition

      Abstract: A disease is rarely a consequence of an abnormality in a single gene but reflects perturbations to the complex intracellular network. Network medicine offer a platform to explore systematically not only the molecular complexity of a particular disease, leading to the identification of disease modules and pathways, but also the molecular relationships between apparently distinct (patho) phenotypes. As an application, I will explore how we use network medicine to uncover the role individual food molecules in our health. Indeed, our current understanding of how diet affects our health is limited to the role of 150 key nutritional components systematically tracked by the USDA and other national databases in all foods. Yet, these nutritional components represent only a tiny fraction of the over 135,000 distinct, definable biochemicals present in our food. While many of these biochemicals have documented effects on health, they remain unquantified in any systematic fashion across different individual foods. Their invisibility to experimental, clinical, and epidemiological studies defines them as the ‘Dark Matter of Nutrition.’ I will speak about our efforts to develop a high-resolution library of this nutritional dark matter, and efforts to understand the role of these molecules on health, opening novel avenues by which to understand, avoid, and control disease.

      https://youtu.be/UmgzUwi6K3E

      10:45–11:00 AMBreak
      11:00 AM–12:00 PMRachel Cummings (Columbia)

      Title: Differentially Private Algorithms for Statistical Estimation Problems

      Abstract: Differential privacy (DP) is widely regarded as a gold standard for privacy-preserving computation over users’ data.  It is a parameterized notion of database privacy that gives a rigorous worst-case bound on the information that can be learned about any one individual from the result of a data analysis task. Algorithmically it is achieved by injecting carefully calibrated randomness into the analysis to balance privacy protections with accuracy of the results.
      In this talk, we will survey recent developments in the development of DP algorithms for three important statistical problems, namely online learning with bandit feedback, causal interference, and learning from imbalanced data. For the first problem, we will show that Thompson sampling — a standard bandit algorithm developed in the 1930s — already satisfies DP due to the inherent randomness of the algorithm. For the second problem of causal inference and counterfactual estimation, we develop the first DP algorithms for synthetic control, which has been used non-privately for this task for decades. Finally, for the problem of imbalanced learning, where one class is severely underrepresented in the training data, we show that combining existing techniques such as minority oversampling perform very poorly when applied as pre-processing before a DP learning algorithm; instead we propose novel approaches for privately generating synthetic minority points.

      Based on joint works with Marco Avella Medina, Vishal Misra, Yuliia Lut, Tingting Ou, Saeyoung Rho, and Ethan Turok.

      https://youtu.be/0cPE6rb1Roo

      12:00–1:30 PMLunch
      1:30–2:30 PMMorgane Austern (Harvard)

      Title: To split or not to split that is the question: From cross validation to debiased machine learning

      Abstract: Data splitting is a ubiquitous method in statistics with examples ranging from cross-validation to cross-fitting. However, despite its prevalence, theoretical guidance regarding its use is still lacking. In this talk, we will explore two examples and establish an asymptotic theory for it. In the first part of this talk, we study the cross-validation method, a ubiquitous method for risk estimation, and establish its asymptotic properties for a large class of models and with an arbitrary number of folds. Under stability conditions, we establish a central limit theorem and Berry-Esseen bounds for the cross-validated risk, which enable us to compute asymptotically accurate confidence intervals. Using our results, we study the statistical speed-up offered by cross-validation compared to a train-test split procedure. We reveal some surprising behavior of the cross-validated risk and establish the statistically optimal choice for the number of folds. In the second part of this talk, we study the role of cross-fitting in the generalized method of moments with moments that also depend on some auxiliary functions. Recent lines of work show how one can use generic machine learning estimators for these auxiliary problems, while maintaining asymptotic normality and root-n consistency of the target parameter of interest. The literature typically requires that these auxiliary problems are fitted on a separate sample or in a cross-fitting manner. We show that when these auxiliary estimation algorithms satisfy natural leave-one-out stability properties, then sample splitting is not required. This allows for sample reuse, which can be beneficial in moderately sized sample regimes.

      https://youtu.be/L_pHxgoQSgU

      2:30–2:45 PMBreak
      2:45–3:45 PMAnkur Moitra (MIT)

      Title: Learning from Dynamics

      Abstract: Linear dynamical systems are the canonical model for time series data. They have wide-ranging applications and there is a vast literature on learning their parameters from input-output sequences. Moreover they have received renewed interest because of their connections to recurrent neural networks.
      But there are wide gaps in our understanding. Existing works have only asymptotic guarantees or else make restrictive assumptions, e.g. that preclude having any long-range correlations. In this work, we give a new algorithm based on the method of moments that is computationally efficient and works under essentially minimal assumptions. Our work points to several missed connections, whereby tools from theoretical machine learning including tensor methods, can be used in non-stationary settings.

      https://youtu.be/UmgzUwi6K3E

      3:45–4:00 PMBreak
      4:00–5:00 PMMark Sellke (Harvard)

      Title: Algorithmic Thresholds for Spherical Spin Glasses

      Abstract: High-dimensional optimization plays a crucial role in modern statistics and machine learning. I will present recent progress on non-convex optimization problems with random objectives, focusing on the spherical p-spin glass. This model is related to spiked tensor estimation and has been studied in probability and physics for decades. We will see that a natural class of “stable” optimization algorithms gets stuck at an algorithmic threshold related to geometric properties of the landscape. The algorithmic threshold value is efficiently attained via Langevin dynamics or by a second-order ascent method of Subag. Much of this picture extends to other models, such as random constraint satisfaction problems at high clause density.

      https://youtu.be/JoghiwiIbT8

      6:00 – 8:00 PMBanquet for organizers and speakers

       

      Friday, September 1, 2023

      9:00 AMBreakfast
      9:30 AMIntroductions
      9:45–10:45 AMJacob Andreas (MIT)

      Title: What Learning Algorithm is In-Context Learning?

      Abstract: Neural sequence models, especially transformers, exhibit a remarkable capacity for “in-context” learning. They can construct new predictors from sequences of labeled examples (x,f(x)) presented in the input without further parameter updates. I’ll present recent findings suggesting that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context, using in-context linear regression as a model problem. First, I’ll show by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, I’ll show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Finally, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners’ late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. This work is joint with Ekin Akyürek at MIT, and Dale Schuurmans, Tengyu Ma and Denny Zhou at Stanford.

      https://youtu.be/UNVl64G3BzA

      10:45–11:00 AMBreak
      11:00 AM–12:00 PMTommi Jaakkola (MIT)

      Title: Generative modeling and physical processes

      Abstract: Rapidly advancing deep distributional modeling techniques offer a number of opportunities for complex generative tasks, from natural sciences such as molecules and materials to engineering. I will discuss generative approaches inspired from physical processes including diffusion models and more recent electrostatic models (Poisson flow), and how they relate to each other in terms of embedding dimension. From the point of view of applications, I will highlight our recent work on SE(3) invariant distributional modeling over backbone 3D structures with ability to generate designable monomers without relying on pre-trained protein structure prediction methods as well as state of the art image generation capabilities (Poisson flow). Time permitting, I will also discuss recent analysis of efficiency of sample generation in such models.

      https://youtu.be/GLEwQAWQ85E

      12:00–1:30 PMLunch
      1:30–2:30 PMMarinka Zitnik (Harvard Medical School)

      Title: Multimodal Learning on Graphs

      Abstract: Understanding biological and natural systems requires modeling data with underlying geometric relationships across scales and modalities such as biological sequences, chemical constraints, and graphs of 3D spatial or biological interactions. I will discuss unique challenges for learning from multimodal datasets that are due to varying inductive biases across modalities and the potential absence of explicit graphs in the input. I will describe a framework for structure-inducing pretraining that allows for a comprehensive study of how relational structure can be induced in pretrained language models. We use the framework to explore new graph pretraining objectives that impose relational structure in the induced latent spaces—i.e., pretraining objectives that explicitly impose structural constraints on the distance or geometry of pretrained models. Applications in genomic medicine and therapeutic science will be discussed. These include TxGNN, an AI model enabling zero-shot prediction of therapeutic use across over 17,000 diseases, and PINNACLE, a contextual graph AI model dynamically adjusting its outputs to contexts in which it operates. PINNACLE enhances 3D protein structure representations and predicts the effects of drugs at single-cell resolution.

      https://youtu.be/hjt4nsN_8iM

      2:30–2:45 PMBreak
      2:45–3:45 PMJianqing Fan (Princeton)

      Title: UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

      Abstract: Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts. Numerous methods are available for constructing prediction intervals, such as quantile regression and conformal predictions, among others. Nevertheless, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this work, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions.  Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics. (Joint work Jiawei Ge and Debarghya Mukherjee).

      https://youtu.be/WY6dr1oEOrk

      3:45–4:00 PMBreak
      4:00–5:00 PMMelissa Dell (Harvard)

      Title: Efficient OCR for Building a Diverse Digital History

      Abstract: Many users consult digital archives daily, but the information they can access is unrepresentative of the diversity of documentary history. The sequence-to-sequence architecture typically used for optical character recognition (OCR) – which jointly learns a vision and language model – is poorly extensible to low-resource document collections, as learning a language-vision model requires extensive labeled sequences and compute. This study models OCR as a character-level image retrieval problem, using a contrastively trained vision encoder. Because the model only learns characters’ visual features, it is more sample-efficient and extensible than existing architectures, enabling accurate OCR in settings where existing solutions fail. Crucially, it opens new avenues for community engagement in making digital history more representative of documentary history.

      https://youtu.be/u0JY9vURUAs

       


      Information about the 2022 Big Data Conference can be found here.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Invariant theory for maximum likelihood estimation
      9:00 am-10:00 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-2.8.2022

      Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

    • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
      9:00 am-1:30 pm
      12/01/2024-02/09/2018

      The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

      There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

      The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The n-queens problem
      9:00 am-10:00 am
      12/01/2024

      Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

      In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

      This is joint work with Peter Keevash.

    • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
      9:00 am-6:15 pm
      12/01/2024-03/26/2018
      GIC-Poster-2-e1520002551865

      On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

      The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

      Please click here to register for the event.

      Confirmed Speakers:

    • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
      9:00 am-11:55 am
      12/01/2024-03/29/2019
      Machine-Learning-Poster

      The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Speakers:

    • CMSA EVENT: The 2017 Charles River Lectures
      9:15 am-5:30 pm
      12/01/2024

      The 2017 Charles River Lectures

      Charles River with Bench at Sunset

      Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

      The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


      ***************************************************

      UPDATED LOCATION

      Harvard University

      Harvard Science Center (Halls C & E)

      1 Oxford Street, Cambridge, MA 02138 (Map)

      Monday, October 2, 2017

      9:15 AM – 5:30 PM

      **************************************************

      Please note that registration has closed.

      Speakers:

      Agenda:

      In Harvard Science Center Hall C:

      8:45 am – 9:15 amCoffee/light breakfast

      9:15 am – 10:15 am: Ofer Zeitouni

      Title: Noise stability of the spectrum of large matrices

      Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

      The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

      10:20 am – 11:20 am: Andrea Montanari

      Title: Algorithms for estimating low-rank matrices 

      Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

      11:20 am – 11:45 amBreak

      11:45 am – 12:45 pm: Paul Bourgade

      Title: Random matrices, the Riemann zeta function and trees

      Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

      1:00 pm – 2:30 pm: Lunch

      In Harvard Science Center Hall E:

      2:45 pm – 3:45 pm: Roman Vershynin

      Title: Deviations of random matrices and applications

      Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

      3:45 pm – 4:15 pm: Break

      4:15 pm – 5:15 pm: Massimiliano Gubinelli

      Title: Weak universality and Singular SPDEs

      Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

      Poster:

      2017 Charles River Lectures Poster

      Organizers:

       Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

    • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
      9:15 am-3:25 pm
      12/01/2024-09/11/2019
      Topology-Poster

      On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

      New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

      Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

      This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Click here for a list of restaurants in the area. 

      Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

      Partial list of speakers:

      Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

    • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
      9:15 am-10:00 am
      12/01/2024-04/17/2019

      As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

      Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

      This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

      In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Videos

      Tentative Speaker List:

      Schedule:

      Monday, April 15

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:15amWelcome and Introduction
      9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

      Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

      10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

      Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

      In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

      I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

      10:45 – 11:15amCoffee Break
      11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

      12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      12:45 – 2:00pmLunch
      2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

      My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

      2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

      Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

      Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

      4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

      Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

      5:30 – 6:30pmReception

       

      Tuesday, April 16

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

      9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

      Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

      11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

      Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

      12:30 – 2:00pmLunch
      2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

      Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

      2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

      Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

      4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

      Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


      Wednesday, April 17

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

      Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

      Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

      (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

      (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

      (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

      University of Jerusalem, Jerusalem, 91904, Israel

      9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

      Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

      This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

      Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

      11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

      Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

      12:30 – 1:30pmLunch
      1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

      Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

      2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

      Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

      3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

      Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

      3:45 – 4:00pmL Mahadevan – summary
    • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
      9:20 am-3:15 pm
      12/01/2024-08/28/2018
      Topological-1

      Screen-Shot-2018-08-13-at-2.28.22-PM

      On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

      This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please register here

      Speakers: 

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Max Wiesner

      Title: Light strings, strong coupling, and the Swampland

      Abstract: In this talk, I will start by reviewing central ideas of the so-called Swampland Program. The Swampland Program aims to identify criteria that distinguish low-energy effective field theories, that can be consistently coupled to quantum gravity, from those theories that become inconsistent in the presence of quantum gravity.

      In my talk I will specialize to four-dimensional effective field theories with N=2 and N=1 supersymmetry. In weakly-coupled regions of the scalar field space of such theories, it has been shown that light strings are crucial to realize certain Swampland criteria. Complementary to that, the focus of this talk will be on the role of such light strings away from these weak-coupling regimes. In this context, I will first discuss a relation between light perturbative strings and strong coupling singularities in the Kähler moduli space of 4d N=1 compactifications of F-theory. More precisely, in regions of moduli space, in which a critical string classically becomes light, I will show that non-perturbative corrections yield to strong coupling singularities for D7-brane gauge theories which obstruct weak-coupling limits. Moreover, I will demonstrate that in the vicinity of this strong coupling singularity, the critical, light string in fact leaves the spectrum of BPS strings thereby providing an explanation for the obstruction of the weak coupling limit.

      I will then move on and discuss the backreaction of perturbative strings in 4d EFTs. Away from the string core, the backreaction of such strings necessarily leads to strong coupling regions where naively the energy stored in the backreaction diverges. I will show how the introduction of additional non-critical strings can regulate this backreaction and how this can be used to study the spectrum of BPS strings and their tensions even beyond weak coupling regions. In this context, I will demonstrate how the requirement, that the total string tension should not exceed the Planck scale, constrains the possible BPS string charges.

    • Special Seminar
      Special Seminar
      3/30/2018 Special Seminar
      9:30 am-11:00 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Speaker: Bong Lian

      Title: Singular Calabi-Yau mirror symmetry

      Abstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors, including Matsumoto, Sasaki, Yoshida and others, mainly from the viewpoint of their moduli spaces and their comparisons.  I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono, Tsung-Ju Lee, Hiromichi Takagi, Shing-Tung Yau.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Tsung-Ju Lee

      Title: Periods for singular CY families and Riemann–Hilbert correspondence

      Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and mirror symmetry. In this talk, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.

    • Member Seminar
      9:30 am-11:30 am
      12/01/2024

      Member Seminar

      Speaker: Chuck Doran

      Title: The Greene-Plesser Construction Revisited

      Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The threshold for stacked triangulations
      9:30 am-10:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10
      CMSA-Combinatorics-Physics-and-Probability-Seminar-05.03.22

      Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{[n]}3$, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle.
      Suppose that every triangle is initially infected independently with probability p=p(n), what is the threshold probability for percolation — the event that all triangles get infected? How many new triangles do get infected in the subcritical regime?

      This notion of percolation can be viewed as a simplification of simple-connectivity. Namely, a stacked triangulation of a triangle is obtained by repeatedly subdividing an inner face into three faces.
      We ask: for which $p$ does the random simplicial complex Y_2(n,p) contain, for every triple $xyz$, the faces of a stacked triangulation of $xyz$ whose internal vertices are arbitrarily labeled in [n].

      We consider this problem in every dimension d>=2, and our main result identifies a sharp probability threshold for percolation, showing it is asymptotically (c_d*n)^(-1/d), where c_d is the growth rate of the Fuss–Catalan numbers of order d.

      The proof hinges on a second moment argument in the supercritical regime, and on Kalai’s algebraic shifting in the subcritical regime.

      Joint work with Eyal Lubetzky.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-Seminar-09.13.22

      Quantum Matter in Mathematics and Physics

      Speaker: Yichul Cho (SUNY Stony Brook)

      Title: Non-invertible Symmetries in Nature

      Abstract: In this talk, I will discuss non-invertible symmetries in
      familiar 3+1d quantum field theories describing our Nature. In
      massless QED, the classical U(1) axial symmetry is not completely
      broken by the ABJ anomaly. Instead, it turns into a discrete,
      non-invertible symmetry. The non-invertible symmetry operator is
      obtained by dressing the naïve U(1) axial symmetry operator with a
      fractional quantum Hall state. We also find a similar non-invertible
      symmetry in the massless limit of QCD, which provides an alternative
      explanation for the neutral pion decay. In the latter part of the
      talk, I will discuss non-invertible time-reversal symmetries in 3+1d
      gauge theories. In particular, I will show that in free Maxwell
      theory, there exists a non-invertible time-reversal symmetry at every
      rational value of the theta angle.

      Based on https://arxiv.org/abs/2205.05086 and https://arxiv.org/abs/2208.04331.

       

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Mathlit_WOODIN

      CMSA/Tsinghua Math-Science Literature Lecture

      woodin_portait_books

      Prof. Hugh Woodin will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

      Date: Wednesday, November 9, 2022

      Time: 9:30 – 11:00 am ET

      Location: Via Zoom Webinar and Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

      Directions and Recommended Lodging

      Registration is required.

       

      Title: Large cardinals and small sets: The AD+ Duality Program

      Abstract: The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers.  The modern view is that determinacy axioms concern generalizations of the borel sets, and deep connections with large cardinal axioms have emerged.

      The study of determinacy axioms has led to a specific technical refinement of AD, this is the axiom AD+. The further connections with large axioms have in turn implicitly led to a duality program, this is the AD+ Duality Program.

      The main open problems here are intertwined with those of the Inner Model Program, which is the central program in the study of large cardinal axioms.

      This has now all been distilled into a series of specific conjectures.

       

      Talk chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)

      Moderator: Alejandro Poveda Ruzafa (Harvard CMSA)

       

      Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

       

      CMSA COVID-19 Policies

    • Member Seminar
      9:30 am-11:00 am
      12/01/2024

      Member Seminar

      Speaker: Sergiy Verstyuk

      Title: Machine Learning the Gravity Equation for International Trade

      Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 11.10.22

      General Relativity Seminar

      Speaker: Pierre Heidmann (Johns Hopkins)

      Title: Schwarzschild-like Topological Solitons in Gravity

      Abstract: We present large classes of non-extremal solitons in gravity that are asymptotic to four-dimensional Minkowski spacetime plus extra compact dimensions. They correspond to smooth horizonless geometries induced by topology in spacetime and supported by electromagnetic flux, which characterize coherent states of quantum gravity. We discuss a new approach to deal with Einstein-Maxwell equations in more than four dimensions, such that they decompose into a set of Ernst equations. We generate the solitons by applying different techniques associated with the Ernst formalism. We focus on solitons with zero net charge yet supported by flux, and compare them to Schwarzschild black holes. These are also ultra-compact geometries with very high redshift but differ in many aspects. At the end of the talk, we discuss the stability properties of the solitons and their gravitational signatures.

    • Algebraic Geometry in String Theory Seminar
    • CMSA EVENT: Math-Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024
      Math-Science Literature Lecture Series

      Mathematics & Literature Lecture Series

      Beginning in Spring 2020, the CMSA will be hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars. Talks will take place throughout the semester. All talks will take place virtually. You must register to attend. Recordings will be posted to this page.

      Written articles will accompany each lecture in this series and be available as part of the publication “The Literature and History of Mathematical Science

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry, transforming Calabi-Yau 3-folds between A- and B-models. In this talk, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X, detail the change of derived categories from its smoothing to its small resolution.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Pok Man Tam (University of Pennsylvania)

      Title: Topology of the Fermi sea: Ordinary metals as topological materials

      Abstract: It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F  to experimental observables, namely: (i) equal-time density/number correlations [1], and (ii) Andreev state transport along a planar Josephson junction [2]. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.

      [1] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)

      [2] P. M. Tam and C. L. Kane, arXiv:2210.08048

       

      https://www.youtube.com/watch?v=AXHLAo8kMHQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=25

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Title: Asymptotic localization, massive fields, and gravitational singularities

      Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-03.09.2022

      Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Prague dimension of random graphs
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-11.23.21

      Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      General Relativity Seminar

      Speaker: Semyon Dyatlov (MIT)

      Title: Ringdown and geometry of trapping for black holes

      Abstract: Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of a black hole merger when the dynamics is expected to be driven by linear effects. In this talk I give an overview of various results in pure mathematics which relate asymptotic behavior of quasi-normal modes at high frequency to the geometry of the set of trapped null geodesics, such as the photon sphere in Schwarzschild (-de Sitter). These trapped geodesics have two kinds of behavior: the geodesic flow is hyperbolic in directions normal to the trapped set (a feature stable under perturbations) and it is completely integrable on the trapped set. It turns out that normal hyperbolicity gives information about the rate of decay of quasi-normal modes, while complete integrability gives rise to a quantization condition.

    • Colloquium
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Elliptic chiral homology and chiral index
      9:30 am-10:30 am
      12/01/2024
      20220330_Si-LI_poster

      Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture - Karen Uhlenbeck
      9:30 am-2:26 pm
      12/01/2024
      Lecture_Uhlenbeck_12921

      Karen Uhlenbeck (Institute for Advanced Study)

      Title: The Noether Theorems in Geometry: Then and Now

      Abstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature.

      Talk Chair: Laura DeMarco

      VIDEO

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Gabriel Wong (Harvard CMSA)

      Title: 3D gravity and gravitational entanglement entropy

      Abstract: Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime. Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge modes.

       

      https://www.youtube.com/watch?v=xD0hWdS-OAc&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=24

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Changji Xu

      Title: On the solution space of the Ising perceptron model

      Abstract:  Consider the discrete cube $\{-1,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk, we will talk about its sharp threshold phenomenon, the frozen structure of the solution space, and the Gardner formula.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Counting invariant curves on a Calabi-Yau threefold with an involution
      9:30 am-10:30 am
      12/01/2024
      Jim-Bryan_poster_3Nov2021

      Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g,h) which are conjectured to be equivalent, one in terms of a version of PT theory, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface, the specialization of n_beta(g,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-04.27.22

      Speaker: Venkatesan Guruswami, UC Berkeley

      Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

      Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.
      We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

      Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

      This is joint work with Xiaoyu He and Ray Li.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Michael Simkin

      Title: Threshold phenomena in random graphs and hypergraphs

      Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields.

      The model is defined as follows: Given a natural number $n$ and a parameter $p \in [0,1]$, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$, independent of all others. Despite their apparent simplicity, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena.

      A central feature is the appearance of threshold phenomena: For all monotone properties (e.g., connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e., with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Speaker: Freid Tong

      Title: The complex Monge-Ampere equation in Kahler geometry

      Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry, with a particular focus on the a priori C^0 estimates and their various applications. In the end, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.

    • Colloquium
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Gradient flows on totally nonnegative flag varieties
      9:30 am-10:30 am
      12/01/2024

      Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Kan Lin

      Title: China’s financial regulatory reform, financial opening-up, and Central Bank Digital Currency (CBDC)

      Abstract: In this talk, I will explain the overall situation of China’s financial industry and review the development of China’s financial regulatory system reform from 1949 to 2021. Then, I will explain the policies of the 3 stages of financial opening-up, 2001–08, 2008–18, 2018≠present. In particular, the latest round of opening-up from 2018 has brought great opportunities for foreign institutions. China has the world’s largest banking industry with assets totaling $53 trillion, and accounts for 1/3 of the growth in global insurance premiums over the next 10 years. I will also introduce the progress of research & development of China’s Central Bank Digital Currency (CBDC, or E-CNY). By October 2021, 140 million people had opened E-CNY wallets, and 1.6 million merchants could accept payments using eCNY wallets, including utilities, catering services, transportation, retail, and government services.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-03.24.2022-1583x2048

      Youtube Video

       

      Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.16.21-1-1

      Abstract: I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine (arxiv:2109.13323).

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 09.30.2022

      Algebraic Geometry in String Theory Seminar

      Speaker:  Mauricio Romo, Tsinghua University

      Title: GLSM, Homological projective duality and nc resolutions
      Abstract: Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.
    • Algebraic Geometry in String Theory Seminar
    • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
      9:30 am-5:00 pm
      12/01/2024-03/01/2019

      From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

      Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
      The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-05.18.22

      Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.07.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Sam Bardwell-Evans, Boston University
      Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
      Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.
    • Algebraic Geometry in String Theory Seminar
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Flip processes
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1

      Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by  $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.

      Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).

      These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).

      We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
      A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Gabriel Wong 

      Title: Universal relations between entanglement, symmetries, and entropy

      Abstract: Entanglement is an essential property of quantum systems that distinguishes them from classical ones.   It is responsible for the nonlocal character of quantum information and provides a resource for quantum teleportation and quantum computation. In this talk I will provide an introduction to quantum entanglement and explain the essential role it plays in two seemingly unrelated subjects: implementation of measurement-based quantum computation and microstate counting of black holes in quantum gravity.   Time permitting, I will also discuss attempts to characterize entanglement in string theory. A unifying theme that illuminates the entanglement structure of these diverse systems is the role of surface symmetries and (entanglement) edge modes. We will explain how these universal aspects of entanglement are captured in the framework of extended topological quantum field theory.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Hypergraph Matchings Avoiding Forbidden Submatchings
      9:30 am-10:30 am
      12/01/2024

      Abstract:  In 1973, Erdős conjectured the existence of high girth (n,3,2)-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős’ conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős’ conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth (n,q,r)-Steiner systems. We prove the approximate version of their conjecture.  This result follows from our general main results which concern finding perfect or almost perfect matchings in a hypergraph G avoiding a given set of submatchings (which we view as a hypergraph H where V(H)=E(G)). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when H is a hypergraph with small codegrees (for which high girth designs is a specific instance). Indeed, the coloring version of our result even yields an almost partition of K_n^r into approximate high girth (n,q,r)-Steiner systems.  If time permits, I will explain some of the other applications of our main results such as to rainbow matchings.  This is joint work with Luke Postle.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.14.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Daniel Pomerleano, UMass Boston

      Title: Singularities of the quantum connection on a Fano variety

      Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty.

      I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M, D).

    • Member Seminar
      9:30 am-11:00 am
      12/01/2024

      Member Seminar

      Speaker: Juven Wang

      Title: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass

      Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1,2,3,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765arXiv:2204.08393arXiv:2202.13498 and references therein.

    • Colloquium
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Daniel Junghans

      Title: AdS with Scale Separation

      Abstract: I will talk about Anti-de Sitter solutions in string theory with a parametric separation between the AdS curvature scale and the Kaluza-Klein scale. In particular, I will discuss recent progress on computing backreaction corrections in such solutions, and I will explain how to construct solutions without Romans mass that can be lifted to M-theory.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.28.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Ahsan Khan, IAS

      Title: 2-Categories and the Massive 3d A-Model

      Abstract: I will outline the construction of a 2-category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two, and three dimensions combined with a three-dimensional version of the Gaiotto-Moore-Witten web formalism.

       

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-GR-Seminar-03.24.22

      Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Vitor Cardoso, IST, Lisbon and The Niels Bohr Institute, Copenhagen

      Title: Testing GR with GWs

      Abstract: One of the most remarkable possibilities of General Relativity concerns gravitational collapse to black holes, leaving behind a geometry with light rings, ergoregions and horizons. These peculiarities are responsible for uniqueness properties and energy extraction mechanisms that turn black holes into ideal laboratories of strong gravity, of particle physics (yes!) and of possible quantum-gravity effects. I will discuss some of the latest progress in tests of General Relativity with black holes.

    • Colloquium
    • Seminars
      Seminars Colloquia & Seminar
      4/18/2019 General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)
      3/2/2022Richard Kenyon (Yale University)
      3/9/2022Richard Tsai (UT Austin)
      3/23/2022Joel Cohen (University of Maryland)
      3/30/2022Rob Leigh (UIUC)
      4/6/2022Johannes Kleiner (LMU München)
      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
      4/20/2022TBA
      4/27/2022TBA
      5/4/2022Melody Chan (Brown University)
      5/11/2022TBA
      5/18/2022TBA
      5/25/2022Heeyeon Kim (Rutgers University)

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-03.17.2022-1-1544x2048-1

      Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)Title: Learning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

      3/2/2022Richard Kenyon (Yale University)Title: Dimers and webs

      Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

      This is joint work with Dan Douglas and Haolin Shi.

      3/9/2022Yen-Hsi Richard Tsai (UT Austin)Title: Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space

      Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

      3/23/2022Joel Cohen (University of Maryland)Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths

      Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

      3/30/2022Rob Leigh (UIUC)Title: Edge Modes and Gravity

      Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

      4/6/2022Johannes Kleiner (LMU München)Title: What is Mathematical Consciousness Science?

      Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)Title: Quantisation in monoidal categories and quantum operads

      Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure.  But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups.

      The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

      In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts

      4/27/2022Venkatesan Guruswami (UC Berkeley)Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

      Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.

      We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

      Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

      This is joint work with Xiaoyu He and Ray Li.

      5/18/2022 David Nelson (Harvard)TitleStatistical Mechanics of Mutilated Sheets and Shells

      Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-01.26.2022

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Yingying Wu

      Title: Moduli Space of Metric SUSY Graphs

      Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties, followed by a discussion on the connection with the classical case.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Dan Kapec

      Title: Black Holes, 2D Gravity, and Random Matrices

      Abstract: I will discuss old and new connections between black hole physics, 2D quantum gravity, and random matrix theory. Black holes are believed to be very complicated, strongly interacting quantum mechanical systems, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model, but this result raises more questions than it answers. If time permits, I will discuss some extensions of these results and possible future directions.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Cohomology of the moduli of Higgs bundles via positive characteristic
      9:30 am-8:30 pm
      12/01/2024

      Abstract: In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the character variety of the curve.  I will then explain how certain symmetries of this cohomology, which are predictions of this conjecture, can be constructed using techniques from non-abelian Hodge theory in positive characteristic.  Based on joint work with Mark de Cataldo, Junliang Shen, and Siqing Zhang.

    • Colloquium
    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.21.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Nicolo Piazzalunga, Rutgers

      Title: The index of M-theory

      Abstract: I’ll introduce the higher-rank Donaldson-Thomas theory for toric Calabi-Yau threefolds, within the setting of equivariant K-theory. I’ll present a factorization conjecture motivated by Physics. As a byproduct, I’ll discuss some novel properties of equivariant volumes, as well as their generalizations to the genus-zero Gromov-Witten theory of non-compact toric varieties.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The singularity probability of random symmetric matrices
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-12.07.2021

      Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-03.30.2022

      Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 12.08.22

      General Relativity Seminar

      Speaker: Allen Fang (Princeton)

      Title: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

      Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vector field techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-04.26.2022

      Abstract:   In “Mirror symmetry for log Calabi–Yau surfaces I,” given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y,D) with at worst du Val singularities. As a corollary, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 03.30.23

      General Relativity Seminar

      Speaker: Alejandra Castro (University of Cambridge)

      Title: Gravitational perturbations near to extreme Kerr

      Abstract: Gravitational perturbations of a black hole illustrate the invaluable synergy between theory, experiment, and numerical simulations in general relativity. A recent development in the theory side has been the identification of the relevant degrees of freedom describing the low energy physics driving a black hole away from extremality.  For simple cases, this low energy sector determines important aspects of the gravitational backreaction, and several properties that are key to our microscopic (quantum) understanding of black hole physics.
      In this talk I will discuss these developments in the context of the (near-)extreme Kerr black hole. In particular, I will revisit the spectrum of linear axisymmetric gravitational perturbations of this black hole. The aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. I will show that for Kerr the low-lying mode sector is subtle and intricate—features that their charged spherical symmetric cousins do not display. This unveils new clues on how to decode a microscopic, and holographic, understanding of the Kerr black hole.
    • Seminars
      Seminars Colloquia & Seminar
      8/4/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Sifan Yu, Vanderbilt University

      Title: Rough solutions of the relativistic Euler equations

      Abstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.

    • Seminars
      Seminars Colloquia & Seminar
      8/11/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/18/2020 Geometry and Physics Seminar
      9:30 am-11:30 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/19/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Conference
      9:30 am-5:00 pm
      12/01/2024-04/08/2022

      General Relativity Conference

      This conference will be held virtually on Zoom. Registration is required.
      Webinar Registration

      A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
      In-Person Registration

      Schedule | April 4–8, 2022

      Schedule (PDF)

      Monday, April 4, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amPieter Blue, University of Edinburgh, UK
      (virtual)
      Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge

      Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of the Einstein equation in this gauge, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975, Chrzanowski introduced the “outgoing radiation gauge”, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently, using a flow along null geodesics, we have constructed a new gauge such that, in this gauge, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge.

      This is joint work with Lars Andersson, Thomas Backdahl, and Siyuan Ma.

      10:30 am–11:30 amPeter Hintz, ETH Zürich
      (virtual)
      Title: Mode stability and shallow quasinormal modes of Kerr-de Sitter
      black holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe, such as our own, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question), mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which, depending on the scaling, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.
      11:30 am–12:30 pmLars Andersson, Albert Einstein Institute, Germany
      (virtual)
      Title: Gravitational instantons and special geometry

      Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

      12:30 pm–1:30 pmbreak
      1:30 pm–2:30 pmMartin Taylor, Imperial College London
      (virtual)
      Title: The nonlinear stability of the Schwarzschild family of black holes

      Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

      2:30 pm–3:30 pmPo-Ning Chen, University of California, Riverside
      (virtual)
      Title: Angular momentum in general relativity

      Abstract:
      The definition of angular momentum in general relativity has been a subtle issue since the 1960s, due to the ‘supertranslation ambiguity’. In this talk, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.
      3:30 pm–4:00 pmbreak
      4:00 pm–5:00 pmDan Lee, Queens College (CUNY)
      (hybrid: in person & virtual)
      Title: Stability of the positive mass theorem

      Abstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem, focusing on recent work with Kazaras and Khuri, in which we proved that if one assumes a lower Ricci curvature bound, then stability holds with respect to pointed Gromov-Hausdorff convergence.

       

      Tuesday, April 5, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amXinliang An, National University of Singapore
      (virtual)
      Title: Anisotropic dynamical horizons arising in gravitational collapse

      Abstract: Black holes are predicted by Einstein’s theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk, we will present several results in these directions. First, in a joint work with Qing Han, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second, in joint works with Dejan Gajic and Ruixiang Zhang, for the spherically symmetric Einstein-scalar field system, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism. If time permits, some results on fluid dynamics will also be addressed.

      10:30 am–11:30 amSergiu Klainerman, Princeton
      (virtual)
      Title: Nonlinear stability of slowly rotating Kerr solutions

      Abstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.

      11:30 am–12:30 pmSiyuan Ma, Sorbonne University
      (virtual)
      Title: Sharp decay for Teukolsky master equation

      Abstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmJonathan Luk, Stanford
      (virtual)
      Title: A tale of two tails

      Abstract: Motivated by the strong cosmic censorship conjecture, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).

      2:30 pm–3:30 pmGary Horowitz, University of California Santa Barbara
      (virtual)
      Title: A new type of extremal black hole

      Abstract: I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero, if quantum matter is added, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmLydia Bieri, University of Michigan
      (virtual)
      Title: Gravitational radiation in general spacetimes

      Abstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

       

      Wednesday, April 6, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amGerhard Huisken, Mathematisches Forschungsinstitut Oberwolfach
      (virtual)
      Title: Space-time versions of inverse mean curvature flow

      Abstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.

      10:30 am–11:30 amCarla Cederbaum, Universität Tübingen, Germany
      (virtual)
      Title: Coordinates are messy

      Abstract: Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M,g,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.

      11:30 am–12:30 pmStefanos Aretakis, University of Toronto
      (virtual)
      Title: Observational signatures for extremal black holes

      Abstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmJared Speck, Vanderbilt University
      (virtual)
      Title: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow

      Abstract: In the last two decades, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia, M. Disconzi, and J. Luk.

      2:30 pm–3:30 pmLan-Hsuan Huang, University of Connecticut
      (virtual)
      Title: Null perfect fluids, improvability of dominant energy scalar, and Bartnik mass minimizers

      Abstract: We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture.

      Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmDemetre Kazaras, Duke University
      (virtual)
      Title: Comparison geometry for scalar curvature and spacetime harmonic functions

      Abstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

       

      Thursday, April 7, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amPiotr Chrusciel, Universitat Wien
      (virtual)
      Title: Maskit gluing and hyperbolic mass

      Abstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.

      10:30 am–11:30 amGreg Galloway, University of Miami (virtual)Title:  Initial data rigidity and applications

      Abstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP, 2021), and look at some consequences.  In a note with Piotr Chruściel (CQG 2021), we showed how to use this result, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.

      11:30 am–12:30 pmPengzi Miao, University of Miami
      (virtual)
      Title: Some remarks on mass and quasi-local mass

      Abstract: In the first part of this talk, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello, and with H.C. Jang.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmYakov Shlapentokh Rothman, Princeton
      (hybrid: in person & virtual)
      Title: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations

      Abstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.

      2:30 pm–3:30 pmMarcelo Disconzi, Vanderbilt University
      (virtual)
      Title: General-relativistic viscous fluids.

      Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmMaxime van de Moortel, Princeton
      (hybrid: in person & virtual)
      Title: Black holes: the inside story of gravitational collapse

      Abstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models, the global structure of the black hole interior has largely remained unexplored.
      These questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.
      I will present my recent resolution of these problems in spherical gravitational collapse, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.

       

      Friday, April 8, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amYe-Kai Wang, National Cheng Kun University, Taiwan
      (virtual)
      Title: Supertranslation invariance of angular momentum at null infinity in double null gauge

      Abstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing
      how Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen, Jordan Keller, Mu-Tao Wang, and Shing-Tung Yau.

      10:30 am–11:30 amZoe Wyatt, King’s College London
      (virtual)
      Title: Global Stability of Spacetimes with Supersymmetric Compactifications

      Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in
      supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.

      11:30 am–12:30 pmElena Giorgi, Columbia University
      (hybrid: in person & virtual)
      Title: The stability of charged black holes

      Abstract: Black hole solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmMarcus Khuri, Stony Brook University
      (virtual)
      Title: The mass-angular momentum inequality for multiple black holes

      Abstract
      : Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected, axisymmetric, maximal, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain, Chrusciel-Li-Weinstein, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from
      R^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han, G. Weinstein, and J. Xiong.
      2:30 pm–3:30 pmMartin Lesourd, Harvard
      (hybrid: in person & virtual)
      Title:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature

      Abstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau, Prof. D. A. Lee, and R. Unger.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmGeorgios Moschidis, Princeton
      (virtual)
      Title: Weak turbulence for the Einstein–scalar field system.

      Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
      In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams.

    • Seminars
      Seminars Colloquia & Seminar
      8/20/2020 Quantum Matter
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/23/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      BCFW recursion relations and non-planar positive geometry
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-04.12.22-1583x2048-1

      Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.

      **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

      All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

      LINK TO FORM

    • Seminars
      Seminars Colloquia & Seminar
      8/25/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/26/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/27/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Special Seminar
      9:30 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Michael Douglas

      Title: Knowledge Graph Embeddings and Inference

      Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.
      A popular KG representation method is graph embedding, which facilitates question answering, inferring missing edges, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning, network learning, and unstructured statistical inference, and describe experiments to measure the contributions of each mechanism.

      Joint work with M. Simkin, O. Ben-Eliezer, T. Wu, S. P. Chin, T. V. Dang and A. Wood.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/30/2020 Condensed Matters Seminar
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/22/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker:An Huang

      Title: Quadratic reciprocity from a family of adelic conformal field theories

      Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories, and ensures that these Green’s functions satisfy an adelic product formula. In particular, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place, the desired holomorphic factorization follows from the global conformal symmetry.

    • Seminars
      Seminars Colloquia & Seminar
      6/24/2020 Quantum Matter Seminar
      9:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-02.10.2022-1544x2048-1

      Speaker: Mohamed Anber (Durham University)

      Title: The global structure of the Standard Model and new nonperturbative processes

      Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Matteo Parisi

      Title: Amplituhedra, Scattering Amplitudes and Triangulations

      Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

    • Geometry and Physics Seminar
      Geometry and Physics Seminar
      Geometry and Physics Seminar
      9:30 am-9:30 pm
      12/01/2024-12/22/2020
      unnamed-537x338

      During the summer of 2020, the CMSA will be hosting a new Geometry Seminar. Talks will be scheduled on Mondays at 9:30pm or Tuesdays at 9:30am, depending on the location of the speaker. This seminar is organized by Tsung-Ju Lee, Yoosik Kim, and Du Pei.

      To learn how to attend this seminar, please contact Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu).

      DateSpeakerTitle/Abstract
      6/2/2020
      9:30am ET
      Siu-Cheong Lau
      Boston University
      This meeting will be taking place virtually on Zoom.

      Speaker: Equivariant Floer theory and SYZ mirror symmetry

      Abstract: In this talk, we will first review a symplectic realization of the SYZ program and some of its applications. Then I will explain some recent works on equivariant Lagrangian Floer theory and disc potentials of immersed SYZ fibers. They are joint works with Hansol Hong, Yoosik Kim and Xiao Zheng.

      6/8/2020
      9:30pm ET
      Youngjin Bae (KIAS)This meeting will be taking place virtually on Zoom.

      TitleLegendrian graphs and their invariants

      Abstract: Legendrian graphs naturally appear in the study of Weinstein manifolds with a singular Lagrangian skeleton, and a tangle decomposition of Legendrian submanifolds. I will introduce various invariant of Legendrian graphs including DGA type, polynomial type, sheaf theoretic one, and their relationship. This is joint work with Byunghee An, and partially with Tamas Kalman and Tao Su.

      6/16/2020
      9:30am ET
      Michael McBreen (CMSA)This meeting will be taking place virtually on Zoom.

      Title: Loops in hypertoric varieties and symplectic duality

      Abstract: Hypertoric varieties are algebraic symplectic varieties associated to graphs, or more generally certain hyperplane arrangements. They make many appearances in modern geometric representation theory. I will discuss certain infinite dimensional or infinite type generalizations of hypertoric varieties which occur in the study of enumerative invariants, focusing on some elementary examples. Joint work with Artan Sheshmani and Shing-Tung Yau.

      6/22/2020
      9:30pm ET
      Ziming Ma (CUHK)This meeting will be taking place virtually on Zoom.

      Title: The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties

      Abstract: In this talk, we construct a \(dgBV algebra PV*(X)\) associated to a possibly degenerate Calabi–Yau variety X equipped with local thickening data. This gives a version of the Kodaira–Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi–Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi–Yau varieties X satisfying Hodge–deRham degeneracy property for cohomology of X, in the spirit of Kontsevich–Katzarkov–Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.

      6/30/2020
      9:30pm ET
      Sunghyuk Park (Caltech)This meeting will be taking place virtually on Zoom.

      Title: 3-manifolds, q-series, and topological strings

      Abstract: \(\hat{Z}\) is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients), which has interesting modular properties. While originally from physics, this invariant has been mathematically constructed for a big class of 3-manifolds, and conjecturally it can be extended to all 3-manifolds. In this talk, I will give a gentle introduction to \(\hat{Z}\) and what is known about it, as well as highlighting some recent developments, including the use of R-matrix, generalization to higher rank, large N-limit and interpretation as open topological string partition functions.

      7/7/2020
      9:30am ET
      Jeremy Lane  (McMaster University)This meeting will be taking place virtually on Zoom.

      TitleCollective integrable systems and global action-angle coordinates

      Abstract: A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates.  Moreover, the image of the moment map is a (non-simple) convex polytope.

      7/13/2020
      9:30pm ET
      Po-Shen Hsin (Caltech)This meeting will be taking place virtually on Zoom.

      TitleBerry phase in quantum field theory

      Abstract: We will discuss Berry phase in family of quantum field theories using effective field theory. The family is labelled by parameters which we promote to be spacetime-dependent sigma model background fields. The Berry phase is equivalent to Wess-Zumino-Witten action for the sigma model. We use Berry phase to study diabolic points in the phase diagram of the quantum field theory and discuss applications to deconfined quantum criticality and new tests for boson/fermion dualities in \((2+1)d\).

      7/20/2020
      9:30pm ET
      Sangwook Lee (KIAS)This meeting will be taking place virtually on Zoom.

      Title: A geometric construction of orbifold Jacobian algebras

      Abstract: We review the definition of a twisted Jacobian algebra of a Landau-Ginzburg orbifold due to Kaufmann et al. Then we construct an A-infinity algebra of a weakly unobstructed Lagrangian submanifold in a symplectic orbifold. We work on an elliptic orbifold sphere and see that above two algebras are isomorphic, and furthermore their structure constants are related by a modular identity which was used to prove the mirror symmetry of closed string pairings. This is a joint work with Cheol-Hyun Cho.

      7/27/2020 9:30pm ETMao Sheng (USTC)This meeting will be taking place virtually on Zoom.

      Title: Parabolic de Rham bundles: motivic vs periodic

      Abstract: Let \($C$\) be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over \($C$\) (with rational weights in parabolic structure). Many examples arise from geometry: let \($f: X\to U$\) be a smooth projective morphism over some nonempty Zariski open subset \($U\subset C$\). Then the Deligne–Iyer–Simpson canonical parabolic extension of the Gauss–Manin systems associated to \($f$\) provides such examples. We call a parabolic de Rham bundle \emph{motivic}, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory, to get a characterization of motivic parabolic de Rham bundles. In this talk, I introduce another subcategory of parabolic de Rham bundles, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan–Sheng–Zuo on Higgs-de Rham flows, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus–Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck–Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz’s work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture, we would like to single out the conjectural arithmetic Simpson correspondence, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.

      8/4/2020
      9:30am Et
      Pavel Safronov (University of Zurich)This meeting will be taking place virtually on Zoom.

      TitleKapustin–Witten TFT on 3-manifolds and skein modules

      Abstract: Kapustin and Witten have studied a one-parameter family of topological twists of \(4d N=4\) super Yang–Mills. They have shown that the categories of boundary conditions on a surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid–Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.

      8/11/2020
      9:30am
      Xujia Chen (Stonybrook)This meeting will be taking place virtually on Zoom.

      TitleLifting cobordisms and Kontsevich-type recursions for counts of real curves

      Abstract: Kontsevich’s recursion, proved in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger’s invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon’s recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon’s approach).

      8/18/2020
      9:30am ET
      Dongmin Gang (Asia Pacific Center for Theoretical Physics)This meeting will be taking place virtually on Zoom.

      Title: M-theoretic genesis of topological phases

      Abstract:  I will talk about a novel way of constructing \((2+1)d\) topological phases using M-theory. They emerge as macroscopic world-volume theories of M5-branes wrapped on non-hyperbolic 3-manifolds. After explaining the algorithm of extracting modular structures of the topological phase  from topological data of the 3-manifold, I will discuss the possibility of full classification of topological orders via the geometrical construction.

      8/25/2020
      9:30pm ET
      Mykola Dedushenko (Caltech)This meeting will be taking place virtually on Zoom.

      TitleAlgebras and traces at the boundary of \(4d N=4\) SYM

      Abstract: I will describe how the structure of supersymmetric boundary correlators in \(4d N=4\) SYM can be encoded in a class of associative algebras equipped with twisted traces. In the case of interfaces, this yields a new connection to integrability.

    • Seminars
      Seminars Colloquia & Seminar
      6/2/2020 Geometry Seminar
      9:30 am-10:30 am
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: In this talk, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian, over the torus fixed points, this representation is a Verma module. The vertex function, a K-theoretic enumerative invariant introduced by A. Okounkov, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application, this gives a proof of the invariance of the quantum q-difference module under variation of GIT.

    • Colloquium
      9:30 am-10:00 am
      12/01/2024

      Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Juven Wang

      Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model

      Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT), or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320.

      In the second part of my talk, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-02.17.2022-1544x2048

      Speaker: Andrea Grigoletto (SISSA & INFN)

      Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

      Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

    • Seminars
      Seminars Colloquia & Seminar
      6/25/2020 Condensed Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-04.06.2022

      Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

    • Seminars
      Seminars Colloquia & Seminar
      7/7/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-04.07.2022-1583x2048-1

      Youtube Video

       

      Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.

      References:
      [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021)
      [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022)
      [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation.
      [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Shahar Hadar (University of Haifa)

      Title: Resolving the photon ring

      Abstract: In the past few years, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes, M87* and SgrA*. It is believed that within these images is embedded a fine, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of strong lensing by the black hole and thereby conveys information on its spacetime geometry, potentially providing a new independent avenue for tests of general relativity in the strong-field regime. In the talk I will briefly review the theory of the photon ring and its corresponding spacetime region, the photon shell, which governs the universal lensing structure. I will then describe some current efforts and future prospects for resolving the ring, which include both the construction of transformative new instruments and the development of novel analysis methods. Focusing on the latter, I will present an upcoming proposal to use spectro-temporal autocorrelations in signals emitted from black hole environs as a probe of strong lensing effects.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024

      This is the Fall 2020 – Spring 2022 Quantum Matter in Mathematics and Physics Archive page.

      To view current seminars, please visit the Fall 2022-Spring 2023 Quantum Matter Seminar Page

      As part of the program on Quantum Matter in Mathematics and Physics, the CMSA hosted two weekly seminars. The Quantum Matter/Quantum Field Theory seminar took place on Wednesdays from 10:30 – 12:00pm on Zoom.

      The Condensed Matter/Math Seminar took place on  Thursdays from 10:30 – 12:00pm on Zoom.  In addition to the Quantum Matter seminar, the CMSA  also hosted a related seminar series on  Strongly Correlated Quantum Materials and High-Temperature Superconductors.

      Videos are available at the Quantum Matter in Mathematics and Physics  Youtube Playlist

      Spring 2022

      DateSpeakerTitle/Abstract
      1/18/2022
      2:30–4:00 pm ET
      Aavishkar Patel (UC Berkeley)Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

      Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

      Video

      1/28/2022 2:30–4:00 pm ETMaria Tikhanovskaya (Harvard)Title: Maximal quantum chaos of the critical Fermi surface

      Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

      2/2/2022
      8:00 -9:30 pm ET
      Yunqin Zheng (IPMU & ISSP, U Tokyo)Title: Kramers-Wannier-like duality defects in higher dimensions

      Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

      2/3/2022
      11:30 – 1:00 pm ET
      Lu Li (U Michigan)Title:  Quantum Oscillations of Electrical Resistivity in an Insulator

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

      2/9/2022
      8:00 –9:30 pm ET
      Yuji Tachikawa (Kavli IPMU, U Tokyo)Title: On the absence of global anomalies of heterotic string theories

      Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
      2/10/2022Mohamed Anber (Durham University)Title: The global structure of the Standard Model and new nonperturbative processes

      Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

      2/16/2022
      10:30 am–12:00 pm ET
      Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part I

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

      2/17/2022
      9:30–11:00 am ET
      Andrea Grigoletto (SISSA & INFN)Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

      Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

      2/23/2022
      10:30 am–12:00 pm ET
      Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part II

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

      2/24/2022
      8:00–9:30 pm ET
      Yohei Fuji (U Tokyo)Title: Bridging three-dimensional coupled-wire models and cellular topological states

      Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/1/2021Keisuke HarigayaTitle: Naturalness and muon anomalous magnetic moment

      Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

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      9/2/2021Joseph Maciejko (University of Alberta)Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

      Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

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      9/8/2021William Witczak-Krempa (U Montreal)Title: Cornering the universal shape of fluctuations and entanglement

      Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

      Ref: arXiv:2102.06223

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      9/9/2021Sung-Sik Lee (McMaster University, Perimeter Institute)Title: Quantum gravity from quantum matter

      Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

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      9/10/2021

      *special time: 3:30pm – 5:00pm ET*

      Ofri Telem (UC Berkeley)Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

      Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
      Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

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      9/15/2021Liang Fu (MIT)Title: Three-particle mechanism for pairing and superconductivity

      Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

      [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
      [2] V. Crepel and L. Fu, arXiv:2103.12060
      [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

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      9/16/2021Shiraz Minwalla (Tata Institute of Fundamental Research)Title: The Hilbert Space of large N Chern-Simons matter theories

      Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of  this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to  a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

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      9/17/2021

      *special time 3:30 pm- 5 pm ET*

      Eslam Khalaf (Harvard)Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

      Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

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      9/22/2021Daniel S Freed (U Texas)Title: Symmetry types in QFT and the CRT theorem

      Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

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      9/23/2021Edward Shuryak (Stony Brook University)Title: Applications of instantons, sphalerons and instanton-dyons in QCD

      Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

      Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

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      9/29/2021

      *special time 11:30 am- 1 pm ET*

      Nai Phuan Ong (Princeton University)Title: Oscillations in the thermal conductivity of a spin liquid*

      Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

      *Czajka et al., Nature Physics 17, 915 (2021).

      Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

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      10/06/2021Gabriel Cuomo (SCGP)Title: Line defects in CFTs: renormalization group flows and semiclassical limits

      Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

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      10/07/2021Ryan Thorngren (Harvard CMSA)Title: A tour of categorical symmetry

      Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

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      10/07/2021

      *special time 8:30 pm- 10 pm ET*

      Nima Arkani-Hamed (IAS Princeton)Title: UV/IR and Effective Field Theory

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      10/21/2021

      *special time 13:30 – 15:00 ET*

      Anton Kapustin (Caltech)Title: Electric-magnetic duality and the Geometric Langlands duality

      Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

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      10/22/2021

      *special time 10:30am – 12:00 noon ET*

      Netta Engelhardt (MIT)Title:  Recent Holographic Developments on the Black Hole Information Problem

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      10/29/2021

      *special time 2:15pm – 3:45pm ET*

      Eric Sharpe (Virginia Tech)Title: Anomaly resolution via decomposition

      Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

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      10/29/2021

      *special time 4:00pm – 5:30pm*

      Biao Lian (Princeton)Title: Integrability and chaos of 1+1d chiral edge states

      Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

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      11/03/2021
      *special time 2:00pm – 3:30pm ET*
      Clay Cordova (U Chicago)Title: Non-Invertible Duality Defects in 3+1 Dimensions

      Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

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      11/04/2021Yifan Wang (NYU)Title: Fusion Category Symmetries in Quantum Field Theory

      Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

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      11/10/21
      *special time 10–11:30 am ET*
      Michael Stone (UIUC)Title: Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT

      Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature.  I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.

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      11/12/21
      *special time 2:30–4:00 pm ET*
      Jeongwan Haah (Microsoft)Title: A degeneracy bound for homogeneous topological order

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      11/16/21
      *special time 3–4:30 pm ET*
      Jie Wang
      (Center for Computational Quantum Physics, Flatiron Institute, Simons Foundation)
      Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

      Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

      [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
      [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
      [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

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      11/18/2021 2:30–4:00 pm ETB. Andrei Bernevig (Princeton University)Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

      Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

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      11/24/21Shinsei Ryu (Princeton University)Title: Multipartitioning topological phases and quantum entanglement

      Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

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      12/1/21
      10:00–11:30 am ET
      Daniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 1

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
      12/2/21 10:30–12:00 pm ETDaniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 2

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

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      12/8/21 10:30–12:00 pm ETFei Yan (Rutgers)Title: Defects, link invariants and exact WKB

      Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

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      12/10/21 2:30–4:00 pm ETLukasz Fidkowski (U Washington)Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

      Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

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      Summer 2021:

      DateSpeakerTitle/Abstract
      6/2/2021Juven Wang (Harvard CMSA)

      Video

      TitleUltra Unification:
      Quantum Fields Beyond the Standard Model
      Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
      6/3/2021Tian Lan (CUHK & U Waterloo)

      Video

      TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

      Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
      6/9/2021Yizhi You (Princeton U)

      Video

      TitleFracton critical point and Topological phase transition beyond renormalization

      Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
      6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)

      Video

      TitleMinimal nondegenerate extensions and an anomaly indicator

      Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

      6/16/2021Arkady Vainshtein (UMN)

      Video

      TitleUses of Wilson Operator Expansion in Gauge Theories

      Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

      It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

      6/17/2021Mikhail Shifman (UMN)

      Video

      TitleWhat can supersymmetry do that other field theory cannot
      7/7/2021Dung Nguyen (Brown)

      Video

      TitleFrom Fractional Quantum Hall to higher rank symmetry

      Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of  W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems.  Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
      7/8/2021

      8:00 – 9:30pm

      Jing-Yuan Chen (Tsinghua)

      Video

      TitleSolvable Lattice Hamiltonians with Fractional Hall Conductivity

      Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]

      7/14/2021Liujun Zou (Perimeter Institute)

      Video

      TitleStiefel liquids: Possible non-Lagrangian quantum criticality from intertwined orders

      Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.

      Ref: arXiv: 2101.07805.

      7/15/2021Nathanan Tantivasadakarn (Harvard)

      Video

      TitleHybrid Fracton Orders

      Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

      Based on 2102.09555 and 2106.03842

      7/21/2021Daniel Bulmash (UMD)TitleAnomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs

      Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.

      Ref: arXiv:2104.14567

      7/22/2021
      8:00pm ET
      Hong Yao (Tsinghua)TitleEmergent spacetime supersymmetry in topological phases of matter

      Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators.
      References:
      [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015)
      [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017)
      [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017)
      [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)

      7/28/2021Max Metlitski (MIT)Title: Boundary criticality of the O(N) model in d = 3 critically revisited.

      Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry.
      Based on arXiv:2009.05119.

      7/29/2021Ady Stern & David Mross (Weizmann)TitleThe nu=5/2 enigma: Recent insights from theory and experiment

      Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

      8/4/2021Nathan Benjamin (Princeton & Caltech)Title: Harmonic analysis of 2d CFT partition functions

      Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.

      8/5/2021Hans-Werner Hammer (TU Darmstadt)Title: Un-nuclear physics: conformal symmetry in nuclear reactions

      Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.

      8/11/2021Piers Coleman (Rutgers)Title: Order Fractionalization*

      Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

      8/12/2012Beni Yoshida (Perimeter Institute)Title: On the firewall puzzle

      Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.

      8/18/2021Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics
      Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
      8/19/2021Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)Title: “Probing the Standard Model of Particle Physics Using the Muon
      Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
      8/25/2021Hitoshi Murayama  (UC Berkely & IPMU)Title: Some Exact Results in QCD-like and Chiral Gauge Theories

      Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/20/2021Thomas Peter Devereaux (Stanford University)

      Video

      Title:  Numerical investigations of models of the cuprates

      Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

      I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

      1/21/2021
      8:30-10:00pm ET
      Masahito Yamazaki (IPMU)

      Video

      TitleConfinement as Analytic Continuation Beyond Infinity
      1/27/2021Luigi Tizzano  (SCGP)

      Video

      TitleInstantons, symmetries and anomalies in five dimensions

      Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

      1/28/2021Simon Catterall (Syracuse University)

      Video

      TitleChiral Fermions from Staggered Fields

      Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.

      2/3/2020Philip Phillips (University of Illinois Urbana-Champaign)

      Video

      TitleBeyond BCS: An Exact Model for Superconductivity and Mottness

      Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
      [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

      2/4/2021Diego Delmastro (Perimeter PI)

      Video

      Title: Domain Walls in 4d N=1 Supersymmetric Yang-Mills

      Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).

      2/10/2021Senthil Todadri (MIT)

      Video

      TitleStrange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

      Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.

      [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789
      [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

      2/11/2021Michael Hermele (University of Colorado Boulder)

      Video

      TitleFamilies of gapped systems and quantum pumps

      Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.

      2/17/2021Jaume Gomis (Perimeter PI)

      Video

      TitleGlobal Anomalies on the Hilbert Space

      Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

      2/18/2021Xiao-Gang Wen (MIT)

      Video

      TitleA solution to the chiral fermion problem

      Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

      2/24/2021Zhenghan Wang (Microsoft Station Q)

      Video

      Title:  A Riemann sum of quantum field theory:  lattice Hamiltonian realization of TQFTs

      Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics.  I will start with the conceptual origin of this model as requested by the organizer.  Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds.  In the end, I will mention lattice models that generalize the Haah codes in two directions:  general three manifolds and more than two qubits per site.

      If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum.  New lattice models in fracton physics raise an interesting question:  what kinds of quantum field theories are they approximating if their continuous limits exist?  Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.

      2/25/2021Justin Kaidi (SCGP)

      Video

      TitleExploring Non-Supersymmetric String Theory

      Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.

      3/3/2021Tim Hsieh (Perimeter PI)

      Video

      Title: Symmetry-protected sign problem and magic in quantum phases of matter

      Abstract:  We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
      3/4/2021Mohamed Anber (Clark University)

      Video

      TitleGeneralized ‘t Hooft anomalies in vector-like theories

      Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories.  Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics.  In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls.  This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.

      3/10/2021

      7:30pm ET

      Satoshi Yamaguchi (Osaka U)

      Video

      TitleSupersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases

      Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.

      3/11/2021Chao-Ming Jian (Cornell)

      Video

      Title: Entanglement Criticality in Random Gaussian Quantum Circuits

      Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.

      3/17/2021Silviu S. Pufu (Princeton)

      Video

      Title:  Exact symmetries and threshold states in two-dimensional models for QCD

      Abstract:  Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

      3/18/2021
      12:00 – 1:30pm ET
      Thomas Dumitrescu (UCLA)

      Video

      Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD

      Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint

      3/24/2021Emily Nardoni (UCLA)

      Video

      Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD: Part 2

      Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.

      3/25/2021Michael Levin (U Chicago)

      Video

      TitleAn introduction to string-net models

      Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.

      3/31/2021Dam Thanh Son (U Chicago)

      Video

      TitleSpin of the fractional quantum Hall magnetoroton through polarized Raman scattering

      Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.

      4/1/2021

      9:00am ET

      Naoto Nagaosa (Tokyo U.)

      Video

      Title: Applied physics of high-Tc theories

      Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

      4/7/2021Sakura Schafer-Nameki (University of Oxford)

      Video

      Title: Higher Form Symmetries in string/M-theory

      Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.

      4/8/2020

      1:00pm ET

      Anton Kapustin (Caltech)

      Video

      TitleChiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics
      Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
      4/14/2021Lakshya Bhardwaj (University of Oxford)

      Video

      TitleConfinement and 1-form Symmetries in 4d from 6d (2,0)

      Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
      4/15/2021Michael Creutz (Brookhaven National Laboratory)

      Video

      TitleQCD without diagrams

      Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.

      4/21/2021Sergei Gukov (Caltech)

      Video

      TitleExotic new animals in the CFT zoo: quasiparticles and anisotropic scaling
      4/22/2021Dung-Hai Lee (UC Berkeley)

      Video

      Title Non-abelian bosonization in two and three spatial dimensions and some applications
      Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
      4/28/2021Dominic Williamson (Stanford)

      Video

      Title1-form symmetry-protected topological phases and measurement-based quantum computation

      Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
      4/29/2021Fiona Burnell (University of Minnesota)

      Video

      TitleSubsystem-Symmetry protected phases of matter

      Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter.  These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states.  After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries.  I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.

      5/5/2021

      8:00pm ET

      Ioannis Papadimitriou (KIAS)

      Video

      TitleAnomalies and Supersymmetry

      Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.

      5/6/2021Weslei Bernardino Fontana (Boston University & Estadual)

      Video

      TitleChern-Simons-like theories for fracton phases

      Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.

      5/12/2021André-Marie Tremblay (University of Sherbrooke)

      Video

      Title: A unified theoretical perspective on the cuprate phase diagram

      Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

      5/13/2021Masataka Watanabe (Weizmann Institute of Science)

      Video

      TitleQuantum Information Theory of the Gravitational Anomaly

      Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].

      5/19/2021Herbert Neuberger (Rutgers)

      Video

      Title:  Construction of Lattice Chiral Gauge Theory

      Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided.
      The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.

      5/20/2021Steven Weinberg (UT Austin)

      Video

      TitleMassless Particles
      6/2/2021Juven Wang (Harvard CMSA)

      Video

      TitleUltra Unification:
      Quantum Fields Beyond the Standard Model
      Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
      6/3/2021Tian Lan (CUHK & U Waterloo)TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

      Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
      6/9/2021Yizhi You (Princeton U)TitleFracton critical point and Topological phase transition beyond renormalization

      Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
      6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)TitleMinimal nondegenerate extensions and an anomaly indicator

      Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

      6/16/2021Arkady Vainshtein (UMN)TitleUses of Wilson Operator Expansion in Gauge Theories

      Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

      It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

      6/17/2021Mikhail Shifman (UMN)TitleWhat can supersymmetry do that other field theory cannot
      8/11/2021Piers Coleman (Rutgers)TBA
      8/26/2021Daniel Harlow (MIT)Title: Symmetries in quantum field theory and quantum gravity
      TBAAdy Stern & David Mross (Weizmann)TBA

      Fall 2020:

      DateSpeakerTitle/Abstract
      9/2/2020Subir Sachdev (Harvard University)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

      Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
      describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

      9/3/2020
      9:30 – 11:00am
      Janet Ling Yan Hung (Fudan University)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleGapped Boundaries, Junctions via (fermionic) anyon condensation

      Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.

      9/9/2020Ying-Hsuan Lin (Caltech)

      Video

      This meeting will be taking place virtually on Zoom.

      Title:  Exotic Consistent (1+1)d Anomalies: A Ghost Story

      Abstract:  We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions.  On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm.  For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection.  Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines.  The holomorphic bc ghost system realizes all the exotic consistent anomalies.

      9/10/2020Maissam Barkeshli (Maryland)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleAbsolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions

      Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553

      9/16/2020Andreas Karch (UT Austin)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleBranes, Black Holes and Islands

      Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.

      9/17/2020Roger Mong (University of Pittsburgh)

      Video

      TitleUniversal multipartite entanglement in quantum spin chains

      Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems.  Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations.  Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment.  The measures are based off of the entanglement of purification and the reflected entropy popular among holography.  For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases.  We conclude with a few remarks regarding applications to 2D phases.

      9/23/2020Subir Sachdev (Harvard University)

      Video

      TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders II

      Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

      9/24/2020
      12:00 – 2:30pm ET
      Inna Vishik (University of California, Davis)

      Video

      TitleUniversality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201

      Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.

      9/30/2020Jordan Cotler (Harvard)

      Video

      Title: Gravitational Constrained Instantons and Random Matrix Theory

      Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action.  We find these instantons in all spacetime dimensions, for AdS and dS.  Many can be written in closed form and are quadratically stable.  In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes.  We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.

      10/1/2020Omri Golan (Weizmann Institute of Science)

      Video

      Title: Intrinsic sign problems in topological matter

      Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions.  Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.

      10/7/2020Romain Vasseur (UMass Amherst)

      Video

      Title“Symmetry-enriched random critical points and topological phase transitions“

      Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.

      10/8/2020Justin Kulp (Perimeter Institute)

      Video

      TitleOrbifold Groupoids

      Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
      10/14/2020Yin-Chen He (Perimeter Institute)

      Video

      TitleNon-Wilson-Fisher Kinks of Conformal Bootstrap: Deconfined Phase Transition and Beyond

      Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.

      10/15/2020Louis Taillefer (University of Sherbrooke)

      Video

      TitleNew signatures of the pseudogap phase of cuprate superconductors

      Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

      10/21/2020Oleg Dubinkin (University of Illinois at Urbana–Champaign)

      Video

      Title: Multipole Insulators and Higher-Form symmetries

      Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.

      10/22/2020Paul Fendley (University of Oxford)

      Video

      TitleThe uses of lattice topological defects

      Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains.
      These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion.  One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.  I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.

      10/28/2020Patrick Lee (MIT)

      Video

      Title: The not-so-normal normal state of underdoped Cuprate

      Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

      10/29/2020Biao Lian (Princeton University)

      Video

      TitleSymmetry, Insulating States and Excitations of Twisted Bilayer Graphene with Coulomb Interaction

      Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.

      11/5/2020Zohar Ringel (Racah Institute of Physics)TitleThe information bottleneck: A numerical microscope for order parameters.

      Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.

      11/6/2020
      12:30pm
      Zhi-Xun Shen (Stanford University)

      Video

      TitleEssential Ingredients for Superconductivity in Cupper Oxide Superconductors

      Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
      Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
      magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
      (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
      experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

      [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
      [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
      [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
      [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
      [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
      [6] A. Lanzara et al., Nature 412, 510 (2001)
      [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
      [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
      [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
      [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
      [11] A.G. Loeser et al., Science 273, 325 (1996)
      [12] S. Chen et al., Science, 366, 6469 (2019)
      [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
      [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
      [15] Yu He et al., Science, 362, 62 (Oct. 2018)
      [16] Z. Chen, Y. Wang et al., preprint, 2020

      11/11/2020Abhishodh Prakash (ICTS)

      Video

      TitleAspects of fermionic SPT phases: boundary supersymmetry and unwinding

      Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
      11/12/2020Chandra Varma (University of California, Riverside)

      Video

      TitleLoop-Current Order and Quantum-Criticality in Cuprates

      This talk is organized as follows:
      1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
      2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
      3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
      4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.

      Time permitting,
      (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
      (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
      (iii) Problems.

      11/18/2020Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

      Video

      Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

      Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

      11/19/2020Eduardo Fradkin (University of Illinois at Urbana-Champaign)

      Video

      TitlePair Density Waves and Intertwined Orders in High Tc Superconductors

      Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

      11/25/2020Qimiao Si (Rice University)

      Video

      Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

      Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

      12/2/2020Andrey Chubukov (University of Minnesota)

      Video

      TitleInterplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

      Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

      12/3/2020David B. Kaplan  (University of Washington)

      Video

      Title: Domain Wall Fermions and Chiral Gauge theories: Topological Insulators in Particle Physics

      Abstract:  Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics.  I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter.  How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!)  remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
      12/9/2020David Hsieh (Caltech)

      Video

      Title:  Signatures of anomalous symmetry breaking in the cuprates 

      Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
      [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

      [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516
      .

      12/10/2020Xinan Zhou (Princeton PCTS)

      Video

      Title: An analytic bootstrap approach for CFTs on RP^d and CFTs with boundaries

      Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
      12/16/2020Zheng-Yu Weng (Tsinghua University)

      Video

      TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

      Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

      12/17/2020Steven Kivelson (Stanford University)

      Video

      Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

      Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
      12/22/2020David Tong (University of Cambridge)

      Video

      TitleGapped Chiral Fermions

      Abstract: I’ll describe some quantum field theories that gap fermions without breaking chiral symmetries.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-04.13.22

      Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure. But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

      In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

      3/2/2022Richard Kenyon (Yale University)
      3/9/2022Richard Tsai (UT Austin)
      3/23/2022Joel Cohen (University of Maryland)
      3/30/2022Rob Leigh (UIUC)
      4/6/2022Johannes Kleiner (LMU München)
      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
      4/20/2022TBA
      4/27/2022TBA
      5/4/2022Melody Chan (Brown University)
      5/11/2022TBA
      5/18/2022TBA
      5/25/2022Heeyeon Kim (Rutgers University)

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024

      Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

      April 20, 2022 | 9:30 – 11:00 am ET

      Title: Mechanism Design

      Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

      Talk chairs: Scott Kominers, Sergiy Verstyuk

      SLIDES | VIDEO

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. Higgs-Coulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wall-crossing results for GLSM and generalizes Landau- Ginzburg/Calabi-Yau correspondence. The talk is based on a joint work in progress with Melissa Liu.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-03.02.2022

      Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

      This is joint work with Dan Douglas and Haolin Shi.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Title: Stable Big Bang formation for the Einstein equations

      Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Itamar Shamir

      Title: Geometry, Entanglement and Quasi Local Data

      Abstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Tropical Lagrangian multi-sections and locally free sheaves
      9:30 am-10:30 am
      12/01/2024

      Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-03.03.2022-1544x2048-1

      Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138

      Member Seminar

      Speaker: Martin Lesourd

      Title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds

      Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, and Prof. D. A. Lee.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Some combinatorics of Wilson loop diagrams
      9:30 am-10:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands.

      **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

      All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

      LINK TO FORM

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 02.03.23

      General Relativity Seminar

      Speaker: Chiara Toldo (Harvard)

      Title: Near extremal de Sitter black holes and JT gravity

      Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

    • Quantum Matter
      9:30 am-10:30 am
      12/01/2024
      CMSA QMMP 1.30.23

      Quantum Matter Seminar

      Title: Group Invariant States as Many-Body Scars

      Speaker: Igor R. Klebanov (Princeton University)

      Abstract: Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies.  The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

       

      https://www.youtube.com/watch?v=O4xizOTzpL4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=18

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024

      Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

      April 22, 2022 | 9:30 – 11:00 am ET

      Title: Auction Theory

      Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

      Talk chairs: Scott Kominers, Sergiy Verstyuk

      SLIDES | VIDEO Answers to Questions from Talks 2 and 3

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Prashant Kocherlakota (BHI)

      Title: Testing spacetime geometry with images of supermassive compact objects: Current status and the future

      Abstract: Astrophysical black holes (BHs) are expected to be described by the Kerr solution of the Einstein equations. Several frameworks have recently been developed to parametrically deform the Kerr metric in significantly different ways, to enable formulations of tests of the no-hair theorems. Testing the viability status of alternative models – such as non-Kerr BHs from general relativity, BHs from alternative theories, wormholes, and other exotic objects – as descriptors of astrophysical objects has been of longstanding interest. The Event Horizon Telescope (EHT) recently imaged Sagittarius A* (Sgr A*), the supermassive compact object at the center of the Galaxy, making such tests possible. In such tests, the shadow critical curve (or simply shadow boundary), defined on the observer’s image plane, has gained prominence as the observable of interest. We will discuss how the EHT is able to extract information regarding the shadow of Sgr A* and the status of associated tests of the spacetime geometry in the strong-field regime. Future imaging measurements expect to detect the so-called photon ring, a strong-gravitational lensing feature that appears in the close vicinity of the critical curve, which houses higher-order images of the emission source. Time permitting, we will also discuss how these can be used to set up more stringent tests of the spacetime metric and gravity in the future.

       

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Strominger-Yau-Zaslow conjecture is one of the guiding principles in mirror symmetry, which not only predicts the geometric structures of Calabi-Yau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricci-flat metrics. In this talk, we will explain how SYZ fibrations on log Calabi-Yau surfaces detect the non-standard semi-flat metric which generalized the semi-flat metrics of Greene-Shapere-Vafa-Yau. Furthermore, we will use the SYZ fibration on log Calabi-Yau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Dan Lee

      Title: Survey on stability of the positive mass theorem

      Abstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk, I will discuss various results related to this question.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The longest induced path in a sparse random graph
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-12.14.2021

      Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Speaker: Du Pei

      Title: Wall-crossing from Higgs bundles to vortices

      Abstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks.  In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.

    • Combinatorics Physics and Probability
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-11.30.2021

      Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
      In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
      Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
      This work was done in collaboration with Renaud Lambiotte.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-04.19.2022

      Abstract:  In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong.

      In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

    • Combinatorics Physics and Probability
      9:30 am-10:30 am
      12/01/2024

      Speaker: Nima Arkani-Hamed, IAS

      Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

      3/2/2022Richard Kenyon (Yale University)
      3/9/2022Richard Tsai (UT Austin)
      3/23/2022Joel Cohen (University of Maryland)
      3/30/2022Rob Leigh (UIUC)
      4/6/2022Johannes Kleiner (LMU München)
      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
      4/20/2022TBA
      4/27/2022TBA
      5/4/2022Melody Chan (Brown University)
      5/11/2022TBA
      5/18/2022TBA
      5/25/2022Heeyeon Kim (Rutgers University)

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures.

      The talk is partially based on joint works with Si Li.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Puskar Mondal

      Title: Stability and convergence issues in mathematical cosmology

      Abstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized, one needs to study its stability properties. Therefore, I will briefly discuss the stability issue and its consequences (e.g., structure formation, etc).

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-02.01.2022

      Abstract: We will consider the following problem: if (C,x_1,…,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,…,y_n, then how many maps f:C -> X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory, the answer may be expressed in terms of the quantum cohomology of X, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle, though in the presence of sufficient positivity, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem, including joint work with Farkas, Pandharipande, and Cela, as well as work of other authors.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 03.09.23

      General Relativity Seminar

      Speaker: Jose Luis Jaramillo (Bourgogne U.)

      Title: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture

      Abstract: Can we measure the ‘effective regularity’ of spacetime from the perturbation of quasi-normal mode (QNM) overtones? Black hole (BH) QNMs encode the resonant response of black holes under linear perturbations, their associated complex frequencies providing an invariant probe into the background spacetime geometry. In the late nineties, Nollert and Price found evidence of a BH QNM instability phenomenon, according to which perturbed QNMs of Schwarzschild spacetime migrate to new perturbed branches of different qualitative behaviour and asymptotics. Here we revisit this BH QNM instability issue by adopting a pseudospectrum approach. Specifically, we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator by adopting a hyperboloidal formulation of spacetime. Non-selfadjoint (more generally non-normal) operators suffer potentially of spectral instabilities, the notion of pseudospectrum providing a tool suitable for their study. We find evidence that perturbed Nollert & Price BH QNMs track the pseudospectrum contour lines, therefore probing the analytic structure of the resolvent, showing the following (in)stability behaviour: i) the slowest decaying (fundamental) mode is stable, whereas ii) (all) QNM overtones are ultraviolet unstable (for sufficiently high frequency). Building on recent work characterizing Burnett’s conjecture as a low-regularity problem in general relativity, we conjecture that (in the infinite-frequency limit) generic ultraviolet spacetime perturbations make BH QNMs migrate to ‘Regge QNM branches’ with a precise universal logarithmic pattern. This is a classical general relativity (effective) low-regularity phenomenon, agnostic to possible detailed (quantum) descriptions of gravity at higher-energies and potentially observationally accessible.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Jue Liu

      Title: Instability of naked singularities in general relativity

      Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, which are called by naked singularities, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method, and it is this wild method that helps us to extend some results to the asymmetric cases.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 02.23.23

      General Relativity Seminar

      Speaker: Nikolaos Athanasiou (University of Crete, Greece)

      Title: Formation of trapped surfaces in the Einstein-Yang-Mills system

      Abstract: The purpose of this talk is to give an overview of a semi-global existence result and a trapped surface formation results in the context of the Einstein-Yang-Mills system. Adopting a “signature for decay rates” approach first introduced by An, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yield the desired semi-global existence result. Once semi-global existence has been established, we will explain how the formation of a trapped surface follows from a standard ODE argument. This is joint work with Puskar Mondal and Shing-Tung Yau.

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024

      Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

      April 18, 2022 | 9:30 – 11:00 am ET

      Title: Game Theory Basics and Classical Existence Theorems

      Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

      Talk chairs: Scott Kominers, Sergiy Verstyuk

      SLIDES | VIDEO

       

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-Seminar-04.14.22-1583x2048-1

      Youtube video

       

      Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields.  Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos.  Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).

      As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role.  Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times.  Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime.  This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole).  It also makes a number of testable predictions.

      (Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Title: On the Observable Shape of Black Hole Photon Rings

      Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

    • Special Seminar
      9:50 am-10:50 am
      12/01/2024-04/26/2016

      The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

      DayNameTitle
      09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
      09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
      09-22-2015Teng FeiSome new solutions to the Strominger system
      09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
      10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
      10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
      10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
      10-27-2015Tom IlmanenFlow of curves by curvature in R^n
      11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
      11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
      11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
      11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
      12-01-2015Tom Ilmanen
      01-26-2016Mao ShengUniformization of p-adic curves
      02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
      02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
      02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
      02-23-2016Junbin LiConstruction of black hole formation spacetimes
      03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
      03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
      03-15-2016Spring Break 
      03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
      03-29-2016Piotr ChruscielMass of characteristic surfaces
      04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
      04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
      04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
      04-26-2016Andre NevesA path to Yau’s conjecture
    • Seminars
      9:50 am-10:50 am
      12/01/2024

      The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

      DateNameTitle
      09-03-2015Long JinScattering Resonances for Convex Obstacles
      09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
      09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
      09-24-2015Felix FinsterCausal fermion systems and the causal action principle
      10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
      10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
      10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
      10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
      10-29-2015Pin YuShock formations for 3 dimensional wave equations
      11-05-2015No talk 
      11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
      11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
      11-26-2015ThanksgivingNo seminar
      12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
      01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
      02-04-2016Pranav PanditCategorical Kähler Geometry
      02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
      02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
      02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
      03-03-2016Piotr ChruscielSingularities in general relativity
      03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
      03-17-2016Spring BreakNo Talk
      03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
      03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
      04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
      04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
      04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
      04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
      05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
      05-12-2016Stefano Bianchini
    • General Relativity Seminar
      10:00 am-11:00 am
      12/01/2024

      Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

    • Workshop
      10:00 am-5:00 pm
      12/01/2024-05/08/2022

      On May 6–8, 2022, the CMSA  hosted a second NSF FRG Workshop.

      This project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology), Computer Science (Scientific Computing and Complexity Theory), and domain sciences, from Data Sciences to Computational Biology.

      Scientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time, however, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing, searching, simulating, analyzing, and comparing shapes. These methods and tools can be applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition, and satellite image analysis.

      This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

      The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.


      Workshop on Discrete Shapes
      May 6–8, 2022

      Organizers:

      • David Glickenstein (University of Arizona)
      • Joel Hass (University of California, Davis)
      • Patrice Koehl (University of California, Davis)
      • Feng Luo (Rutgers University, New Brunswick)
      • Maria Trnkova (University of California, Davis)
      • Shing-Tung Yau (Harvard)

      Speakers:

      • Miri Ben-Chen (Technion)
      • Alexander Bobenko (TU Berlin)
      • John Bowers (James Madison)
      • Steven Gortler (Harvard)
      • David Gu (Stony Brook)
      • Anil Hirani (UIUC)
      • Yanwen Luo (Rutgers)
      • Peter Schroeder (Caltech)
      • Justin Solomon (MIT)
      • Tianqi Wu (Clark University)

      Contributed Talk Speakers:

      • Oded Stein (MIT)
      • Bohan Zhou (Dartmouth)

      Schedule
      Schedule (PDF)

      Friday, May 6, 2022

      10:00–10:05 amWelcome Opening
      10:05–10:55 amAnil N. HiraniTitle: Discrete vector bundles with connection

      Abstract: We have recently initiated a generalization of discrete exterior calculus to differential forms with values in a vector bundle. A discrete vector bundle with connection over a simplicial complex has fibers at vertices and transport maps on edges, just as in lattice gauge theory. The first part of this work involves defining and examining properties of a combinatorial exterior covariant derivative and wedge product. We find that these operators commute with pullback under simplicial maps of the base space. From these definitions emerges a combinatorial curvature. In the second part of this work we showed that the curvature behaves as one expects: it measures failure of parallel transport to be independent of the path, and is the local obstruction to a trivialization. For a bundle with metric, metric compatibility of the discrete connection is equivalent to a Leibniz rule.  Vanishing curvature is indeed equivalent to an appropriately defined discrete flat connection, and curvature obstructs trivializability. In this talk I will focus on just the first part, and talk about naturality of the discrete exterior covariant derivative and discrete wedge product using simple examples. Joint work with Daniel Berwick-Evans (UIUC) and Mark Schubel (Apple, Inc.).

      11:10–12:00 pmDavid GuTitle: Surface Quadrilateral Meshing Based on Abel-Jacobi Theory

      Abstract: Surface quadrilateral meshing plays an important role in many fields. For example, in CAD (computer-aided design), all shapes are represented as Spline surfaces, which requires structured quad-meshing; in CAE (computer-aided engineering), the surface tessellation greatly affects the accuracy and efficiency of numerical simulations. Although the research on mesh generation has a long history, it remains a great challenge to automatically generate structured quad-meshes with high qualities. The key is to find the governing equation for the singularities of the global structured quad-meshes.

      In this talk, we introduce our recent discovery:  the singularities of a quad-mesh are governed by the Abel theorem. We show that each quad-mesh determines a conformal structure and a meromorphic quadratic differential, the configuration of the mesh singularities can be described as the divisor of the differential. The quad-mesh divisor minus four times of the divisor of a holomorphic one-form is principal and satisfies the Abel theorem: its image under the Jacobi map is zero in the Jacobi variety.

      This leads to a rigorous and efficient algorithm for surface structured quadrilateral meshing. After determining the singularities, the metric induced by the quad-mesh can be computed using the discrete Yambe flow, and the meromorphic quartic differential can be constructed, the trajectories of the differentials give the quad-mesh. The method can be applied directly for geometric modeling and computational mechanics.

      12:00–2:00 pmLunch Break
      2:00–2:50 pm Justin SolomonTitle:  Geometry Processing with Volumes

      Abstract:  Many algorithms in geometry processing are restricted to two-dimensional surfaces represented as triangle meshes.  Drawing inspiration from simulation, medical imaging, and other application domains, however, there is a substantial demand for geometry processing algorithms targeted to volumes represented as tetrahedral meshes or grids.  In this talk, I will summarize some efforts in our group to develop a geometry processing toolkit specifically for volumes.  Specifically, I will cover our recent work on hexahedral remeshing via cuboid decomposition, volumetric correspondence, and minimal surface computation via geometric measure theory.

      3:00–3:20 pmOded SteinTitle: Optimization for flip-free parametrization

      Abstract: Parametrizations without flipped elements are desirable in a variety of applications such as UV mapping and surface/volume correspondence. Computing flip-free parametrizations can be challenging, and there are many different approaches to the problem. In this talk we will look at multiple strategies for flip-free parametrizations that are based on the optimization of continuous energies. Due to the nature of the problem, these energies are often nonconvex and unbounded, which is a challenge for optimization methods. We will also take a closer look at our recently developed method for computing flip-free parametrizations using the Alternating Direction Method of Multipliers (ADMM).

      3:20–4:00 pmBreak
      4:00–4:50 pmJohn BowersTitle: Koebe-Andre’ev-Thurston Packings via Flow

      Abstract: Recently, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation, flip-and-flow, that allows two tangency packings whose contact graphs differ by a combinatorial edge flip to be continuously deformed from one to the other while maintaining tangencies across all of their common edges. Starting from a canonical tangency circle packing with the desired number of circles a finite sequence of flip-and-flow operations may be applied to obtain a circle packing for any desired (proper) contact graph with the same number of circles.

      The full Koebe-Andre’ev-Thurston theorem generalizes the circle packing theorem to allow for neighboring circles to overlap by angles up to $\pi/2$. In this talk I will show that the Connelly-Gortler method can be extended to allow for circles to overlap to angles up to $\pi/2$. This results in a new proof of the general Koebe-Andre’ev-Thurston theorem for disk patterns on $\mathbb{S}^2$ as well as a numerical algorithm for computing them. The proof involves generalizing a notion of convexity for circle polyhedra that was recently used to prove the global rigidity of certain circle packings, which is then used to show that all convex circle polyhedra are infinitesimally rigid, a result of independent interest.

      5:00–5:30 pmMovies “conform!” & ”Koebe polyhedra”

       

      Saturday, May 7, 2022

      9:30–10:20 amAlexander BobenkoTitle: The Bonnet problem: Is a surface characterized by its metric and curvatures?

      Abstract: We consider a classical problem in differential geometry, known as the Bonnet problem, whether a surface is characterized by a metric and mean curvature function. Generically, the answer is yes. Special cases when it is not the case are classified. In particular, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas

      10:20–11:00 amBreak
      11:00–11:50 amMiri Ben ChenTitle: Surface Multigrid via Intrinsic Prolongation

      Abstract: The solution of a linear system is a required ingredient in many geometry processing applications, and multigrid methods are among the most efficient solution techniques. However, due to the unstructured nature of triangle meshes, mapping functions between different multigrid levels is challenging. In this talk I will present our recent work that uses an intrinsic prolongation operator as the main building block in a multigrid solver for curved triangle meshes. Our solver can be used as a black-box in any triangle-mesh based system that requires a linear solve, and leads to order of magnitude time-efficiency improvement compared to direct solvers.

      12:00–2:00 pmLunch Break
      2:00–2:50 pmSteven GortlerTitle: Reconstructing configurations and graphs from unlabeled distance measurements

      Abstract: Place a configuration of n  points (vertices) generically in R^d. Measure the Euclidean lengths of m point-pairs (edges). When is the underlying graph determined by these $m$ numbers (up to isomorphism)? When is the point configuration determined by these $m$ numbers (up to congruence)? This question is motivated by a number of inverse problem applications. In this talk, I will review what is known about this question.

      3:00–3:20 pmBohan ZhouTitle: Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs

      Abstract: Optimal transport has profound and wide applications since its introduction in 1781 by Monge. Thanks to the Benamou-Brenier formulation, it provides a meaningful functional in the image science like image and shape registrations. However, exact computation through LP or PDE is in general not practical in large scale, while the popular entropy-regularized method introduces additional diffusion noise, deteriorating shapes and boundaries. Until the recent work [Jacobs and Leger, A Fast Approach to Optimal Transport: the back-and-forth method, Numerische Mathematik, 2020], solving OT in a both accurate and fast fashion finally becomes possible. Multiple marginal optimal transport is a natural extension from OT but has its own interest and is in general more computationally expensive. The entropy method suffers from both diffusion noise and high dimensional computational issues. In this work with Matthew Parno, we extend from two marginals to multiple marginals, on a wide class of cost functions when those marginals have a graph structure. This new method is fast and does not introduce diffusion. As a result, the new proposed method can be used in many fields those require sharp boundaries. If time allows, we will illustrate by examples the faithful joint recover via MMOT of images with sharp boundaries, with applications on sea ice prediction.

      3:20–4:00 pmBreak
      4:00–4:50 pmPeter SchroederTitle: Constrained Willmore Surfaces

      Abstract: The Willmore energy of a surface is a canonical example of a squared curvature bending energy. Its minimizers are therefore of interest both in the theory of surfaces and in practical applications from physical and geometric modeling. Minimizing the bending energy alone however is insufficient. Taking a cue from univariate splines which incorporate an isometry constraint we consider Willmore minimizers subject to a conformality constraint. In this talk I will report on a numerical algorithm to find such constrained minimizers for triangle meshes.

      Joint work with Yousuf Soliman (Caltech), Olga Diamanti (UGraz), Albert Chern (UCSD), Felix Knöppel (TU Berlin), Ulrich Pinkall (TU Berlin).

      5:00–5:50 pmProblems and Application discussions

       

      Sunday, May 8, 2022

      9:00–9:50 amTianqi WuTitle: Convergence of discrete uniformizations

      Abstract: The theory of discrete conformality, based on the notion of vertex scaling, has been implemented in computing conformal maps or uniformizations of surfaces. We will show that if a Delaunay triangle mesh approximates a smooth surface, then the related discrete uniformization will converge to the smooth uniformization, with an error bounded linearly by the size of the triangles in the mesh.

      10:10–11:00 amYanwen LuoTitle:  Recent Progress in Spaces of Geodesic Triangulations of Surfaces

      Abstract:
      Spaces of geodesic triangulations of surfaces are natural discretization of the groups of surface diffeomorphisms isotopy to the identity. It has been conjectured that these spaces have the same homotopy type as their smooth counterparts. In this talk, we will report the recent progress in this problem. The key ingredient is the idea in Tutte’s embedding theorem. We will explain how to use it to identify the homotopy types of spaces of geodesic triangulations. This is joint work with Tianqi Wu and Xiaoping Zhu.
      11:10–12:00 pmProblems and Application discussions
      12:00–1:00 pmMovie“The Discrete Charm of Geometry”

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Meng Cheng (Yale)

      Title: Symmetry and many-body topology in mixed states

      Abstract: It is by now well-understood that gapped ground states of local Hamiltonians can be classified topologically, and the nontrivial states exhibit many interesting topological phenomena. In this talk I’ll discuss recent developments in generalizing the topological classification to mixed states. Global symmetry plays a key role in understanding phases in pure states. For mixed states, certain “weak” symmetries may hold “on average” for the entire ensemble, in contrast to “strong” symmetries respected by each state in the ensemble. I will show that the interplay between these two kinds of symmetries lead to a rich landscape of symmetry-protected mixed states, and can also be used to characterize mixed state topological order.

       

    • CMSA EVENT: Computational Biology Symposium
      10:00 am-4:00 pm
      12/01/2024
      Compbiotextlessfeature-600x338

      On May 3, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo.

      The symposium will begin at 10:00am ET. There will be a morning and afternoon session, with an hour break for lunch.

      Videos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.

      Confirmed participants:

      Schedule:

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/19/2021 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Swampland Seminar
      10:00 am-11:00 am
      12/01/2024

      Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Aleksey Cherman (UMN)

      Title: Exact lattice chiral symmetry in 2d gauge theory

      Abstract: Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory.  I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

    • Swampland Seminar
      10:00 am-11:00 am
      12/01/2024

      Swampland Seminar

      Speakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech)

      Title: Causality constraints on corrections to Einstein gravity

      Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

    • Quantum Matter
    • Seminars
      Seminars Colloquia & Seminar
      13/3/2018 Topology Seminar
      10:00 am-11:30 am
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/26/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/22/2018 Topology Seminar
      10:00 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 05.05.23 (2)

      Quantum Matter Seminar

      Speaker: Sona Najafi (IBM Quantum)

      Title: Detecting central charge in a superconducting quantum processor

      Abstract: Physical systems at the continuous phase transition point exhibit conformal symmetry rendering local scaling invariance. In two dimensions, the conformal group possesses infinite generators described by Virasoro algebra with an essential parameter known as a central charge. While the central charge manifests itself in a variety of quantities, its detection in experimental setup remains elusive. In this work, we utilize Shannon-Renyi entropy on a local basis of a one-dimensional quantum spin chain at a critical point. We first use a simulated variational quantum eigen solver to prepare the ground state of the critical transfer field Ising model and XXZ model with open and periodic boundary conditions and perform local Pauli X and Z basis measurements. Using error mitigation such as probabilistic error cancellation, we extract an estimation of the local Pauli observables needed to determine the Shannon-Renyi entropy with respect to subsystem size. Finally, we obtain the central charge in the sub-leading term of Shannon-Renyi entropy.

      https://www.youtube.com/watch?v=Os26XRahD0c&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=5

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024

      Speaker: Haoyu Guo (Harvard)

      Title: Transport in large-N critical Fermi surface

      Abstract:
       A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermion-scalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and show that a previously proposed mega^{-2/3} contribution to the optical conductivity at frequency mega has vanishing co-efficient. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity behaves like a Fermi liquid. Arxiv references: 2203.04990, 2207.08841

    • Topological Quantum Matter Seminar
      10:00 am-11:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 12.07.22

      Topological Quantum Matter Seminar

      Speaker: Vasil Rokaj (Harvard)

      Title: Controlling Quantum Matter with Quantum Cavity Fields

      Abstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free electron gas [5]. The exact analytic solution of the Sommerfeld model in the cavity will be presented as well as its fundamental properties. Then, in the second part of the talk, I will focus on a many-particle system of cold ions in a harmonic trap coupled to the cavity field. I will show how this system couples collectively to the cavity and that hybrid states between light and matter, known as polaritons, emerge. The formation of polaritons leads to the modification of the properties of the cold ions and enhances the localization of the many-body wave function [6]. Connections to experiments will be discussed as well.

      [1] F. Garcia-Vidal, C. Ciuti, T. W. Ebbesen, Science, 373, 178 (2021)

      [2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)

      [3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)

      [4] T. W. Ebbesen, Acc. Chem. Res. 49, 11, 2403–2412 (2016)

      [5] V. Rokaj, M. Ruggenthaler, F. G. Eich, A. Rubio, Phys. Rev. Research 4, 013012 (2022)

      [6] V. Rokaj, S.I. Mistakidis, H.R. Sadeghpour, arXiv:2207.03436 (2022)

    • Algebraic Geometry in String Theory Seminar
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Pre-talk Speaker: David Wu (Harvard Physics): 10:00-10:30 am

      Speaker: Damian van de Heisteeg, CMSA

      Title: Species Scale across String Moduli Spaces

      Abstract: String theories feature a wide array of moduli spaces. We propose that the energy cutoff scale of these theories – the so-called species scale – can be determined through higher-curvature corrections. This species scale varies with the moduli; we use it both asymptotically to bound the diameter of the field space, as well as in the interior to determine a “desert point” where it is maximized.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      10:00 am-11:00 am
      12/01/2024

      Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or, Neumann) eigenvalues. Using the results on the Birkhoff conjecture, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks, which Kac proved to be uniquely determined, these are the only domains for which it is known that one can hear their shape.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Andreas Bauer  (Freie Universität Berlin)

      Title: Tensorial TQFT and disentangling modular Walker-Wang models

      Abstract: I will introduce simple “tensorial” definitions for many algebraic and categorical structures appearing in the classification of topological phases of matter. Such “tensorial TQFTs” will be defined as maps that associate tensors to geometric/topological objects of some type, subject to gluing axioms. Tensorial TQFTs are very directly related to microscopic physical models in terms of discrete path integrals. I will use those tensorial definitions to construct invertible boundaries which disentangle modular Walker-Wang models.

       

      https://www.youtube.com/watch?v=MJ8NRSrvihQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=12

    • Topological Quantum Matter Seminar
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 11.16.22

      Topological Quantum Matter Seminar

      Speaker: Jérôme Faist  (ETH Zurich)

      Title: Vacuum fluctuations in cavities: breakdown of the topological protection in the integer Quantum Hall effect

      Abstract: When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling ΩR is such that the coupling energy becomes close to the one of the bare matter resonance ω0. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian.

      In a microcavity, the strength of the electric field caused by the vacuum fluctuations, to which the strength of the light-matter coupling ΩR is proportional, scales inversely with the cavity volume. One very interesting feature of the circuit-based metamaterials is the fact that this volume can be scaled down to deep subwavelength values in all three dimension of space.1 Using metamaterial coupled to two-dimensional electron gases under a strong applied magnetic field, we have now explored to which extend this volume can be scaled down and reached a regime where the stability of the polariton is limited by diffraction into a continuum of plasmon modes2.

      We have also used transport to probe the ultra-strong light-matter coupling3, and show now that the latter can induce a breakdown of the integer quantum Hall effect4. The phenomenon is explained in terms of cavity-assisted hopping, an anti-resonant process where an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity5. We are also evaluating a proposal suggesting that the value of the quantization voltage can be renormalized by the cavity6.

       

      1. Scalari, G. et al. Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial. Science 335, 1323–1326 (2012).
      2. Rajabali, S. et al. Polaritonic Nonlocality in Light Matter Interaction. Nat Photon 15, 690–695 (2021).
      3. Paravicini-Bagliani, G. L. et al. Magneto-Transport Controlled by Landau Polariton States. Nat. Phys. 15, 186–190 (2019).
      4. Appugliese, F. et al. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science 375, 1030–1034 (2022).
      5. Ciuti, C. Cavity-mediated electron hopping in disordered quantum Hall systems. Phys. Rev. B 104, 155307 (2021).
      6. Rokaj, V., Penz, M., Sentef, M. A., Ruggenthaler, M. & Rubio, A. Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance. Phys. Rev. B 105, 205424 (2022).

       

    • Quantum Matter
      10:00 am-11:00 am
      12/01/2024
      CMSA QMMP 03.10.23

      Quantum Matter Seminar

      Speaker: Yichen Huang (Harvard)

      Title: Quantum entropy thermalization

      Abstract: In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization.

      References: arXiv:2302.10165, 2209.09826; Joint work with Aram W. Harrow

       

      https://www.youtube.com/watch?v=8b4g9SEFn_Y&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=13

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Scalable Dynamic Graph Algorithms
      10:00 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      CMSA Interdisciplinary Science Seminar

      Speaker: Quanquan Liu, Northwestern University

      Title: Scalable Dynamic Graph Algorithms

      Abstract: The field of dynamic graph algorithms seeks to understand and compute statistics on real-world networks that undergo changes with time. Some of these networks could have up to millions of edge insertions and deletions per second. In light of these highly dynamic networks, we propose various scalable and accurate graph algorithms for a variety of problems. In this talk, I will discuss new algorithms for various graph problems in the batch-dynamic model in shared-memory architectures where updates to the graph arrive in multiple batches of one or more updates. I’ll also briefly discuss my work in other dynamic models such as distributed dynamic models where the communication topology of the network also changes with time (ITCS 2022). In these models, I will present efficient algorithms for graph problems including k-core decomposition, low out-degree orientation, matching, triangle counting, and coloring.

      Specifically, in the batch-dynamic model where we are given a batch of B updates, I’ll discuss an efficient O(B log^2 n) amortized work and O(log^2 n log log n) depth algorithm that gives a (2+\epsilon)-approximation on the k-core decomposition after each batch of updates (SPAA 2022). We also obtain new batch-dynamic algorithms for matching, triangle counting, and coloring using techniques and data structures developed in our k-core decomposition algorithm. In addition to our theoretical results, we implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyper-threading on 11 graphs of varying densities and sizes. Our experiments show improvements over state-of-the-art algorithms even on machines with only 4 cores (your standard laptop). I’ll conclude with a discussion of some open questions and potential future work that these lines of research inspire.

      Bio: Quanquan C. Liu is a postdoctoral scholar at Northwestern University under the mentorship of Prof. Samir Khuller. She completed her PhD in Computer Science at MIT where she was advised by Prof. Erik Demaine and Prof. Julian Shun. Before that, she obtained her dual bachelor’s degree in computer science and math also at MIT. She has worked on a number of problems in algorithms and the intersection between theory and practice. Her most recent work focuses on scalable dynamic and static graph algorithms as well as differentially private graph algorithms for problems including k-core decomposition, densest subgraphs, subgraph counting, matching, maximal independent set and coloring. She has earned the Best Paper Award at SPAA 2022, a NSF Graduate Research Fellowship, and participated in the 2021 EECS Rising Stars workshop. Outside of research, she is extensively involved in programming outreach as a coach for the USA Computing Olympiad (USACO) and as a trainer for the North America Programming Camp (NAPC).

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Margarita Davydova (MIT)

      Title: Floquet codes, automorphisms, and quantum computation

      Abstract: In this talk, I will introduce a new kind of measurement-based quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of low-weight measurements which simultaneously encode logical information and enable error correction.  We introduce a new class of quantum error-correcting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes.

      As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of time-like domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model.  This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes.

      The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two- and, rarely three-body measurements. Using adaptive two-body measurements, we can achieve a non-Clifford gate in 3+1d, making the first step towards universal quantum computation in this model.

      The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].

    • CMSA EVENT: Frontiers in Applied Mathematics and Computation
      10:00 am-2:00 pm
      12/01/2024-04/29/2020
      Frontiers In Applied Mathematics And Computation

      Together with the School of Engineering and Applied Sciences, the CMSA will be hosting a lecture series on the Frontiers in Applied Mathematics and Computation. Talks in this series will aim to highlight current research trends at the interface of applied math and computation and will explore the application of these trends to challenging scientific, engineering, and societal problems.

      Lectures will take place on March 25, April 1, and April 29, 2021.

      Speakers:

      • George Biros (U.T. Austin)
      • Laura Grigori (INRIA Paris)
      • Samory K. Kpotufe (Columbia)
      • Jonas Martin Peters (University of Copenhagen)
      • Joseph M. Teran (UCLA)

      The schedule below will be updated as talks are confirmed.

       

      Date/TimeSpeakerTitle/Abstract
      3/25/2021
      10:00 – 11:00am ET
      Joseph M. TeranTitle: Affine-Particle-In-Cell with Conservative Resampling and Implicit Time Stepping for Surface Tension Forces

      Abstract: The Particle-In-Cell (PIC) method of Harlow is one of the first and most widely used numerical methods for Partial Differential Equations (PDE) in computational physics. Its relative efficiency, versatility and intuitive implementation have made it particularly popular in computational incompressible flow, plasma physics and large strain elastoplasticity. PIC is characterized by its dual particle/grid (Lagrangian/Eulerian) representation of material where particles are generally used to track material transport in a Lagrangian way and a structured Eulerian grid is used to discretize remaining spatial derivatives in the PDE. I will discuss the importance of conserving linear and angular momentum when switching between these two representations and the recent Affine-Particle-In-Cell (APIC) extension to PIC designed for this conservation. I will also discuss a recent APIC technique for discretizing surface tension forces and their linearizations needed for implicit time stepping. This technique is characterized by a novel surface resampling strategy and I will discuss a generalization of the APIC conservation to this setting.

      4/1/2021
      9:00 – 10:00am ET
      George BirosTitle: Inverse biophysical modeling and its application to neurooncology

      Abstract: A predictive, patient-specific, biophysical model of tumor growth would be an invaluable tool for causally connecting diagnostics with predictive medicine. For example, it could be used for tumor grading, characterization of the tumor microenvironment, recurrence prediction, and treatment planning,  e.g., chemotherapy protocol or enrollment eligibility for clinical trials. Such a model also would provide an important bridge between molecular drivers of tumor growth and imaging-based phenotypic signatures, and thus,  help identify and quantify mechanism-based associations between these two. Unfortunately, such a predictive biophysical model does not exist. Existing models undergoing clinical evaluation are too simple–they do not even capture the MRI phenotype. Although many highly complex models have been proposed, the major hurdle in deploying them clinically is their calibration and validation.

      In this talk, I will discuss the challenges related to the calibration and validation of biophysical models, and in particular the mathematical structure of the underlying inverse problems. I will also present a new algorithm that localizes the tumor origin within a few millimeters.

      4/1/2021
      10:00 – 11:00am ET
      Samory K. KpotufeTitle: From Theory to Clustering

      Abstract: Clustering is a basic problem in data analysis, consisting of partitioning data into meaningful groups called clusters. Practical clustering procedures tend to meet two criteria: flexibility in the shapes and number of clusters estimated, and efficient processing. While many practical procedures might meet either of these criteria in different applications, general guarantees often only hold for theoretical procedures that are hard if not impossible to implement. A main aim is to address this gap.
      We will discuss two recent approaches that compete with state-of-the-art procedures, while at the same time relying on rigorous analysis of clustering. The first approach fits within the framework of density-based clustering, a family of flexible clustering approaches. It builds primarily on theoretical insights on nearest-neighbor graphs, a geometric data structure shown to encode local information on the data density. The second approach speeds up kernel k-means, a popular Hilbert space embedding and clustering method. This more efficient approach relies on a new interpretation – and alternative use – of kernel-sketching as a geometry-preserving random projection in Hilbert space.
      Finally, we will present recent experimental results combining the benefits of both approaches in the IoT application domain.
      The talk is based on various works with collaborators Sanjoy Dasgupta, Kamalika Chaudhuri, Ulrike von Luxburg, Heinrich Jiang, Bharath Sriperumbudur, Kun Yang, and Nick Feamster.

      4/29/2021
      12:00 – 1:00pm ET
      Jonas Martin PetersTitle: Causality and Distribution Generalization

      Abstract: Purely predictive methods do not perform well when the test distribution changes too much from the training distribution. Causal models are known to be stable with respect to distributional shifts such as arbitrarily strong interventions on the covariates, but do not perform well when the test distribution differs only mildly from the training distribution. We discuss anchor regression, a framework that provides a trade-off between causal and predictive models. The method poses different (convex and non-convex) optimization problems and relates to methods that are tailored for instrumental variable settings. We show how similar principles can be used for inferring metabolic networks. If time allows, we discuss extensions to nonlinear models and theoretical limitations of such methodology.

      4/29/2021
      1:00 – 2:00pm ET
      Laura GrigoriTitle: Randomization and communication avoiding techniques for large scale linear algebra

      Abstract: In this talk we will discuss recent developments of randomization and communication avoiding techniques for solving large scale linear algebra operations. We will focus in particular on solving linear systems of equations and we will discuss a randomized process for orthogonalizing a set of vectors and its usage in GMRES, while also exploiting mixed precision.  We will also discuss a robust multilevel preconditioner that allows to further accelerate solving large scale linear systems on parallel computers.

    • Math Science Literature Lecture Series
      10:00 am-11:30 am
      12/01/2024

      Zhengwei Liu (Tsinghua University)

      Title: Subfactors–in Memory of Vaughan Jones

      Abstract: Jones initiated modern subfactor theory in early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial, for which Jones won the Fields Metal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed.

      Talk chair: Arthur Jaffe

      Slides | Video 

    • Swampland Seminar
      10:00 am-11:30 am
      12/01/2024

      Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

    • Quantum Matter
      10:00 am
      12/01/2024
      CMSA QMMP 03.03.23

      Quantum Matter Seminar

      Speaker: Anna Hasenfratz (University of Colorado)

      Title: Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions
      Abstract: 4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the conformal phase is well established, very little is known about the nature of the phase transition or the strong coupling phase.
      Lattice QCD methods can predict the RG $\beta$ function, but the calculations are often limited by non-physical bulk phase transition that prevent exploring the strong coupling region of the phase diagram. Even the critical flavor number is controversial, estimates vary between $N_f=8$ and 14 for fundamental fermions.
      Using an improved lattice actions that include heavy Pauli-Villars (PV) type bosons to reduce ultraviolet fluctuations, I was able to simulate an SU(3) system with 8 fundamental flavors at much stronger renormalized coupling than previously possibly. The numerical results indicate a smooth phase transition from weak coupling to a strongly coupled phase.
      I investigate the critical behavior of the transition using finite size scaling. The result of the scaling analysis is not consistent with a first order phase transition, but it is well described by   Berezinsky-Kosterlitz-Thouless or BKT scaling. BKT scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that warrants further investigations.
      The strongly coupled phase appear to be chirally symmetric but gapped, suggesting symmetric mass generation (SMG). This could be the consequence of the lattice fermions used in this study. Staggered fermions in the massless limit are known to be anomaly free, allowing an SMG phase in the continuum limit.

       


      References:
      Phys.Rev.D 106 (2022) 1, 014513 • e-Print: 2204.04801
      Phys.Rev.D 104 (2021) 7, 074509 • e-Print: 2109.02790
      For anomalies and staggered fermion, see
      Phys.Rev.D 104 (2021) 9, 094504 • e-Print: 2101.01026
      https://www.youtube.com/watch?v=3jtNsFGszjE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=14
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Xiao-Gang Wen (MIT)

      Title: A 6-year journey: from gravitational anomaly to a unified theory of generalized symmetry

      Abstract: Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topological-order correspondence. I will also discuss some applications of emergent generalized symmetry.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/16/2020 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Swampland Seminar
      10:00 am-11:30 am
      12/01/2024
      Speakers: Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)
      Title4d strings at strong coupling
      As usual, the format will be 45 min talk + 30 min discussion, to encourage participation from the audience.
      Looking forward to seeing you there!
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      General Relativity Program Minicourses
      10:00 am-1:00 pm
      12/01/2024-05/17/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Minicourses

      General Relativity Program Minicourses

      During the Spring 2022 semester, the CMSA hosted a program on General Relativity.

      This semester-long program included four minicourses running in March, April, and May;  a conference April 4–8, 2022;  and a workshop from May 2–5, 2022.

       

      ScheduleSpeakerTitleAbstract
      March 1 – 3, 2022
      10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
      Dr. Stefan CzimekCharacteristic Gluing for the Einstein EquationsAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).
      March 22 – 25, 2022
      22nd & 23rd, 10:00 am – 11:30am ET
      24th & 25th, 11:00 am – 12:30pm ET
      Location: Hybrid. CMSA main seminar room, G-10.
      Prof. Lan-Hsuan HuangExistence of Static Metrics with Prescribed Bartnik Boundary DataAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is

      1. The conjecture and an overview of the results
      2. Static regular: a sufficient condition for existence and local uniqueness
      3. Convex boundary, isometric embedding, and static regular
      4. Perturbations of any hypersurface are static regular

      Video on Youtube: March 22, 2022

      March 29 – April 1, 2022 10:00am – 12:00pm ET, each day

      Location: Hybrid. CMSA main seminar room, G-10.

      Prof. Martin TaylorThe nonlinear stability of the Schwarzschild family of black holesAbstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.
      April 19 & 21, 2022
      10 am – 12 pm ET, each dayZoom only
      Prof. Håkan AndréassonTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.

      Video 4/19/2022

      Video 4/22/2022

      May 16 – 17, 2022
      10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
      Prof. Marcelo DisconziA brief overview of recent developments in relativistic fluidsAbstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.

      1. Set-up, review of standard results, physical motivation.
      2. The relativistic Euler equations: null structures and the problem of shocks.
      3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
      4. Relativistic viscous fluids.

      Video 5/16/2022

      Video 5/17/2022

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: John Baez (University of California, Riverside)

      Title: Two of my favorite numbers: 8 and 24

      Abstract: The numbers 8 and 24 play special roles in mathematics. The number 8 is special because of Bott periodicity, the octonions and the E8 lattice, while 24 is special for many reasons, including the binary tetrahedral group, the 3rd stable homotopy group of spheres, and the Leech lattice. The number 8 does for superstring theory what the number 24 does for bosonic string theory. In this talk, which is intended to be entertaining, I will overview these matters and also some connections between the numbers 8 and 24.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 05.12.23

      Quantum Matter Seminar

      Speaker: Carolyn Zhang (U Chicago)

      Title: Anomalies of (1+1)D categorical symmetries

      Abstract: We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $A$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the \emph{electric} Lagrangian algebra, that describes a phase with $A$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $A$. We observe that if there exists a different gapped boundary, given by a \emph{magnetic} Lagrangian algebra, then there exists a gapped phase where $A$ is not spontaneously broken at all, which means that $A$ is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $A$ being anomaly-free. As an application, we consider the Drinfeld centers of $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.

      https://www.youtube.com/watch?v=hSzBMYEY_q8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=4

    • Swampland Seminar
      10:00 am-11:00 am
      12/01/2024

      Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 06.30.23

      Quantum Matter Seminar

      Speaker: Marieke Van Beest (SCGP)

      Title: Monopoles, Scattering, and Generalized Symmetries

      Abstract: In this talk, we will discuss the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle, as they can carry fractional quantum numbers. We argue that such outgoing particles live in the twisted sector of a topological co-dimension 1 surface, which ends topologically on the monopole. This symmetry defect is often non-invertible, and as such the outgoing radiation not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory, which is a new prediction.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 06.26.23

      Quantum Matter Seminar

      Title: Chiral fermionic CFTs of central charge ≤ 16

      Abstract: We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac’s theorem and bosonization/fermionization. This talk will discuss the derivation of this result, its application to the classification of non-supersymmetric heterotic string theories, and along the way we’ll address some oft-overlooked subtleties of bosonization from the point of view of anomalies and topological phases.

    • Quantum Matter
      10:00 am-12:00 pm
      12/01/2024
      CMSA QMMP 06.13.23

      Quantum Matter Seminar

      Speaker: Brandon C. Rayhaun (C. N. Yang ITP, Stony Brook University)

      Title: Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality

      Abstract: Conformal field theories in (1+1)D are key actors in many dramas of physics and mathematics. Their classification has therefore been an important and long-standing problem. In this talk, I will explain the main ideas behind the classification of (most) “small” bosonic CFTs. Here, I use the adjective “small” informally to refer to theories with low central charge (less than 24) and few primary operators (less than 5). Time and attention permitting, I will highlight two applications of this result. First, I will describe how it can be used in tandem with bosonization and fermionization techniques to establish the classification of chiral fermionic CFTs with central charge less than 23. Second, I will showcase how it can be used to bootstrap generalized global symmetries using the concept of “symmetry/subalgebra duality.”

      Talk based on arXiv:2208.05486 [hep-th] (joint work with Sunil Mukhi) and arXiv:2303.16921 [hep-th].

      https://www.youtube.com/watch?v=NrOcsiUmSh0&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=1&t=2s

       

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 03.24.23

      Quantum Matter Seminar

      Speaker: Alexander Zlokapa, MIT

      Title: Traversable wormhole dynamics on a quantum processor

      Abstract: The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

       

      https://www.youtube.com/watch?v=iYkVuju_sP8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=11

    • CMSA EVENT: 2020 Big Data Conference (Virtual)
      10:00 am-2:05 pm
      12/01/2024-08/25/2020

      On August 24-25, 2020 the CMSA hosted our sixth annual Conference on Big Data. The Conference featured many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. The 2020 Big Data Conference took place virtually.

      Videos of the talks are available in this youtube playlist.

       

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
      • Sergiy Verstyuk, CMSA, Harvard University

      Speakers:

      Schedule:
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/1/2021 Math Physics
      10:00 am-11:00 am
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/22/2021 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Cheryne Jonay (Stanford)

      Title: A Physical Theory of Two-stage Thermalization

      Abstract: One indication of thermalization time is subsystem entanglement reaching thermal values. Recent studies on local quantum circuits reveal two exponential stages with decay rates $r_1$ and $r_2$ of the purity before and after thermalization. We provide an entanglement membrane theory interpretation, with $r_1$ corresponding to the domain wall free energy. Circuit geometry can lead to $r_1 < r_2$, producing a “phantom eigenvalue”. Competition between the domain wall and magnon leads to $r_2 < r_1$ when the magnon prevails. However, when the domain wall wins, this mechanism provides a practical approach for measuring entanglement growth through local correlation functions.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 04.28.23

      Quantum Matter Seminar

      Title: Fracton Self-Statistics

      Speaker: Hao Song (ITP-CAS)

      Abstract: Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating other excitations are called fractons. Here we address a fundamental open question — can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged, and show their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of abelian fracton orders. Finally, we show the existence of semionic or fermionic fracton self-statistics in some twisted variants of the checkerboard model and Haah’s code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.

      References: H Song, N Tantivasadakarn, W Shirley, M Hermele, arXiv:2304.00028.

      https://www.youtube.com/watch?v=TBAEif9XVww&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=6

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 04.21.23 (1)

      Quantum Matter Seminar

      Speaker: Prof. Subir Sachdev (Harvard)

      Title: A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order

      Abstract: Soon after the discovery of high-temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low-temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the “pseudogap metal” phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.
      As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.
      This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Mathias S. Scheurer, and S. S., arXiv:2302.07885

      https://www.youtube.com/watch?v=ueT28iMdjzE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=7

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/12/2021 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/5/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/5/2021 Interdisciplinary Science Seminar
      10:00 am-11:00 am
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Pre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am

      Pre-talk Title: Introduction to the singularities of the MMP


      Speaker: Dori Bejleri (Harvard Math & CMSA)

      Title: Moduli of boundary polarized Calabi-Yau pairs

      Abstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher, H. Blum, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang.

       

       

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 04.14.23

      Quantum Matter Seminar

      Speaker: Guanyu Zhu (IBM Quantum, T. J. Watson Research Center)

      Title: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries

      Abstract: Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects.

      References:
      1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua
      2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O&#39;Connor, Guanyu Zhu
      3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

       

      https://www.youtube.com/watch?v=APcDMMRI9VU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=8

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/8/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Mathematical Physics Seminar, Mondays
      10:00 am-11:00 am
      12/01/2024

      The seminar on mathematical physics will be held on Mondays from 10:00 – 11:00am ET on Zoom. Please email the seminar organizers to learn how toattend. This year’s Seminar will be organized by Yoosik Kim (yoosik@cmsa.fas.harvard.edu), Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu), and Yang Zhou (yangzhou@cmsa.fas.harvard.edu).

      Join the Math-Physics mailing list

      The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

      Spring 2021:

      DateSpeakerTitle/Abstract
      2/1/2021Choa Dongwook
      (KIAS)Video
      TitleFukaya category of Landau-Ginzburg orbifolds.

      Abstract: Landau-Ginzburg orbifold is just another name for a holomorphic function W with its abelian symmetry G. Its Fukaya category can be viewed as a categorification of a homology group of its Milnor fiber. In this introductory talk, we will start with some classical results on the topology of isolated singularities and its Fukaya-Seidel category. Then I will explain a new construction for such category to deal with a non-trivial symmetry group G. The main ingredients are classical variation map and the Reeb dynamics at the contact boundary. If time permits, I will show its application to mirror symmetry of LG orbifolds and its Milnor fiber. This is a joint work with C.-H. Cho and W. Jeong

      2/8/2021Jérémy Guéré (Fourier Institute)TitleCongruences on K-theoretic Gromov-Witten invariants

      Abstract: K-theoretic Gromov-Witten invariants of smooth projective varieties have been introduced by YP Lee, using the Euler characteristic of a virtual structure sheaf. In particular, they are integers. In this talk, I look at these invariants for the quintic threefold and I will explain how to compute them modulo 41, using the virtual localization formula under a finite group action, up to genus 19 and degree 40.

      2/15/2021Zhiwei Zheng (Max Planck Institute)

      Video

      Title: Some new results on automorphisms of hypersurfaces

      Abstract: It is natural to study automorphisms of hypersurfaces in projective spaces. In this talk, I will discuss a new approach to determine all possible orders of automorphisms of smooth hypersurfaces with fixed degree and dimension. Then we consider the specific case of cubic fourfolds, and discuss the relation with Hodge theory.

      2/22/2021Yu-Shen Lin (Boston University)

      Video

      TitleFull SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

      Abstract: Strominger–Yau–Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi–Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

      3/1/2021Carlos S. Shahbazi (Hamburg University)

      Video

      TitleMathematical supergravity and its applications to differential geometry.

      Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

      3/8/2021Miguel Moreira (ETH)

      Video

      TitleVirasoro constraints for stable pairs.

      Abstract: The theory of stable pairs (PT) with descendents, defined on a 3-fold X, is a sheaf theoretical curve counting theory. Conjecturally, it is equivalent to the Gromov-Witten (GW) theory of X via a universal (but intricate) transformation, so we can expect that the Virasoro conjecture on the GW side should have a parallel in the PT world. In joint work with A. Oblomkov, A. Okounkov, and R. Pandharipande, we formulated such a conjecture and proved it for toric 3-folds in the stationary case. The Hilbert scheme of points on a surface S might be regarded as a component of the moduli space of stable pairs on S x P1, and the Virasoro conjecture predicts a new set of relations satisfied by tautological classes on S[n] which can be proven by reduction to the toric case.

      3/15/2021Spring break
      3/22/2021Ying Xie (Shanghai Center for Mathematical Sciences)Title: Derived categories for Grassmannian flips

      Abstract: Flip is a fundamental surgery operation for constructing minimal models in higher-dimensional birational geometry. In this talk, I will introduce a series of flips from Lie theory and investigate their derived categories. This is a joint program with Conan Leung.

      3/29/2021Emanuel Scheidegger (Peking University)Title:  On the quantum K-theory of the quintic.

      Abstract: Quantum cohomology is a deformation of the cohomology of a projective variety governed by counts of stable maps from a curve into this variety. Quantum K-theory is in a similar way a deformation of K-theory but also of quantum cohomology, It has recently attracted attention in physics since a realization in a physical theory has been found. Currently, both the structure and examples in quantum K-theory are far less understood than in quantum cohomology.
      We will explain the properties of quantum K-theory in comparison with quantum cohomology, and we will discuss the examples of projective space and the quintic hypersurface in P^4.
      4/5/2021Gaëtan Borot (HU Berlin)

      Video

      TitleTopological recursion in 4d N = 2 supersymmetric gauge theories

      Abstract: According to the Alday-Gaiotto-Tachikawa conjecture (proved in this case by Schiffman and Vasserot), the instanton partition function in 4d N = 2 SU(r) supersymmetric gauge theory on P^2 with equivariant parameters \epsilon_1,\epsilon_2 is the norm of a Whittaker vector for W(gl_r) algebra. I will explain how these Whittaker vectors can be computed (at least perturbatively in the energy scale) by topological recursion for \epsilon_1 +\epsilon_2 = 0, and by a non-commutation version of the topological recursion in the Nekrasov-Shatashvili regime where \epsilon_1/\epsilon_2 is fixed. This is a joint work to appear with Bouchard, Chidambaram and Creutzig.

      4/12/2021Fei Yan (Rutgers)TitleNetworks and quantization

      Abstract: I will describe two quantization scenarios. The first scenario involves the construction of a quantum trace map computing a link “invariant” (with possible wall-crossing behavior) for links L in a 3-manifold M, where M is a Riemann surface C times a real line. This construction unifies the computation of familiar link invariant with the refined counting of framed BPS states for line defects in 4d N=2 theories of class S. Certain networks on C play an important role in the construction. The second scenario concerns the study of Schroedinger equations and their higher order analogues, which could arise in the quantization of Seiberg-Witten curves in 4d N=2 theories. Here similarly certain networks play an important part in the exact WKB analysis for these Schroedinger-like equations. At the end of my talk I will also try to sketch a possibility to bridge these two scenarios.

      4/19/2021Hazel Mak (Brown University)TitleBranching Rules and Young Tableaux Methods: 10D & 11D Supergravity

      Abstract: In this talk, I will review 4D, N = 1 off-shell supergravity. Then I present explorations to construct 10D and 11D supergravity theories in two steps. The first step is to decompose scalar superfield into Lorentz group representations which involves branching rules and related methods. Interpretations of component fields by Young tableaux methods will be presented. The second step is to implement an analogue of Breitenlohner’s approach for 4D supergravity to 10D and 11D theories.

      4/26/2021Owen Gwilliam (UMass. Amherst)

      Video

      TitleTopological-holomorphic field theories and their BV quantizations

      Abstract: Topological field theories and holomorphic field theories have each had a substantial impact in both physics and mathematics, so it is natural to consider theories that are hybrids of the two, which we call topological-holomorphic and denote as THFTs. Examples include Kapustin’s twist of N=2, D=4 supersymmetric Yang-Mills theory and Costello’s 4-dimensional Chern-Simons theory. In this talk about joint work with Rabinovich and Williams, I will define THFTs, describe several examples, and then explain how to quantize them rigorously and explicitly, by building on techniques of Si Li.  Time permitting, I will indicate how these results offer a novel perspective on the Gaudin model via 3-dimensional field theories.


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/14/2020Lino Amorim (Kansas State University)TitleNon-commutative Gromov-Witten invariants

      Abstract:  I will describe an analogue of Saito’s theory of primitive forms for Calabi-Yau A-infinity categories. Under some conditions on the Hochschild cohomology of the category, this construction recovers the (genus zero) Gromov-Witten invariants of a symplectic manifold from its Fukaya category. This includes many compact toric manifolds, in particular projective spaces.

      9/21/2020Yuhan Sun (Rutgers)Title: Displacement energy of Lagrangian 3-spheres

      Abstract:  We study local and global Hamiltonian dynamical behaviors of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that there is a one-parameter family of Lagrangian tori near S, which are nondisplaceable in X. When dim S = 3, we obtain a new estimate of the displacement energy of S, by estimating the displacement energy of a one-parameter family of Lagrangian tori near S.

      9/28/2020Shota Komatsu (CERN)Title: Wilson loops as matrix product states

      Abstract:  In this talk, I will discuss a reformulation of the Wilson loop in large N gauge theories in terms of matrix product states. The construction is motivated by the analysis of supersymmetric Wilson loops in the maximally super Yang–Mills theory in four dimensions, but can be applied to any other large N gauge theories and matrix models, although less effective. For the maximally super Yang–Mills theory, one can further perform the computation exactly as a function of ‘t Hooft coupling by combining our formulation with the relation to integrable spin chains.

      10/5/2020Ming Zhang (UBC)Title: Verlinde/Grassmannian correspondence and applications.

      Abstract: In the 90s’, Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten’s work by relating the $\text{GL}_{n}$ Verlinde numbers to the level $l$ quantum K-invariants of the Grassmannian $\text{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence.

      The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will discuss the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.  At the end of the talk, I will describe some applications of this correspondence.

      10/12/2020Cancelled -Columbus Day
      10/19/2020Ben Gammage (Harvard)Title3d mirror symmetry for abelian gauge groups

      Abstract: 3d mirror symmetry is a proposed duality relating a pair of 3-dimensional supersymmetric gauge theories. Various consequences of this duality have been heavily explored by representation theorists in recent years, under the name of “symplectic duality”. In joint work in progress with Justin Hilburn, for the case of abelian gauge groups, we provide a fully mathematical explanation of this duality in the form of an equivalence of 2-categories of boundary conditions for topological twists of these theories. We will also discuss some applications to homological mirror symmetry and geometric Langlands duality.

      10/26/2020Cancelled
      11/2/2020Haoyu Sun (Berkeley)TitleDouble-Janus linear sigma models and generalized quadratic reciprocity

      Abstract: We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d N=4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T^2 fibered over S^1) times a circle with an SL(2,Z) duality wall inserted on S^1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2,Z), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
      11/9/2020An Huang (Brandeis)Titlep-adic strings, Einstein equations, Green’s functions, and Tate’s thesis

      Abstract: I shall discuss a recent work on how p-adic strings can produce perturbative quantum gravity, and an adelic physics interpretation of Tate’s thesis.
      11/16/2020
      10:00am ET
      Matt Kerr (WUSTL)Title:  Differential equations and mixed Hodge structures

      Abstract: We report on a new development in asymptotic Hodge theory, arising from work of Golyshev–Zagier and Bloch–Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry.  The talk will focus exclusively on the Hodge/period-theoretic aspects through two main examples.
      Given a variation of Hodge structure M on a Zariski open in P^1, the periods of the limiting mixed Hodge structures at the punctures are interesting invariants of M.  More generally, one can try to compute these asymptotic invariants for iterated extensions of M by “Tate objects”, which may arise for example from normal functions associated to algebraic cycles. The main point of the talk will be that (with suitable assumptions on M) these invariants are encoded in an entire function called the motivic Gamma function, which is determined by the Picard-Fuchs operator L underlying M. In particular, when L is hypergeometric, this is easy to compute and we get a closed-form answer (and a limiting motive).  In the non-hypergeometric setting, it yields predictions for special values of normal functions; this part of the story is joint with V. Golyshev and T. Sasaki.

      11/23/2020

      11:30am ET

      Kyoung-Seog Lee (U of Miami)TitleDerived categories and motives of moduli spaces of vector bundles on curves

      Abstract: Derived categories and motives are important invariants of algebraic varieties invented by Grothendieck and his collaborators around 1960s. In 2005, Orlov conjectured that they will be closely related and now there are several evidences supporting his conjecture. On the other hand, moduli spaces of vector bundles on curves provide attractive and important examples of algebraic varieties and there have been intensive works studying them. In this talk, I will discuss derived categories and motives of moduli spaces of vector bundles on curves. This talk is based on joint works with I. Biswas and T. Gomez.

      11/30/2020Zijun Zhou (IPMU)Title: 3d N=2 toric mirror symmetry and quantum K-theory

      Abstract: In this talk, I will introduce a new construction for the K-theoretic mirror symmetry of toric varieties/stacks, based on the 3d N=2 mirror symmetry introduced by Dorey-Tong. Given the toric datum, i.e. a  short exact sequence 0 -> Z^k -> Z^n -> Z^{n-k} -> 0, we consider the toric Artin stack of the form [C^n / (C^*)^k]. Its mirror is constructed by taking the Gale dual of the defining short exact sequence. As an analogue of the 3d N=4 case, we consider the K-theoretic I-function, with a suitable level structure, defined by counting parameterized quasimaps from P^1. Under mirror symmetry, the I-functions of a mirror pair are related to each other under the mirror map, which exchanges the K\”ahler and equivariant parameters, and maps q to q^{-1}. This is joint work with Yongbin Ruan and Yaoxiong Wen.

      12/7/2020Thomas Grimm (Utrecht)TitleModuli Space Holography and the Finiteness of Flux Vacua

      Abstract: In this talk I describe a holographic perspective to study field spaces that arise in string compactifications. The constructions are motivated by a general description of the asymptotic, near-boundary regions in complex structure moduli spaces of Calabi-Yau manifolds using asymptotic Hodge theory. For real two-dimensional field spaces, I introduce an auxiliary bulk theory and describe aspects of an associated sl(2) boundary theory. The bulk reconstruction from the boundary data is provided by the sl(2)-orbit theorem of Schmid and Cattani, Kaplan, Schmid, which is a famous and general result in Hodge theory. I then apply this correspondence to the flux landscape of Calabi-Yau fourfold compactifications and discuss how this allows us, in work with C. Schnell, to prove that the number of self-dual flux vacua is finite

      For a listing of previous Mathematical Physics Seminars, please click here.

    • Seminars
      Seminars Colloquia & Seminar
      Social Science Applications Forum
      10:00 am-11:00 am
      12/01/2024

      During the Summer of 2020, the CMSA will be hosting a periodic Social Science Applications Seminar.

      The list of speakers is below and will be updated as details are confirmed.

      For a list of past Social Science Applications talks, please click here.
      DateSpeakerTitle/Abstract
      7/13/2020 10:00-11:00am ETLudovic Tangpi (Princeton)Please note, this seminar will take place online using Zoom.

      Title: Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls

      Abstract: This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in non-cooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space.
      For security reasons, you will have to show your full name to join the meeting.

      7/27/2020
      10:00pm
      Michael Ewens (Caltech)Please note, this seminar will take place online using Zoom.

      Title: Measuring Intangible Capital with Market Prices

      Abstract: Despite the importance of intangibles in today’s economy, current standards prohibit the capitalization of internally created knowledge and organizational capital, resulting in a downward bias of reported assets. As a result, researchers estimate this value by capitalizing prior flows of R&D and SG&A. In doing so, a set of capitalization parameters, i.e. the R&D depreciation rate and the fraction of SG&A that represents a long-lived asset, must be assumed. Parameters now in use are derived from models with strong assumptions or are ad hoc. We develop a capitalization model that motivates the use of market prices of intangibles to estimate these parameters. Two settings provide intangible asset values: (1) publicly traded equity prices and (2) acquisition prices. We use these parameters to estimate intangible capital stocks and subject them to an extensive set of diagnostic analyses that compare them with stocks estimated using existing parameters. Intangible stocks developed from exit price parameters outperform both stocks developed by publicly traded parameters and those stocks developed with existing estimates. (Joint work with Ryan Peters and Sean Wang.)

    • Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

       

      Speaker: Carlos S. Shahbazi (Hamburg University)

      Title: Mathematical supergravity and its applications to differential geometry

      Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA QMMP 04.07.23

      Quantum Matter Seminar

      Speaker: Nishad Maskara (Harvard)

      Title: Enhancing Detection of Topological Order by Local Error Correction

      Abstract: The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator.  Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.

       

      https://www.youtube.com/watch?v=oWIelx6_taU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=9

    • Algebraic Geometry in String Theory Seminar
      10:00 am-11:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA AGST Seminar 04.03.2023

      Algebraic Geometry in String Theory Seminar

      Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse

      Title: Kähler-Einstein metrics on families of Fano varieties

      Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Nat Tantivasadakarn (Caltech)

      Title: From wave-function collapse and Galois solvability to the realization of non-Abelian topological order on a quantum device

      Abstract: I will review our recent set of theoretical works on efficiently preparing long range quantum entanglement with adaptive quantum circuits: the combination of measurements with unitary gates whose choice can depend on previous measurement outcomes. I will show that this additional ingredient can be leveraged to prepare the long sought-after non-Abelian topological phases with a circuit depth that is independent of system size. Using this framework, we uncover a complexity hierarchy of long-range entangled states based on the minimal number of measurement layers required to create the state. Moreover, we find that certain non-Abelian states that cannot be efficiently prepared with adaptive circuits have a surprising connection to the unsolvability of the quintic polynomial.

      Finally, I will describe our recent collaboration with Quantinuum where we present the first unambiguous realization of non-Abelian D4 topological order and demonstrate control of its anyons. In particular, we are able to detect a non-trivial braiding where three non-Abelian anyons trace out the Borromean rings in spacetime, a signature unique to non-Abelian topological order.

    • Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024

      Speaker: Yu-Shen Lin (Boston University)

      Title: Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

      Abstract: Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi-Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/15/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Quantum Matter Seminar

      Speaker: Abijith Krishnan (MIT)

      Title: A Plane Defect in the 3d O(N) Model

      Abstract: It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

       

      https://www.youtube.com/watch?v=6cDK3TJ_H8w&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=10

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      2/10/2021 Strongly Correlated Quantum Materials
      10:00 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 06.09.23

      Quantum Matter Seminar

      Speakers: Gerald Höhn (Kansas State University) & Sven Möller (University of Hamburg)

      Title: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24

      Abstract: We discuss the classfication of self-dual vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely chiral 2-dimensional fermionic conformal field theories with just one primary field.

      There are exactly 969 such SVOAs under suitable regularity assumptions and the assumption that the shorter moonshine module VB^# is the unique self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1 spaces vanish.

      We construct and classify the self-dual SVOAs by determining the 2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central charge 24 and also by realising them as simple-current extensions of a dual pair containing a certain maximal lattice VOA. We show that all SVOAs besides VB^# x F and potential fake copies thereof stem from elements of the Conway group Co_0, the automorphism group of the Leech lattice.

      By splitting off free fermions F, if possible, we obtain the classification for all central charges less than or equal to 24.
      Reference: G. Höhn, S. Möller, arXiv:2303.17190.

      https://www.youtube.com/watch?v=U0alYxX05xU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=2

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Previous Random Matrix & Probability Theory Seminars
      10:26 am-10:27 am
      12/01/2024

      Spring 2020:

      DateSpeakerTitle/Abstract
      2/26/2020Louigi Addario-Berry (McGill University)Title: Hipster random walks and their ilk 

      Abstract: I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.

      4/1/2020Ian Jauslin (Princeton)This meeting will be taking place virtually on Zoom.

      Title: A simplified approach to interacting Bose gases
      Abstract: I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.

      4/22/2020Martin Gebert (UC Davis)This meeting will be taking place virtually on Zoom.

      TitleLieb-Robinson bounds for a class of continuum many-body fermion systems

      Abstract: We introduce a class of UV-regularized two-body interactions for
      fermions in $\R^d$ and prove a Lieb-Robinson estimate for the dynamics
      of this class of many-body systems. As a step towards this result, we
      also prove a propagation bound of Lieb-Robinson type for continuum
      one-particle Schr\“odinger operators. We apply the propagation bound to
      prove the existence of a strongly continuous infinite-volume dynamics on
      the CAR algebra.

      4/29/2020Marcin Napiórkowski (University of Warsaw)This meeting will be taking place virtually on Zoom.

      TitleFree energy asymptotics of the quantum Heisenberg spin chain

      Abstract: Spin wave theory suggests that low temperature properties of the Heisenberg model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction. Based on joint work with Robert Seiringer.

      5/6/2020Antti Knowles (University of Geneva)TitleField theory as a limit of interacting quantum Bose gases

      Abstract: We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the mean-field limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions d = 1,2,3. For d > 1 the Gibbs measure is supported on distributions of negative regularity and we have to renormalize the interaction. The proof is based on a functional integral representation of the grand canonical Gibbs state, in which convergence to the mean-field limit follows formally from an infinite-dimensional stationary phase argument for ill-defined non-Gaussian measures. We make this argument rigorous by introducing a white-noise-type auxiliary field, through which the functional integral is expressed in terms of propagators of heat equations driven by time-dependent periodic random potentials. Joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.
      5/13/2020Sven Bachmann (University of British Columbia)TitleQuantized quantum transport and Abelian anyons

      Abstract: I’ll discuss recent developments in the study of quantized quantum transport, focussing on the quantum Hall effect. Beyond presenting an index taking rational values, and which is the Hall conductance in the adapted setting, I will explain how the index is intimately paired with the existence of quasi-particle excitations having non-trivial braiding properties.

      5/20/2020Kristina Schubert (TU Dortmund)TitleFluctuation Results for General Ising Models — Block Spin Ising Models and Random Interactions

      Abstract: Starting from the classical Curie-Weiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins in which the vertices are divided into a finite number of blocks and where pair interactions are given according to their blocks. The magnetization is then the vector of magnetizations within each block, and we are interested in its behaviour and in particular in its fluctuations. On the other hand, we consider Ising models on Erdős-Rényi random graphs. Here, I will also present results on the fluctuations of the magnetization.

       

      Fall 2019:

      DateSpeakerTitle/Abstract
      9/11/2019Subhabrata SenTitle: Sampling convergence for random graphs: graphexes and multigraphexes

      Abstract: We will look at structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs, Chayes, Cohn and Veitch ’17). Sam- pling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We will introduce this framework and motivate the components of a graphex. Subsequently, we will discuss the graphex limit for several well-known sparse random (multi)graph models. This is based on joint work with Christian Borgs, Jennifer Chayes, and Souvik Dhara.

      9/25/2019Jeff Schenker (Michigan State)Title: An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states  

      Abstract: Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one — “entanglement breaking’’ – channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh)

      10/3/2019

       

      Thursday

      4:30pm

      Jian Ding (UPenn)Title: Distances associated with Liouville quantum gravity

      Abstract: I will review some recent progresses on distances associated with Liouville quantum gravity, which is a random measure obtained from exponentiating a planar Gaussian free field.

      The talk is based on works with Julien Dubédat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne, Ofer Zeitouni and Fuxi Zhang in various combinations.

      10/9/2019Ruth Williams (UCSD)Title: Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

      Abstract: Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy. It has been a standing problem to prove stability of this general model when the average load on the system is less than the network’s capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and indicate how to prove stability of the fluid model under mild conditions.

      This talk is based on joint work with Yingjia Fu.

      10/11/2019Cancelled
      10/16/2019Wei-Kuo Chen (University of Minnesota)Title: The generalized TAP free energy

      Abstract: Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag.

      10/23/2019Souvik Dhara (MIT)Title: A new universality class for critical percolation on networks with heavy-tailed degrees

      Abstract: The talk concerns critical behavior of percolation on finite random networks with heavy-tailed degree distribution. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdős-Rényi random graph. Subsequently, there has been a surge in the literature identifying two universality classes for the critical behavior depending on whether the asymptotic degree distribution has a finite or infinite third moment.

      In this talk, we will present a completely new universality class that arises in the context of degrees having infinite second moment. Specifically, the scaling limit of the rescaled component sizes is different from the general description of multiplicative coalescent given by Aldous and Limic (1998). Moreover, the study of critical behavior in this regime exhibits several surprising features that have never been observed in any other universality classes so far.

      This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden.

      10/30/2019Aram Harrow (MIT)Title: Random quantum circuits, phase transitions and complexity

      Abstract: Random unitary dynamics are a toy model for chaotic quantum dynamics and also have applications to quantum information theory and computing. Recently, random quantum circuits were the basis of Google’s announcement of “quantum computational supremacy,” meaning performing a task on a programmable quantum computer that would difficult or infeasible for any classical computer. Google’s approach is based on the conjecture that random circuits are as hard to classical computers to simulate as a worst-case quantum computation would be. I will describe evidence in favor of this conjecture for deep random circuits and against this conjecture for shallow random circuits. (Deep/shallow refers to the number of time steps of the quantum circuit.) For deep random circuits in Euclidean geometries, we show that quantum dynamics match the first few moments of the Haar measure after roughly the amount of time needed for a signal to propagate from one side of the system to the other. In non-Euclidean geometries, such as the Schwarzschild metric in the vicinity of a black hole, this turns out not to be always true. I will also explain how shallow quantum circuits are easier to simulate when the gates are randomly chosen than in the worst case. This uses a simulation algorithm based on tensor contraction which is analyzed in terms of an associated stat mech model.

      This is based on joint work with Saeed Mehraban (1809.06957) and with John Napp, Rolando La Placa, Alex Dalzell and Fernando Brandao (to appear).

      11/6/2019Bruno Nachtergaele (UC Davis)TitleThe transmission time and local integrals of motion for disordered spin chains

      Abstract:  We investigate the relationship between zero-velocity Lieb-Robinson bounds and the existence of local integrals of motion (LIOMs) for disordered quantum spin chains. We also study the effect of dilute random perturbations on the dynamics of many-body localized spin chains. Using a notion of transmission time for propagation in quantum lattice systems we demonstrate slow propagation by proving a lower bound for the transmission time. This result can be interpreted as a robustness property of slow transport in one dimension. (Joint work with Jake Reschke)

      11/13/2019Gourab Ray (University of Victoria)Title: Logarithmic variance of height function of square-iceAbstract: A homomorphism height function on a finite graph is a integer-valued function on the set of vertices constrained to have adjacent vertices take adjacent integer values. We consider the uniform distribution over all such functions defined on a finite subgraph of Z^2 with predetermined values at some fixed boundary vertices. This model is equivalent to the height function of the six-vertex model with a = b = c = 1, i.e. to the height function of square-ice. Our main result is that in a subgraph of Z^2 with zero boundary conditions, the variance grows logarithmically in the distance to the boundary. This establishes a strong form of roughness of the planar uniform homomorphisms.

       

      Joint work with: Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran Raoufi.

      11/20/2019Vishesh Jain (MIT)Title: A combinatorial approach to the quantitative invertibility of random matrices.

       

      Abstract: Abstract: Let $s_n(M_n)$ denote the smallest singular value of an $n\times n$ random matrix $M_n$. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood–Offord theory or net arguments) for obtaining upper bounds on the probability that $s_n(M_n)$ is smaller than $\eta \geq 0$ for quite general random matrix models. Such estimates are a fundamental part of the non-asymptotic theory of random matrices and have applications to the strong circular law, numerical linear algebra etc. In several cases of interest, our approach provides stronger bounds than those obtained by Tao and Vu using inverse Littlewood–Offord theory.

       

       

       

      2018-2019

      DateSpeakerTitle/Abstract
      9/28/2018

      *Friday, 10:00am*

      Yash Deshpande (MIT)Title: Estimating low-rank matrices in noise: phase transitions from spin glass theory

      Abstract: Estimating low-rank matrices from noisy observations is a common task in statistical and engineering applications. Following the seminal work of Johnstone, Baik, Ben-Arous and Peche, versions of this problem have been extensively studied using random matrix theory. In this talk, we will consider an alternative viewpoint based on tools from mean field spin glasses. We will present two examples that illustrate how these tools yield information beyond those from classical random matrix theory. The first example is the two-groups stochastic block model (SBM), where we will obtain a full information-theoretic understanding of the estimation phase transition. In the second example, we will augment the SBM with covariate information at nodes, and obtain results on the altered phase transition.

      This is based on joint works with Emmanuel Abbe, Andrea Montanari, Elchanan Mossel and Subhabrata Sen.

      10/3/2018Ian Jauslin (IAS)Title: Liquid Crystals and the Heilmann-Lieb model

      Abstract: In 1979, O.Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb.

      10/10/2018Afonso Bandeira (NYUTitle: Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment

      Abstract: Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions and orientations; Cryo-Electron Microscopy (Cryo-EM) imaging where projections of a molecule density are taken from unknown rotations, and several others.

      One fundamental example of this type of problems is Multi-Reference Alignment: Given a group acting in a space, the goal is to estimate an orbit of the group action from noisy samples. For example, in one of its simplest forms, one is tasked with estimating a signal from noisy cyclically shifted copies. We will show that the number of observations needed by any method has a surprising dependency on the signal-to-noise ratio (SNR), and algebraic properties of the underlying group action. Remarkably, in some important cases, this sample complexity is achieved with computationally efficient methods based on computing invariants under the group of transformations.

      10/17/2018

      3:30pm

      Thomas Chen (UT Austin)Title: Dynamics of a heavy quantum tracer particle in a Bose gas

      Abstract: We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R^3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit where N tends to infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. This is joint work with Avy Soffer (Rutgers University).

      10/24/2018

      *Room G02*

      Tselil Schramm (Harvard/MIT)Title: (Nearly) Efficient Algorithms for the Graph Matching Problem in Correlated Random Graphs

      Abstract: The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known.

      Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng.

      10/30/2018

      *Tuesday

      10:30am

      SC 507*

      Lauren Williams (Harvard)Title: Introduction to the asymmetric simple exclusion process (from a combinatorialist’s point of view)

      Abstract: The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, subject to the condition that there is at most one particle per site. This model was introduced in 1970 by biologists (as a model for translation in protein synthesis) but has since been shown to display a rich mathematical structure. There are many variants of the model — e.g. the lattice could be a ring, or a line with open boundaries. One can also allow multiple species of particles with different “weights.” I will explain how one can give combinatorial formulas for the stationary distribution using various kinds of tableaux. I will also explain how the ASEP is related to interesting families of orthogonal polynomials, including Askey-Wilson polynomials, Koornwinder polynomials, and Macdonald polynomials.

      11/7/2018Willhelm Schlag (Yale)Title: on the Bourgain-Dyatlov fractal uncertainty principle

      Abstract: We will present the Bourgain-Dyatlov theorem on the line, it’s connection with other uncertainty principles in harmonic analysis, and my recent partial progress with Rui Han on the problem of higher dimensions.

      11/14/2018David Gamarnik (MIT)Title: Two Algorithmic Hardness Results in Spin Glasses and Compressive Sensing.

      Abstract: I will discuss two computational problems in the area of random combinatorial structures. The first one is the problem of computing the partition function of a Sherrington-Kirkpatrick spin glass model. While the the problem of computing the partition functions associated with arbitrary instances is known to belong to the #P complexity class, the complexity of the problem for random instances is open. We show that the problem of computing the partition function exactly (in an appropriate sense) for the case of instances involving Gaussian couplings is #P-hard on average. The proof uses Lipton’s trick of computation modulo large prime number, reduction of the average case to the worst case instances, and the near uniformity of the ”stretched” log-normal distribution.

      In the second part we will discuss the problem of explicit construction of matrices satisfying the Restricted Isometry Property (RIP). This challenge arises in the field of compressive sensing. While random matrices are known to satisfy the RIP with high probability, the problem of explicit (deterministic) construction of RIP matrices eluded efforts and hits the so-called ”square root” barrier which I will discuss in the talk. Overcoming this barrier is an open problem explored widely in the literature. We essentially resolve this problem by showing that an explicit construction of RIP matrices implies an explicit construction of graphs satisfying a very strong form of Ramsey property, which has been open since the seminal work of Erdos in 1947.

      11/28/2018Sean O’ Rourke (UC Boulder)Title: Universality and least singular values of random matrix products

      Abstract: We consider the product of m independent iid random matrices as m is fixed and the sizes of the matrices tend to infinity.  In the case when the factor matrices are drawn from the complex Ginibre ensemble, Akemann and Burda computed the limiting microscopic correlation functions.  In particular, away from the origin, they showed that the limiting correlation functions do not depend on m, the number of factor matrices. We show that this behavior is universal for products of iid random matrices under a moment matching hypothesis.  In addition, we establish universality results for the linear statistics for these product models, which show that the limiting variance does not depend on the number of factor matrices either. The proofs of these universality results require a near-optimal lower bound on the least singular value for these product ensembles.

      12/5/2018

      *Room G02*

      Omer Angel (UBC)Title: balanced excited random walks

      Abstract: I will present results on the scaling limit and asymptotics of the balanced excited random walk and related processes. This is a walk the that moves vertically on the first visit to a vertex, and horizontally on every subsequent visit. We also analyze certain versions of “clairvoyant scheduling” of random walks.

      Joint work with Mark Holmes and Alejandro Ramirez.

      2/7/2019

      Science Center 530

      Ramis Movassagh (IMB Research)Title: Generic Gaplessness, and Hamiltonian density of states from free probability theory

      Abstract: Quantum many-body systems usually reside in their lowest energy states. This among other things, motives understanding the gap, which is generally an undecidable problem. Nevertheless, we prove that generically local quantum Hamiltonians are gapless in any dimension and on any graph with bounded maximum degree.

      We then provide an applied and approximate answer to an old problem in pure mathematics. Suppose the eigenvalue distributions of two matrices M_1 and M_2 are known. What is the eigenvalue distribution of the sum M_1+M_2? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions. We will describe FPT and show examples of its powers for approximating physical quantities such as the density of states of the Anderson model, quantum spin chains, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly (provably NP-hard). Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in fresh new contexts.

      2/14/2019Nike Sun (MIT)Title: Capacity lower bound for the Ising perceptron

      Abstract: The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results.

      2/21/2019Michael Loss (Georgia Tech)Title: Some results for functionals of Aharonov-Bohm type

      Abstract: In this talk I present some variational problems of Aharonov-Bohm type, i.e., they include a  magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a  variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.

      3/6/2019

      4:15pm

      Science Center 411

      Ilya Kachkovskiy (Michigan State University)Title: Localization and delocalization for interacting 1D quasiperiodic particles.

      Abstract: We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large coupling localization depends on symmetries of the single-particle potential. If the potential has no cosine-type symmetries, then we are able to show large coupling localization at all energies, even if the interaction is not small (with some assumptions on its complexity). If symmetries are present, we can show localization away from finitely many energies, thus removing a fraction of spectrum from consideration. We also demonstrate that, in the symmetric case, delocalization can indeed happen if the interaction is strong, at the energies away from the bulk spectrum. The result is based on joint works with Jean Bourgain and Svetlana Jitomirskaya.

      3/14/2019

      5:45pm

      Science Center 232

      Anna Vershynina (University of Houston)Title: How fast can entanglement be generated in quantum systems?

      Abstract: We investigate the maximal rate at which entanglement can be generated in bipartite quantum systems. The goal is to upper bound this rate. All previous results in closed systems considered entanglement entropy as a measure of entanglement. I will present recent results, where entanglement measure can be chosen from a large class of measures. The result is derived from a general bound on the trace-norm of a commutator, and can, for example, be applied to bound the entanglement rate for Renyi and Tsallis entanglement entropies.

      3/28/2019

      Room G02

      Xuwen Chen (University of Rochester)Title: The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics

      Abstract: We derive the 3D energy-critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. We develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false sharp trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new HUFL (hierarchical uniform frequency localization) property for the GP hierarchy and use it to prove a new type of uniqueness theorem.

      4/4/2019Paul Bourgade (NYU)Title: Log-correlations and branching structures in analytic number theory

      Abstract: Fyodorov, Hiary and Keating have predicted the size of local maxima of L-function along the critical axis, based on analogous random matrix statistics. I will explain this prediction in the context of the log-correlated universality class and branching structures. In particular I will explain why the Riemann zeta function exhibits log-correlations, and outline the proof for the leading order of the maximum in the Fyodorov, Hiary and Keating prediction. Joint work with Arguin, Belius, Radziwill and Soundararajan.

      4/9/2019

      Tuesday

      12:00pm

      Room G02

      Giulio Biroli (ENS Paris)Title: Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices

      Abstract: I consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. I will show how to obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $\theta>1$, in large deviations characterized by a small value of $u$, i.e. $u<1-1/\theta$, the second-largest eigenvalue pops out from the Wigner semi-circle and the associated eigenvector orients in the direction corresponding to the rank-one perturbation. These results can be generalized to the Wishart Ensemble, and extended to the first $n$ eigenvalues and the associated eigenvectors.

      Finally, I will discuss motivations and applications of these results to the study of the geometric properties of random high-dimensional functions—a topic that is currently attracting a lot of attention in physics and computer science.

      4/11/2019Rui Han (Georgia Tech)Title: Spectral gaps in graphene structures

      Abstract: We present a full analysis of the spectrum of graphene in magnetic fields with constant flux through every hexagonal comb. In particular, we provide a rigorous foundation for self-similarity by showing that for irrational flux, the spectrum of graphene is a zero measure Cantor set. We also show that for vanishing flux, the spectral bands have nontrivial overlap, which proves the discrete Bethe-Sommerfeld conjecture for the graphene structure. This is based on joint works with S. Becker, J. Fillman and S. Jitomirskaya.

      4/25/2019Benjamin Fehrman (Oxford)Title:  Pathwise well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

      Abstract:  We present a pathwise well-posedness theory for stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise.  Such equations arise in the theory of mean field games, approximate the Dean-Kawasaki equation in fluctuating fluid dynamics, describe the fluctuating hydrodynamics of the zero range process, and model the evolution of a thin film in the regime of negligible surface tension.  Motivated by the theory of stochastic viscosity solutions, we pass to the equation’s kinetic formulation, where the noise enters linearly and can be inverted using the theory of rough paths. The talk is based on joint work with Benjamin Gess.

      4/30/2019TBATBA
      5/2/2019Jian Ding (UPenn)TBA

      2017-2018

      Date…………Name…………….Title/Abstract
      2-16-20183:30pm

      G02

      Reza Gheissari (NYU)Dynamics of Critical 2D Potts ModelsAbstract: The Potts model is a generalization of the Ising model to $q\geq 3$ states with inverse temperature $\beta$. The Gibbs measure on $\mathbb Z^2$ has a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the phase transition is continuous while when $q>4$, the phase transition is discontinuous and the disordered and ordered phases coexist.

      We will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat bath/Metropolis) for the 2D Potts model, where the mixing time on an $n \times n$ torus should transition from $O(\log n)$ at high temperatures to $\exp(c_\beta n)$ at low temperatures, via a critical slowdown at $\beta_c(q)$ that is polynomial in $n$ when $q \leq 4$ and exponential in $n$ when $q>4$.

      2-23-20183:30pm

      G02

      Mustazee Rahman (MIT)On shocks in the TASEPAbstract: The TASEP particle system runs into traffic jams when the particle density to the left is smaller than the density to the right. Macroscopically, the particle density solves Burgers’ equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP shock whereby we identify the microscopic fluctuations around the shock by using exact formulas for the correlation functions of TASEP and its KPZ scaling limit. The resulting laws are related to universal laws of random matrix theory.

      For the curious, here is a video of the shock forming in Burgers’ equation:

      4-20-20182:00-3:00pmCarlo Lucibello(Microsoft Research NE)The Random Perceptron Problem: thresholds, phase transitions, and geometryAbstract: The perceptron is the simplest feedforward neural network model, the building block of the deep architectures used in modern machine learning practice. In this talk, I will review some old and new results, mostly focusing on the case of binary weights and random examples. Despite its simplicity, this model provides an extremely rich phenomenology: as the number of examples per synapses is increased, the system undergoes different phase transitions, which can be directly linked to solvers’ performances and to information theoretic bounds. A geometrical analysis of the solution space shows how two different types of solutions, akin to wide and sharp minima, have different generalization capabilities when presented with new examples.  Solutions in dense clusters generalize remarkably better,  partially closing the gap with Bayesian optimal estimators.  Most of the results I will present were first obtained using non rigorous techniques from spin glass theory and many of them haven’t been rigorously established yet,  although some big steps forward have been taken in recent years.
      4-20-20183:00-4:00pmYash Despande(MIT)Phase transitions in estimating low-rank matricesAbstract: Low-rank perturbations of Wigner matrices have been extensively studied in random matrix theory; much information about the corresponding spectral phase transition can be gleaned using these tools. In this talk, I will consider an alternative viewpoint based on tools from spin glass theory, and two examples that illustrate how these they yield information beyond traditional spectral tools. The first example is the stochastic block model,where we obtain a full information-theoretic picture of estimation. The second example demonstrates how side information alters the spectral threshold. It involves a new phase transition that interpolates between the Wigner and Wishart ensembles.
      DateNameTitle/Abstract
      9-27-17Herbert Spohn, Technische Universität MünchenHydrodynamics of integrable classical and quantum systems

      Abstract:  In the cold atoms community there is great interest in developing Euler-type hydrodynamics for one-dimensional integrable quantum systems, in particular with application to domain wall initial states.  I provide some mathematical physics background and also compare with integrable classical systems.

      10-23-17

      *12:00-1:00pm, Science Center 232*

       Madhu Sudan, Harvard SEASGeneral Strong Polarization

      A recent discovery (circa 2008) in information theory called Polar Coding has led to a remarkable construction of error-correcting codes and decoding algorithms, resolving one of the fundamental algorithmic challenges in the field. The underlying phenomenon studies the “polarization” of a “bounded” martingale. A bounded martingale, X_0,…,X_t,…  is one where X_t in [0,1]. This martingale is said to polarize if Pr[lim_{t\to infty} X_t \in {0,1}] = 1. The questions of interest to the results in coding are the rate of convergence and proximity: Specifically, given epsilon and tau > 0 what is the smallest t after which it is the case that Pr[X_t in (tau,1-tau)] < epsilon? For the main theorem, it was crucial that t <= min{O(log(1/epsilon)), o(log(1/tau))}. We say that a martingale polarizes strongly if it satisfies this requirement. We give a simple local criterion on the evolution of the martingale that suffices for strong polarization. A consequence to coding theory is that a broad class of constructions of polar codes can be used to resolve the afore-mentioned algorithmic challenge.

      In this talk I will introduce the concepts of polarization and strong polarization.  Depending on the audience interest I can explain why this concept is useful to construct codes and decoding algorithms, or explain the local criteria that help establish strong polarization (and the proof of why it does so).

      Based on joint work with Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, and Atri Rudra.

      10-25-17

      *2:00-4:00pm*

      Subhabrata Sen (Microsoft and MIT)

      Noga Alon,(Tel Aviv University)

      Subhabrata Sen, “Partitioning sparse random graphs: connections with mean-field spin glasses”

      Abstract: The study of graph-partition problems such as Maxcut, max-bisection and min-bisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cut-sizes on sparse Erd\ ̋{o}s-R\'{e}nyi and random regular graphs.

      Based on joint work with Aukosh Jagannath.

      Noga Alon, “Random Cayley Graphs”

      Abstract: The study of random Cayley graphs of finite groups is related to the  investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given  group with a prescribed number of generators.  Several intriguing questions that remain open will be mentioned as well.

      11-1-17

      *2:00-4:00pm*

      Kay Kirkpatrick (Illinois)

      and

      Wei-Ming Wang (CNRS)

      Kay Kirkpatrick, Quantum groups, Free Araki-Woods Factors, and a Calculus for Moments

       Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to free Araki-Woods factors, and cases where we have surprisingly good rates of convergence. This is joint work with Michael Brannan. Time permitting, we’ll mention another quantum central limit theorem for Bose-Einstein condensation and work in progress.

      Wei-Min Wang, Quasi-periodic solutions to nonlinear PDE’s

      Abstract: We present a new approach to the existence of time quasi-periodic solutions to nonlinear PDE’s. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a Lagrangian approach to KAM theory, as suggested by J. Moser.

      11-8-17Elchanan MosselOptimal Gaussian Partitions.

      Abstract: How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution.

      The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory.

      I will survey the little we know about this problem and the major open problems in the area.

      11-10-17

      *12pm SC 232*

      Zhe Wang (NYU)A Driven Tagged Particle in One-dimensional Simple Exclusion Process

      Abstract: We study the long-time behavior of a driven tagged particle in a one-dimensional non-nearest- neighbor simple exclusion process.  We will discuss two scenarios when the tagged particle has a speed. Particularly, for the ASEP, the tagged particle can have a positive speed even when it has a drift with negative mean; for the SSEP with removals, we can compute the speed explicitly. We will characterize some nontrivial invariant measures of the environment process by using coupling arguments and color schemes.

      11-15-17

      *4:00-5:00pm*

      *G02*

      Daniel Sussman (BU)Multiple Network Inference: From Joint Embeddings to Graph Matching

      Abstract: Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiple-network framework remains a relatively under-explored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, face-to-face interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, we’ll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching.

      11-20-17

      *Monday

      12:00-1:00pm*

       Yue M. Lu

      (Harvard)

      Asymptotic Methods for High-Dimensional Inference: Precise Analysis, Fundamental Limits, and Optimal Designs
      Abstract: Extracting meaningful information from the large datasets being compiled by our society presents challenges and opportunities to signal and information processing research. On the one hand, many classical methods, and the assumptions they are based on, are simply not designed to handle the explosive growth of the dimensionality of the modern datasets. On the other hand, the increasing dimensionality offers many benefits: in particular, the very high-dimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will mention recent work on exploiting such blessings of dimensionality via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widely-used spectral method for nonconvex signal recoveries; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and mean-field limits to analyze nonconvex optimization algorithms for high-dimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with high-dimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices.
      11-29-17David Gamarink (MIT)(Arguably) Hard on Average Constraint Satisfaction Problems

      Abstract: Many combinatorial optimization problems defined on random instances such as random graphs, exhibit an apparent gap between the optimal value, which can be estimated by non-constructive means, and the best values achievable by fast (polynomial time) algorithms. Through a combined effort of mathematicians, computer scientists and statistical physicists, it became apparent that a potential and in some cases a provable obstruction for designing algorithms bridging this gap is an intricate geometry of nearly optimal solutions, in particular the presence of chaos and a certain Overlap Gap Property (OGP), which we will introduce in this talk. We will demonstrate how for many such problems, the onset of the OGP phase transition indeed nearly coincides with algorithmically hard regimes. Our examples will include the problem of finding a largest independent set of a graph, finding a largest cut in a random hypergrah, random NAE-K-SAT problem, the problem of finding a largest submatrix of a random matrix, and a high-dimensional sparse linear regression problem in statistics.

      Joint work with Wei-Kuo Chen, Quan Li, Dmitry Panchenko,  Mustazee Rahman, Madhu Sudan and Ilias Zadik.

      12-6-17

      *2:00-4:00pm*

      Philippe Rigollet (MIT)

      2-3 pm

      &

      Ankur Moitra (MIT)

      3-4 pm

      Philippe Rigollet (MIT), Exact Recovery in the Ising Block Model 

      Abstract: Over the past fifteen years, the problem of learning Ising models from independent samples has been of significant interest in the statistics, machine learning, and statistical physics communities. Much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models, primarily in the case where the interaction graph is sparse. In parallel, stochastic blockmodels have played a more and more preponderant role in community detection and clustering as an average case model for the minimum bisection model. In this talk, we introduce a new model, called Ising blockmodel for the community structure in an Ising model. It imposes a block structure on the interactions of a dense Ising model and can be viewed as a structured perturbation of the celebrated Curie-Weiss model. We show that interesting phase transitions arise in this model and leverage this probabilistic analysis to develop an algorithm based on semidefinite programming that recovers exactly the community structure when the sample size is large enough. We also prove that exact recovery of the block structure is actually impossible with fewer samples.

      This is joint work with Quentin Berthet (University of Cambridge) and Piyush Srivastava (Tata Institute).

      Ankur Moitra (MIT), A New Approach to Approximate Counting and Sampling 

      Abstract: Over the past sixty years, many remarkable connections have been made between statistical physics, probability, analysis and theoretical computer science through the study of approximate counting. While tight phase transitions are known for many problems with pairwise constraints, much less is known about problems with higher-order constraints.
      Here we introduce a new approach for approximately counting and sampling in bounded degree systems. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random. In our setting, the solution space is not even connected and we introduce alternatives to the usual Markov chain paradigm.

      12-14-17TBD
      DateNameTitle
      09-16-2015Scott Aaronson, MITBosonSampling and the Permanents of Gaussian Matrices
      09-23-2015Xin Sun, MITAlmost sure multi fractal spectrum of SLE
      09-28-2015Li-Cheng Tsai, StanfordKPZ equation limit of interacting particle systems
      09-30-2015Kyle Luh, YaleRandom Matrices: l1 Concentration and Dictionary Learning with Few Samples
      10-07-2015Martin Zirnbauer, Cologne/Simons CenterBott periodicity and the “Periodic Table” of topological insulators and superconductors
      10-14-2015Benjamin Schweinhart, Harvard CMSAUniversality Conjectures for Curvature Flow on Graphs
      10-21-2015Nicholas Cook, UCLA
      10-28-2015Vu-Lan Nguyen, Université Paris DiderotVariants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer
      11-04-2015Vadim Gorin, MITLargest eigenvalues in random matrix beta-ensembles: structures of the limit.
      11-18-2015Louis-Pierre Arguin, CUNYThe maximum of the characteristic polynomial of random unitary matrices 
      11-19-2015Nicholas Zygouras, Univ. of WarwickFrom disorder relevance to the 2d Stochastic Heat Equation
      11-25-2015ThanksgivingNo seminar
      12-02-2015Eero Saksman (Helsinki)The uniqueness of Gaussian multiplicative chaos revisited
      12-04-2015Guillaume Barraquand, ColumbiaRandom walks in Beta random environment
      01-27-2016Louigi Addario-Berry, McGillSlowdown of the front for branching Brownian motion with decay of mass
      02-03-2016Antti Knowles, ETH ZurichAn optimal rotational invariant estimator for general covariance matrices
      02-10-2016No Seminar this week
      02-17-2016Florent Bekerman, MITTransport Methods and Universality for beta-matrix models
      02-24-2016Aukosh Jagannath, Courant InstituteThe Parisi variational problem
      03-02-2016No Seminar this weekTwo next week
      03-09-2016Adam Marcus, PrincetonPolynomials and (finite) free probability
      03-11-2016Hao Shen, ColumbiaThe Sine-Gordon stochastic PDE and regularity structures
      03-16-2016Spring Recess
      03-23-2016Zeev Rudnick, Tel-Aviv and IASQuantum chaos, eigenvalue statistics and the Fibonacci sequence
      03-30-2016Nikolai Makarov, CaltechRandom normal matrices with hard edge spectrum
      04-06-2016Timo Seppalainen, WisconsinVariational formulas and Busemann functions for random paths in a random medium
      04-11-2016 (Science Center 530)Milton D. Jara, IMPAAround the strong KPZ universality conjecture
      04-20-2016Mark Rudelson, MichiganDelocalization of eigenvectors of random matrices
      04-27-2016Marek Biskup, UCLALocal limit theory for extreme values of 2D Discrete Gaussian Free Field
      05-04-2016No Talk
      05-11-2016 (2:30-3:30pm, Room G10)Laure Saint-Raymond, École Normale SupérieureFluctuating dynamics for a 2D rarified gas of hard disks
      06-01-2016Jun Yin, University of WisconsinGeneralized Circular Law
      06-08-2016Paul Bourgade, NYUExtremes of random matrices and log-correlated fields
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Aghil Alaee, Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form.

      The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      2/10/2022Tin Yau Tsang (UC Irvine)Title: Dihedral ridigity and mass

      Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

      2/17/2022Shiraz Minwalla
      (Tata Institute of Fundamental Research, Mumbai)
      Title: Black Hole dynamics at Large D

      Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

      2/24/2022Achilleas Porfyriadis
      (Harvard Black Hole Initiative)
      Title: Extreme Black Holes: Anabasis and Accidental Symmetry

      Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2) transformation properties of the spherically symmetric linear perturbations of
      AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of  AdS_2.

      3/10/2022David Fajman (University of Vienna)Title: The Einstein-flow on manifolds of negative curvature

      Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.
      3/21/2022Prof. Arick Shao (Queen Mary University of London)Title: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

      Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

      In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

      This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

      3/24/2022Qian Wang, University of OxfordTitle: Rough solutions of the $3$-D compressible Euler equations

      Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

      3/28/2022Emanuele Berti, Johns Hopkins UniversityTitle: Black Hole Spectroscopy

      Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

      4/7/2022CMSA General Relativity Conference
      4/14/2022Chao Liu, Huazhong University of Science and TechnologyTitle: Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4

      Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

      4/21/2022Jinhua Wang,
      Xiamen University
      Title: Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system

      Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

      4/28/2022Allen Fang, Sorbonne UniversityTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

      Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/10/2021

      (10:30am – 11:30am (Boston time)

      Philippe G. LeFloch, Sorbonne University and CNRSTitle: Asymptotic localization, massive fields, and gravitational singularities

      Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

      9/17/2021

      (10:30am – 11:30am (Boston time)

      Igor Rodnianski, Princeton UniversityTitle: Stable Big Bang formation for the Einstein equations

      Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

      9/24/2021

      (10:30am – 11:30am (Boston time)

      Alex LupsascaTitle: On the Observable Shape of Black Hole Photon Rings

      Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

      10/1/2021

      (10:30am – 11:30am (Boston time)

      Zhongshan An, University of ConnecticutTitle: Static vacuum extensions of Bartnik boundary data near flat domains

      Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

      10/8/2021

      (10:30am – 11:30am (Boston time)

      Xiaoning Wu, Chinese Academy of SciencesTitleCausality Comparison and Postive Mass

      Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

      10/15/2021

      (10:30am – 11:30am (Boston time)

      Jiong-Yue Li, Sun Yat-Sen UniversityTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations

      Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

      10/22/2021

      (11:00am – 12:30pm (Boston time)

      Roberto Emparan, University of BarcelonaTitleThe Large D Limit of Einstein’s Equations

      Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

      10/28/2021Jorge Santos, University of CambridgeTitle: The classical interior of charged black holes with AdS asymptotics

      Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

      11/4/2021
      at 10 am ET
      Elena Giorgi, Columbia UniversityTitle: The stability of charged black holes

      Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

      11/11/2021
      *9:30 am ET*
      Siyuan Ma, Sorbonne UniversityTitle: Sharp decay for Teukolsky equation in Kerr spacetimes

      Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

      11/19/2021

      (10:30–11:30 am ET)

      Nishanth Gudapati, Clark UniversityTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes

      Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

      12/2/2021Professor Geoffrey Comp
      ére, Université Libre de Bruxelles
      Title: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger

      Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

      12/16/2021Xinliang An, University of SingaporeTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation

      Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker: Yifan Wang (NYU)

      Title: Fusion Category Symmetries in Quantum Field Theory

      Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti

      ble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

    • Swampland Seminar
      10:30 am-12:00 pm
      12/01/2024

      During the 2021-22 academic year, the CMSA will be co-hosting a seminar on Swampland, with the Harvard Physics Department, organized by Miguel Montero, Cumrun Vafa, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend, please subscribe here.

      Talks will be posted on the Swampland Seminars YouTube channel. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/31/2022Rafael Álvarez-García (DESY Hamburg)Title: Membrane Limits in Quantum Gravity
      2/7/2022Du Pei (Harvard CMSA)Title: Holomorphic CFTs and topological modular forms

      Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

      2/28/2022 Tom Rudelius (UC, Berkeley)Title: Generalized Global Symmetries and the Weak Gravity Conjecture
      3/7/2022Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)Title: 4d strings at strong coupling
      3/21/2022Patrick Draper (Univ. of Illinois) and Alvaro Herraez (IPhT Saclay).Open Mic Discussion
      Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)
      3/28/2022Fernando Quevedo (Cambridge)Title: On renormalisation group induced moduli stabilisation and brane-antibrane inflation

      Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

      4/5/2022Simon Caron-Huot (McGill University) and Julio Parra (Caltech)Title: Causality constraints on corrections to Einstein gravity

      Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

      4/11/2022Timm Wrase and Eduardo Gonzalo (Lehigh)Title: Type IIB flux compactifications with $h^{1,1}=0$

      Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

      4/18/2022José Calderón (IFT Madrid)Open mic Swampland Discussion

      Topic: Cobordism

      5/9/2022Georges Obie (Harvard)Title: Inflation and light Dark Matter constraints from the Swampland

      Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/13/2021John Stout (Harvard)Title: Decoding Divergent Distances

      Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

      9/20/2021Manki Kim (MIT)Title: Small Cosmological Constants in String Theory

      Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

      9/27/2021Eran Palti (Ben Gurion)Title: Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

      Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

      10/18/2021Thomas Van Riet (KU Leuven)Title: The Festina Lente Bound

      Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for  phenomenology, both top-down and bottom-up.

      10/25/2021Joe Conlon (Oxford)Title: Exploring the Holographic Swampland

      Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

      11/01/2021Pieter Bomans (Princeton)Title: Bubble instability of mIIA on AdS_4 x S^6

      Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

      11/15/2021Nima Arkani-Hamed (IAS), and Gary Shiu (UW-Madison) This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be Swampland constraints, Unitarity and Causality. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.
      11/22/2021Thomas Grimm (Utrecht University)Title: Taming the Landscape

      Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

      11/29/2021Timm Wrase (Lehigh University)Title: Scale separated AdS vacua?

      Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

      12/6/2021Lars Aalsma (University of Wisconsin-Madison)Title: Extremal Black Hole Corrections from Iyer-Wald

      Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024

      Speaker: Michail Savvas, UT Austin

      Title: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds

      Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
      In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

      Organizer: Seminars
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      peaker: Ady Stern & David Mross (Weizmann)

      Speaker: Ady Stern & David Mross (Weizmann

      Title: The nu=5/2 enigma: Recent insights from theory and experiment

      Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:30 pm
      12/01/2024

       

      Nathanan Tantivasadakarn (Harvard)

      Video

      TitleHybrid Fracton Orders

      Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

      Based on 2102.09555 and 2106.03842

       

       

       

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024
      CMSA-QMMP-12.01.21-1544x2048

      Speaker: Daniel Harlow (MIT)

      Title: Symmetry in quantum field theory and quantum gravity 1

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

    • Quantum Matter
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-11.24.21-1583x2048

      Speaker: Shinsei Ryu (Princeton University)

      Title: Multipartitioning topological phases and quantum entanglement

      Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024

      Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
      In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      2/3/2021 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-11:30 am
      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      10:30 am-11:30 am
      12/01/2024
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:30 pm
      12/01/2024
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      5/21/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      5/28/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      2/20/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • General Relativity Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10/9/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      9/10/18 Topology Seminar
      10:30 am-12:00 am
      12/01/2024-09/11/2018
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      10:30 am
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      12/01/2024
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      4/24/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      4/25/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      4/26/2019 Topology
      10:30 am-12:40 pm
      12/01/2024
    • Seminars
      10:30 am-11:42 am
      12/01/2024
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      9/13/2019 General Relativity
      10:30 am-11:30 am
      12/01/2024
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      9/18/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      9/20/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      9/25/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10/2/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      10/11/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
    • Seminars
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      2/13/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      10/16/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      10/18/2019 General Relativity
      10:30 am-11:30 am
      12/01/2024
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      General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      10/30/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      11/1/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      11/6/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      11/8/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
    • Seminars
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      11/13/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      11/27/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      12/11/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      2/06/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • General Relativity Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      6/18/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      7/9/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/16/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/17/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-12/23/2020
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-01/29/2021
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker:  Jaume Gomis (Perimeter PI)

      Title: Global Anomalies on the Hilbert Space

      Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers” that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker:  Xiao-Gang Wen (MIT)

      Title: A solution to the chiral fermion problem

      Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-02/25/2021
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-02/26/2021
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/7/2020 Math Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-03/18/2021

      Speaker: Silviu Pufu (Princeton University)

      Title: Exact symmetries and threshold states in two-dimensional models for QCD

      Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of confinement in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
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      unnamed-3-600x338

      In the 2020-2021 academic year, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom.

      Cuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator, several fascinating phases emerge, including a d-wave superconductor, a pseudo-gap metal, and strange metal. After intensive studies from experimental, theoretical, and numerical communities for more than three decades, remarkable progress has been made, but basic questions remain:

      1. What is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling, spin fluctuations, or resonating-valence-bonds?
      2. How do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters, or do we need an unconventional picture involving fractionalization?
      3. Is the strange metal at optimal doping associated with a quantum critical point? And if so, what is the driving force of this phase transition?

      The cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics, such as quantum spin liquids, topological order, and non-Fermi liquids. In the coming years, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series, we hope to accelerate this process by bringing together deeper conversations between experimental, theoretical, and numerical experts with different backgrounds and perspectives.

      The Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar.

      Seminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard).

      Scientific program advisors: Professor Subir Sachdev (Harvard), Professor Patrick Lee (MIT).

      In order to learn how to attend this series, please fill out this form.

      For more information, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu)

      Spring 2022

      April 20, 2022 | 11:30 – 1:00 pm ET

      Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)

      Title: Superconductivity in infinite-layer nickelates

      Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.


      February 3, 2022 | 11:30 – 1:00 pm ET

      Lu Li (U Michigan)

      Title: Quantum Oscillations of Electrical Resistivity in an Insulator

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

      2020 – 2021

      September 2, 2020 | 10:30am ET

      Sachdev
      Subir Sachdev (Harvard)

      TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

      Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
      describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

      Video

      September 23, 2020 | 10:30am ET

      Sachdev
      Subir Sachdev (Harvard)

      Title: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II

      Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

      Video

      September 24, 2020 | 12:00pm ET

      hqdefault
      Inna Vishik (University of California, Davis)

      Title: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video

      October 15, 2020 | 10:30am ET

      unnamed
      Louis Taillefer (Université de Sherbrooke)

      TitleNew signatures of the pseudogap phase of cuprate superconductors

      Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

      Video

      October 28, 2020 | 10:30am ET

      lee_patrick
      Patrick Lee (MIT)

      Title: The not-so-normal normal state of underdoped Cuprate

      Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

      Video

      November 6, 2020 |12:30pm ET

      Shen
      Zhi-Xun Shen (Stanford University)

      Title: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors

      Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
      Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
      magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
      (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
      experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

      [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
      [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
      [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
      [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
      [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
      [6] A. Lanzara et al., Nature 412, 510 (2001)
      [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
      [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
      [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
      [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
      [11] A.G. Loeser et al., Science 273, 325 (1996)
      [12] S. Chen et al., Science, 366, 6469 (2019)
      [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
      [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
      [15] Yu He et al., Science, 362, 62 (Oct. 2018)
      [16] Z. Chen, Y. Wang et al., preprint, 2020

      Video

      November 12, 2020 |10:30am ET

      Chandra-Varma
      Chandra Varma (Visting Professor, University of California, Berkeley.
      Emeritus Distinguished Professor, University of California, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:
      1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
      2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
      3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
      4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting,
      (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
      (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
      (iii) Problems.Video

      November 18, 2020 |10:30am ET

      download
      Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

      Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

      Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

      Video

      November 19, 2020 |10:30am ET

      Fradkin
      Eduardo Fradkin (University of Illinois at Urbana-Champaign)

      Title: Pair Density Waves and Intertwined Orders in High Tc Superconductors

      Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

      Video

      November 25, 2020 |10:30am ET

      Si-1coborc
      Qimiao Si (Rice University)

      Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

      Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

      December 2, 2020 |10:30am ET

      Chubukov
      Andrey Chubukov (University of Minnesota)

      Title: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

      Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

      December 9, 2020 |10:30am ET

      Hsieh
      David Hsieh (Caltech)

      Title:  Signatures of anomalous symmetry breaking in the cuprates  

      Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
      [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

      [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516

      December 16, 2020 |10:30am ET

      weng
      Zheng-Yu Weng (Tsinghua University)

      TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

      Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

      December 17, 2020 |10:30am ET

      60cf9077a3c10b1135231e866012bda8
      Steven Kivelson (Stanford University)

      Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

      Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.

      January 20, 2021 |10:30am ET

      Devereaux
      Thomas Peter Devereaux (Stanford University)

      Title:  Numerical investigations of models of the cuprates

      Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

      I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

      February 3, 2021 |10:30am ET

      viewphoto
      Philip Phillips (University of Illinois Urbana-Champaign)

      Title: Beyond BCS: An Exact Model for Superconductivity and Mottness

      Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
      [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

      February 10, 2021 |10:30am ET

      todadri_senthil
      Senthil Todadri (MIT)

      Title: Strange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

      Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
      [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.07896
      [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

      April 1, 2021 |9:00am ET

      weng
      Naoto Nagaosa (University of Tokyo)

      TitleApplied physics of high-Tc theories

      Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

      April 22, 2021 |10:30am ET

      lee
      Dung-Hai Lee (UC Berkeley)

      Title: “Non-abelian bosonization in two and three spatial dimensions and some applications”

      Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.

      May 12, 2021 |10:30am ET

      weng
      André-Marie Tremblay (Université de Sherbrooke)

      Title: A unified theoretical perspective on the cuprate phase diagram

      Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

      August 11, 2021 |10:30am ET

      image
      Piers Coleman (Rutgers)

      Title: Order Fractionalization*

      Abstract: I will discuss the interplay of spin fractionalization with broken
      symmetry. When a spin fractionalizes into a fermion, the resulting particle
      can hybridize or pair with the mobile electrons to develop a new kind of
      fractional order parameter. The concept of “order fractionalization” enables
      us to extend the concept of off-diagonal order to encompass the formation of
      such order parameters with fractional quantum numbers, such as spinorial
      order[1].
      A beautiful illustration of this phenomenon is provided by a model
      which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This
      model explicitly exhibits order fractionalization and is expected to undergo a
      discrete Ising phase transition at finite temperature into an
      order-fractionalized phase with gapless Majorana excitations.
      The broader implications of these considerations for Quantum
      Materials and Quantum Field Theory will be discussed.
      Work done in collaboration with Yashar Komijani, Anna Toth and Alexei
      Tsvelik.
      [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018).
      [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

      September 15, 2021 |10:30am ET

      0049_7858_headshot-scaled-aspect-ratio-420-334-2-scaled-840x668-c-default
      Liang Fu (MIT)

      Title: Three-particle mechanism for pairing and superconductivity

      Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

      [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
      [2] V. Crepel and L. Fu, arXiv:2103.12060
      [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

      September 29, 2021 |11:30am ET (special time)

      Ong
      Nai Phuan Ong (Princeton University)

      Title:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al., Nature Physics 17, 915 (2021).Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

      Date TBA |10:30am ET

      image_normal
      Suchitra Sebastian (University of Cambridge)

      Title: TBA

      Date TBA |10:30am ET

      hoffman
      Jenny Hoffman (Harvard University)

      Title: TBA

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/14/2020 Mathematical Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/21/2020 Math-Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      9/23/2020 Strongly Correlated Quantum Materials Series
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/1/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/05/2020 Math Physics Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/25/2020 Strongly Correlated Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/19/2020 Math Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      10/28/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/9/2020 Math-Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/12/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/18/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/19/20 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-12.02.21-1544x2048-1

      Speaker: Daniel Harlow (MIT)

      Title: Symmetry in quantum field theory and quantum gravity 2

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/2/2020 Math-Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Xueyang Song (MIT)

      Title: Phase transitions out of quantum Hall states in moire TMD bilayers

      Abstract: Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\’e Transition Metal Dichalcogenide (TMD) bilayers, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth.  At filling -2/3, we describe a direct transition between the FQAH state and a Charge Density Wave (CDW) insulator. The critical theory resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by  Barkeshli and McGreevy.   Crucially we show that translation symmetry alone is enough to enable a second order CFL-FL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order.  A striking signature is a universal jump of resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFL-FL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist.  We also present a critical theory for the CFL to FL transition at filling -3/4.  Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-04.06.2022-1583x2048-1

      Youtube Video

       

      Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024
      CMSA QMMP 02.17.23

      Quantum Matter Seminar

      Speaker: Rahul Sahay (Harvard)

      Title: Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics

      Abstract: While many-body quantum systems can in principle host exotic quantum spin liquid (QSL) states, realizing them as ground states in experiments can be prohibitively difficult. In this talk, we show how non-equilibrium dynamics can provide a streamlined route toward creating QSLs. In particular, we show how a simple Hamiltonian parameter sweep can dynamically project out condensed anyons from a family of initial product states (e.g. dynamically “un-Higgs”), yielding a QSL-like state. We christen such states “quantum spin lakes” which, while not thermodynamically large QSLs, enable their study in NISQ-era quantum simulators. Indeed, we show that this mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. Time permitting, we will discuss how our theory motivates a tree tensor network-based numerical tool—reliant on our theory—that quantitatively reproduces the experimental data two orders of magnitude faster than conventional brute-force simulation methods. Finally, we will highlight that even spin liquid states that are unstable in equilibrium—namely, 2 + 1D U(1) spin liquid states—can be robustly prepared by non-equilibrium dynamics.

       

      https://www.youtube.com/watch?v=ECT9nozk2SY&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=15

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Professor Harvey Reall (University of Cambridge) 

      Title: The second law of black hole mechanics in effective field theory

      Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs.

      Video
    • Quantum Matter
      10:30 am-12:30 pm
      12/01/2024

      Speaker: Kenichi Konishi (UNIPI.IT)

      Title: Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: Recent developments

      Abstract: After many years of efforts, still very little is known today about the physics of strongly-coupled chiral gauge theories in four dimensions, in spite of an important role they might play in the physics of fundamental interactions beyond the standard SU(3)xSU(2)xU(1) model. This is in stark contrast with the vectorlike gauge theories for which we have many solid results, thanks to some exact theorems, to the lattice simulation studies, to the Seiberg-Witten exact solution of N=2 supersymmetric gauge theories, and last, but not the least, to the real-world strong-interaction phenomenology and experimental tests of Quantum Chromodynamics.

      The purpose of this seminar is to discuss the results of our recent efforts to improve the understanding of the strongly-coupled chiral gauge theories. Among the main tools of analysis are the consideration of anomalies. We use both the conventional ’t Hooft anomaly-matching ideas, and new, more stringent constraints coming from the generalized anomalies involving some higher-form symmetries. Also, the so-called strong anomalies, little considered in the context of chiral gage theories, are found to carry significant implications.

      As the playground we study several classes of SU(N) gauge theories, the so-called Bars-Yankielowicz models, the generalized Georgi-Glashow models, as well as a few other simple theories with the fermions in complex, anomaly-free representations of the color SU(N).

      Color-flavor-locked dynamical Higgs phase and dynamical Abelianization, emerge, among others, as two particularly interesting possible phases the system can flow into in the infrared, depending on the matter fermion content of the model.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Sheldon Katz, UIUC

      Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants

      Abstract:  A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3.  These X are nodal CY threefolds which do not admit a projective small resolution.  B-model techniques can be applied to compute GV invariants up to g \le 32.  This raises the question: what is the geometric meaning of these invariants?

      Evidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by Kuznetsov.  One of these moduli stacks is a stacky small resolution X’ of X itself.  This leads to another geometric interpretation of the invariants as being associated with moduli of sheaves on X’ twisted by a Brauer class.  Geometric computations based on these working definitions always agree with the B-model computations.

      This talk is based on joint work with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe.

       

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Speaker: Seth Koren (University of Chicago)

      Title: Baryon Minus Lepton Number BF Theory for the Cosmological Lithium Problem

      Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+  3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      unnamed-file

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024

      Topological Quantum Matter Seminar

      Speaker: Amanda Young, UIUC

      Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential

      Abstract: Haldane pseudopotentials were first introduced as Hamiltonian models for the fractional quantum Hall effect, and it has been long expected that they should exhibit the characteristic properties of this exotic phase of matter, including a spectral gap above the ground state energy. We will discuss recent work that verified this gap conjecture for a truncated version of the 1/3-filled Haldane pseudopotential in the cylinder geometry. Numerical evidence suggested that for open boundary conditions the gap of the truncated model closes as the cylinder radius converges to zero and that this closure is due to the presence of edge modes; in contrast, for periodic boundary conditions, the gap remains robustly order one in the same radius limit. The standard scheme for applying spectral gap estimating techniques to the model with periodic boundary conditions, though, produces a lower bound on the bulk gap that still reflects the energy of the edge modes. To obtain an estimate on the bulk gap that reflects its true behavior, a new gap estimating strategy was developed. By customizing the spectral gap method to key invariant subspaces of the Hamiltonian, we are able to successfully avoid the edge states and produce a more accurate lower bound on the bulk gap. In this talk, we discuss this invariant subspace strategy for proving bulk gaps in the presence of edge states. This is based off joint work with S. Warzel.

       

       

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-04.28.22-1583x2048

      Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Superconductivity in infinite-layer nickelates
      10:30 am-1:00 pm
      12/01/2024
      CMSA-Strongly-Correlated-Quantum-Materials-and-High-Temperature-Superconductors-04.20.21-1583x2048

      Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Thorsten Schimannek (Utrecht University)

      Title: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants

      Abstract: The physics of M-theory and Type IIA strings on a projective nodal CY 3-folds is determined by the geometry of a small resolution, even if the latter is not Kähler. We will demonstrate this explicitly in the context of a family of Calabi-Yau double covers of P^3. Using conifold transitions, we prove that the exceptional curves in any small resolution are torsion while M-theory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary Gopakumar-Vafa invariants, that is associated to the singular Calabi-Yau and captures the enumerative geometry of the non-Kähler resolutions. We further argue that twisted circle compactifications of the 5d theory are dual to IIA compactifications on the nodal CY 3-fold with a flat but topologically non-trivial B-field. As a result, the torsion refined invariants are encoded in the topological string partition functions with different choices for the global topology of a flat B-field.

      The talk is based on 2108.09311, 2212.08655 (with S. Katz, A. Klemm, and E. Sharpe) and 2307.00047 (with S. Katz).

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: An Huang (Brandeis)

      Pre-talk Speaker: TBA: 10:00-10:30 am

      Title: A p-adic Laplacian on the Tate curve

      Abstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.30.2022-1583x2048-1

      Youtube Video

       

      Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy.  This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport.  We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation.  Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem.  The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories.  Our techniques generalize to other RG flow equations beyond Polchinski’s.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 09.15.22
      General Relativity Seminar
      Title: The Gregory-Laflamme instability of black strings revisited
       
      Abstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string.
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA GR Seminar 04.27.23

      General Relativity Seminar

      Speaker: Philippe G. LeFloch, Sorbonne University and CNRS

      Title: The localized seed-to-solution method for the Einstein constraints

      Abstract: I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set, we define a “localized seed-to-solution” map, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly, as we prove it, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis, we discover the notion of ‘asymptotic modulators’, as we call them, or “correctors” to the standard ADM invariants.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.23.2022-1583x2048

      Youtube Video

       

      Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.16.2022-1544x2048-1

      Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv  2201.00903.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker: Petr Hořava (UC Berkeley)

      Title: Topological Quantum Gravity and the Ricci Flow – Part I

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-02.16.2022-1544x2048

      Speaker: Petr Hořava (UC Berkeley)

      Title: Topological Quantum Gravity and the Ricci Flow – Part I

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Jonah Herzog-Arbeitman, Princeton University

      Title: Exact Results in Flat Band Hubbard Models

      Abstract: Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multi-orbital case: the mean-field theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and low-energy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution reveals the importance of quantum geometry in escaping (some of) BCS phenomenology within a tractable and nontrivial strong coupling theory.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.09.2022-1544x2048-1

      Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Pre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am

      Speaker: Kai Xu (CMSA)

      Title: Motivic decomposition of moduli space from brane dynamics

      Abstract: Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.02.2022-1544x2048

      Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Ho Tat Lam, MIT

      Title: Dipolar and modulated symmetry protected topological phases

      Abstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-02.24.2022-1544x2048-1

      Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Maksym Fedorchuk (Boston College)

      Title: CM-minimizers and standard models of Fano fibrations over curves

      Abstract: A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of K-stable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CM-minimizers without base change. In answering this question, we arrive at a theory of Koll\’ar stability for fibrations over one-dimensional bases, and standard models of Fano fibrations. I will explain the joint work with Hamid Abban and Igor Krylov in which we show that the CM-minimizers for del Pezzo fibrations are Corti’s standard models and related work in progress on quartic threefold hypersurfaces.

       

    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Ho Tat Lam (MIT)

      Title: Non-invertible Symmetry Enforced Gaplessness

      Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

       

      https://www.youtube.com/watch?v=A-47aZ4HS1k&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=16

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: David Favero, University of Minnesota

      Title: Gauged Linear Sigma Models and Cohomological Field Theories

      Abstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker.  Gauged Linear Sigma Models (GLSMs)  serve as a means of interpolating between Kahler geometry and singularity theory.  In enumerative geometry, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.   In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs.  Furthermore, we proved that these invariants form a Cohomological Field Theory.   In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss the construction of these general invariants.  Briefly, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”.  This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Professor Oscar Dias (University of Southampton)

      Title: Strong Cosmic Censorship

      Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally, I will discuss some possibilities (quantum effects, non-smooth initial data,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024

      Topological Quantum Matter Seminar

      Speaker: Shenghan Jiang, Kavli Institute for Theoretical Sciences UCAS

      Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States

      Abstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has been established that topological insulator phases persist as stable phases. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wavefunctions for numerical simulations is highly desirable.
      In this talk, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions, we write down tensor equations, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems.

       

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Naqing Xie (Fudan University)

      Title: Gravitational Wave, Angular Momentum, and Supertranslation Ambiguity
      Abstract: The supertranslation ambiguity of angular momentum is a long-standing and conceptually important issue in general relativity. Recently, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However, in the compact binary coalescence community, supertranslation ambiguity is often ignored. We have shown that, in the linearised theory of gravitational wave, the new angular momentum coincides with the classical definition at the quadrupole level. This talk is based on a recent joint work with Xiaokai He and Xiaoning Wu.
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar

      General Relativity Seminar

      Speaker: Nikolaos Athanasiou
      Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
      Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Sergei Dubovsky (New York University)
      Title: Love Symmetry of Black Holes
      Abstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2,ℝ) symmetry in the suitably defined near zone approximation. We show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2,ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2,ℝ) representations. It is this highest-weight property that forces the static Love numbers to vanish. We show that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. The Love symmetry also exhibits a peculiar UV/IR mixing.
    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024
      CMSA QMMP 02.03.23

      Quantum Matter Seminar

      Speaker: Han Yan (Rice U)

      Title: Fracton orders in hyperbolic space and its excitations with fractal mobility

      Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.

      Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

       

      https://www.youtube.com/watch?v=ekfKNCKzZyE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=17

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA GR Seminar 09.29.22

      General Relativity Seminar

      Speaker: Marcelo Disconzi, Vanderbilt University

      Title: Generalrelativistic viscous fluids
      Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.
    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Andrew Harder, Lehigh University

      Pre-talk Speaker: TBA: 10:00-10:30 am

      Title: Deformations of Landau-Ginzburg models and their fibers

      Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-12.08.21-1544x2048

      Speaker: Fei Yan (Rutgers)

      Title: Defects, link invariants and exact WKB

      Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Pengyu Le (BIMSA)

      Title: Asymptotic geometry of null hypersurface in Schwarzschild spacetime and null Penrose inequality

      Abstract: Null Penrose inequality is an important case of the well-known Penrose inequality on a null hypersurface. It conjectures the relation between the area of the outmost marginally trapped surface and the Bondi mass at null infinity. Following the proposal of Christodoulou and Sauter, we employ the perturbation method to study the asymptotic geometry of null hypersurfaces at null infinity in a perturbed vacuum Schwarzshild spacetime. We explain how to apply this perturbation theory to prove null Penrose inequality on a nearly spherically symmetric null hypersurface in a perturbed vacuum Schwarzschild spacetime.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Uri Kol, CMSA

      Title: Duality in Einstein’s Gravity

      Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-02-2016 Random Matrix & Probability Theory Seminar
      10:32 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      10:36 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-07-16 Mathematical Physics Seminar
      10:38 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      11-04-16 Special Seminar
      10:42 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      10:43 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-09-2016 Random Matrix & Probability Theory Seminar
      10:44 am
      12/01/2024

      No additional detail for this event.

    • Program
      10:44 am-11:04 am
      12/01/2024-06/12/2021
      CMSA-2-600x338

      The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

      Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

      In this course, we will start with an introduction to computer programming, algorithm, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

      The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

      This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard related perks (such as a place to live if you are in Boston over the summer.)

      However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

      If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited to 10 people, so don’t wait too long to apply.

    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Quantum Matter Seminar
      10:45 am-12:45 pm
      12/01/2024
    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Birational geometry
      10:45 am-12:15 pm
      12/01/2024
      Lecture_Shokurov-pdf

      Vyacheslav V. Shokurov (Johns Hopkins University)

      Title: Birational geometry

      Abstract: About main achievements in birational geometry during the last fifty years.

      Talk chair: Caucher Birkar

      Video

    • Seminars
      Seminars Colloquia & Seminar
      9-29-2016 Homological Mirror Symmetry Seminar
      10:46 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-08-2016 Social Sciences Applications Forum
      10:56 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-15-2016 Social Sciences Applications Forum
      10:57 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-14-16 Mathematical Physics Seminar
      10:58 am
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Rodrigo Silva, University of Maryland

      Title: Quantization of causal diamonds in 2+1 dimensional gravity

      Abstract: We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with a fixed boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that has the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required — in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham’s group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

       

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Black Hole Formation
      11:00 am-12:00 pm
      12/01/2024
      Lecture_Bieri-pdf

      Lydia Bieri (University of Michigan)

      Title: Black Hole Formation

      Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the dynamical mathematical structures of the Einstein equations. Black holes are related to the presence of trapped surfaces in the spacetime manifold. Christodoulou proved that in the regime of pure general relativity and for arbitrarily dispersed initial data, trapped surfaces form through the focusing of gravitational waves provided the incoming energy is large enough in a precisely defined way. The proof combines new ideas from geometric analysis and nonlinear partial differential equations as well as it introduces new methods to solve large data problems. These methods have many applications beyond general relativity. D. Christodoulou’s result was generalized in various directions by many authors. It launched mathematical activities going into multiple fields in mathematics and physics. In this talk, we will discuss the mathematical framework of the above question. Then we will outline the main ideas of Christodoulou’s result and its generalizations, show relations to other questions and give an overview of implications in other fields.

      Video

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Michael Freedman
      11:00 am-12:30 pm
      12/01/2024
      20bottfeatureplain-1

      20bottfeatureplain
      On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.

      This will be the third annual lecture series held in honor of Raoul Bott.

      Lecture 1
      October 4th, 11:00am (Boston time)
      Title: The Universe from a single Particle

      Abstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.

      Video

      Lecture 2
      October 5th, 11:00am (Boston time)
      Title: Controlled Mather Thurston Theorems.

      Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374  

      Video

       

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Shuaijie Qian (Harvard CMSA)

      Title: Some non-concave dynamic optimization problems in finance

      Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present our recent work on some non-concave dynamic optimization problems, where the concavification principle may not hold and the resulting value function is indeed non-concave.

      The first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation, where the average tax basis and the average mining cost serves as an approximation, respectively. This approximation results in a non-concave value function, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover, the penalty method still works and converges to the value function.

      The second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints, which makes the concavification principle invalid, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous, we introduce a new definition of viscosity solution, prove the corresponding comparison principle, and show that a monotone, stable, and consistent finite difference scheme converges to the solution of the utility maximization problem.

       

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Mauricio Romo

      Title: Quantum trace and length conjecture for hyperbolic knot

      Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Diandian Wang(Harvard University)

      Title: Pole skipping, quasinormal modes, shockwaves and their connection to chaos

      Abstract: A chaotic quantum system can be studied using the out-of-time-order correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function — that seems to also know things: things like the Lyapunov exponent and the butterfly velocity, which are important quantifiers of the OTOC. Then I will talk about a systematic way of deriving pole-skipping conditions for general holographic CFTs dual to classical bulk theories and how to use this framework to derive a few interesting statements including: (1) theories with higher spins generally violate the chaos bound; (2) the butterfly velocity calculated using pole skipping agrees with that calculated using shockwaves for arbitrary higher-derivative gravity coupled to ordinary matter; (3) shockwaves are related to a special type of quasinormal modes. As we will see, the techniques are entirely classically gravitational, which I will go through with a certain level of details.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Maria Rodriguez (Utah)

      Title: Tidal Squeezing of Black Holes

      Abstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Chethan Krishnan (IISc Bangalore)

      Title: A Smooth Horizon without a Smooth Horizon

      Abstract: I will talk about some work that is about to appear, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls, fuzzballs, Type I algebras,…)

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Alejandro Poveda

      Title: Compactness and Anticompactness Principles in Set Theory

      Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.

    • Seminars
      Seminars Colloquia & Seminar
      3/30/2020 Math Physics Seminar
      11:00 am-12:00 pm
      12/01/2024
    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      17 Oxford St, Cambridge, MA 02138

      Swampland Seminar

      Location: Jefferson Physical Laboratory, Seminar room J356

      Speaker: Markus Dierigl (LMU Munich)

      Title: IIB Explored – Dualities, Bordisms, and the Swampland

      Abstract: In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries, we discuss which defects need to be included to break them completely. Interestingly, we find many backgrounds that are well-known in the F-theory literature, such as [p,q]-7-branes, non-Higgsable clusters, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications, which I will discuss in more detail.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Damian van de Heisteeg

      Title: Light states in the interior of CY moduli spaces

      Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Lionel Mason (Oxford)

      Title: Geometry at Strong coupling for amplitudes/Wilson loops

      Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024

      General Relativity Seminar

      Speaker: Andras Vasy (Stanford)

      Title: The Feynman propagator and self-adjointness

      Abstract: In this talk I will discuss the Feynman and anti-Feynman inverses for wave operators on certain Lorentzian manifolds; these are two inverses which from a microlocal analysis perspective are more natural than the standard causal (advanced/retarded) ones. For instance, for the spectral family of the wave operator, these are the natural inverses when the spectral parameter is non-real. Indeed, I will explain that these connect to the self-adjointness of the wave operator, and the positivity properties that follow.

       

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Fernando Marchesano (IFT Madrid)

      Title: EFT strings and emergence

      Abstract: We revisit the Emergence Proposal in 4d N=2 vector multiplet sectors that arise from  type II string Calabi-Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA compactifications, where EFT strings arise from NS5-branes wrapping internal four-cycles, and consider a set of infinite-distance moduli-space limits that can be classified in terms of a scaling weight w=1,2,3. It has been shown before how one-loop threshold effects of an infinite tower of BPS particles made up of D2/D0-branes generate the asymptotic behaviour of  the gauge kinetic functions along limits with $w=3$. We extend this result to w=2 limits, by taking into account D2-brane multi-wrapping numbers. In w=1 limits the leading tower involves EFT string oscillations, and one can reproduce the behaviour of both weakly and strongly-coupled U(1)’s independently on whether the EFT string is critical or not, by assuming that charged modes dominate the light spectrum.

    • Seminars
      Seminars Colloquia & Seminar
      5/8/2020 General Relativity Seminar
      11:00 am
      12/01/2024
    • Active Matter Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter
      Active Matter Seminar
      Speaker: Shenshen Wang, UCLA
      Title:  Limit and potential of adaptive immunity
      Abstract: The adaptive immune system is able to learn from past experiences to better fit an
      unforeseen future. This is made possible by a diverse and dynamic repertoire of cells
      expressing unique antigen receptors and capable of rapid Darwinian evolution within an
      individual. However, naturally occurring immune responses exhibit limits in efficacy,
      speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical
      frameworks we developed to (1) explore functional impacts of non-equilibrium antigen
      recognition, and (2) identify conditions under which natural selection acting local in time
      can find adaptable solutions favorable in the long run, through exploiting environmental
      variations and functional constraints.
    • Seminars
      Seminars Colloquia & Seminar
      5/15/2020 General Relativity Seminar
      11:00 am
      12/01/2024
    • Probability Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA Probability Seminar 03.09.23

      Probability Seminar

      Speaker: Jean-Christophe Mourrat (ENS Lyon)

      Title: On the free energy of spin glasses with multiple types

      Abstract: In the simplest spin-glass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups, which we can visualize as forming two layers, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there, and some partial progress.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Member Seminar
      Speaker: Shai Chester
      Title: Derivation of AdS/CFT for Vector Models

      Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories, and at finite temperature.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Ben McKenna

      Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance

      Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Jake McNamara (Caltech)
      Title: Parity and Cobordism
      Abstract: The swampland cobordism conjecture provides a convenient way to discuss conserved charges associated with the topology of spacetime. However, much of the power of the cobordism conjecture comes from a mathematical black box: the Adams spectral sequence. In this talk, I will give physical meaning to this black box through a concrete example: domain walls arising from the spontaneously breaking of parity symmetry, which arise in particle physics in Nelson-Barr models. I will argue that parity domain walls are exactly stable, and interpret this stability as the result of an unusual type of gauge symmetry that can only occur in gravitational theories.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-16-2016 Random Matrix & Probability Theory Seminar
      11:00 am
      12/01/2024

      No additional detail for this event.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Jie Wang

      Title: Kahler geometry in twisted materials

      Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making many-body states less stable in flatbands.

      In this talk, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform, but still exhibit exact properties such as model wavefunctions, density algebra, exact parent Hamiltonians. I will discuss both the theory of ideal flatband, its experimental realization in Dirac materials as well as implications.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar 

      Speaker: Zhigang Yao

      Title: Principal flow, sub-manifold and boundary

      Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold, a manifold passing through the center of the data, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find, use and interpret the principal sub-manifold, by which a principal boundary can be further defined for data sets on manifolds.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Swampland Seminar
      Speaker: Aasmund Folkestad (MIT)
      Title: The Penrose Inequality as a Constraint on Low Energy Quantum Gravity
      Abstract: In this talk, I argue that the Penrose inequality (PI) can be used to constrain low energy theories compatible AdS/CFT, and possibly also quantum gravity in flat space. Focusing on AdS/CFT, it is shown that the PI can be violated for minimally coupled scalar fields, and I produce exclusion plots on couplings that respect the PI. I also present numerical evidence that top-down scalar theories and supersymmetric theories respect the PI. Finally, similar to the Breitenlohner-Freedman bound, I give a necessary condition for the stability AdS that constrains coupling constants (beyond the scalar mass).
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/28/2020 Mathematical Physics Seminar
      11:00 am-12:00 pm
      12/01/2024
    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: David Andriot (Annecy, LAPTH)

      Title: String theory scalar potentials and their critical points

      Abstract: Positive scalar potentials in string effective theories could provide an origin to Dark Energy, responsible for the accelerated expansion of our universe today or during inflation. It is thus crucial to characterize these scalar potentials, namely their slope, their critical points (de Sitter solutions) and the associated stability, as also advocated by the Swampland Program. We will present such characterizations. Going further, we will also discuss negative scalar potentials, and make related observations on anti-de Sitter solutions, in particular on a new mass bound, as well as comments on scale separation.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Paul-Konstantin Oehlmann(Northeastern)

      Title: Anomalies of Discrete Gauge Symmetries and their Cancellation in 6D F-theory

      Abstract: We consider 6D SUGRAs with a discrete gauge group G, engineered via F-theory compactifications on genus-one fibered threefolds. We argue that group G suffers from Dai-Freed anomalies that can be canceled via a discrete Green-Schwarz mechanism. We comment on the ambiguity to assign this GS term in the 7D Anomaly theory which leads to choices that are not all compatible with F-theory.

      In F-theory we then deduce this Anomaly coefficient explicitly by computing the elliptic genera of the non-critical strings that couple to the 6D two-form fields: Their 2D worldsheet theories inherits a G Flavor symmetries whose t’Hooft anomaly cancels the 6D Dai-Freed anomaly in the bulk via inflow. This talk is based on work in preparation together with Markus Dierigl and Thorsten Schimmanek.

    • CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
      11:00 am-8:45 pm
      12/01/2024-05/09/2021
      Summer,Warm,Sun,Light,Forest,Aerial,View

      This workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom

      The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data.

      This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

      The first half of the workshop will feature talks aimed at graduate students, newcomers, and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications.

      For the discussions, we are soliciting open problems in mathematical theory and applications of shape analysis. You are encouraged to post problems by sending an email to geometricproblemsfrg@gmail.com.

      We invite junior researchers to present a short talk in the workshop. The session will be held on Friday, May 7th or Saturday, May 8th at 4pm and are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks, the organizers will review the submissions and let you know if you have been selected. If you are interested please send your title and abstract to tianqi@cmsa.fas.harvard.edu by the end of May 2nd.

       

      Organizers:

      • David Glickenstein, University of Arizona
      • Joel Hass, University of California, Davis
      • Patrice Koehl, University of California, Davis
      • Feng Luo, Rutgers University, New Brunswick
      • Tianqi Wu, Harvard University
      • Shing-Tung Yau, Harvard University

      Featured lectures:

      • Christopher Bishop, Stony Brook
      • Keenan Crane, Carnegie Mellon

      Speakers include:

      • Miri Ben-Chen, Technion – Israel Institute of Technology
      • Alexander Bobenko, Technische Universität Berlin, Germany
      • Ulrike Buecking, Free University, Germany
      • Nadav Dym, Duke University
      • Ivan Izmestiev, Vienna University of Technology
      • Yanwen Luo, Rutgers
      • Stephan Tillmann, The University of Sydney
      • Max Wardetzky, University of Goettingen
      • Xu Xu, Wuhan University
    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics

      Title: Quantum magnet chains and Kashiwara crystals

      Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva, Joel Kamnitzer, and Alex Weekes.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Swampland Seminar
      Speaker: Samir Mathur (Ohio State)
      Title: The story of the information paradox
      Abstract:  In 1975 Hawking argued that black hole evaporation would lead to a loss of unitarity in quantum theory.  The small corrections theorem made Hawking’s argument into a precise statement: if semiclassical physics hold to leading order in any gently curved region of spacetime, then there can be no resolution to the paradox. In string theory, whenever people have been able to construct microstates explicutly, the states turned out to be horizon sized objects (fuzzballs) with no horizon; such a structure of microstates resolves the information paradox since their is no pair creation at a vacuum horizon. There have been a set of parallel attempts to resolve the paradox (with ideas involving wormholes, islands etc) where the horizon is smooth in some leading approximation. An analysis of such models however indicated that in each case the exact quantum gravity theory would either have to be nonunitary or to have dynamics at infinity that is conflict with usual low energy physics in the lab.
    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Swampland Seminar 01.30.23

      Swampland Seminar

      Speaker: Ignatios Antoniadis (LPTHE Paris)
      Title: Swampland program, extra dimensions and supersymmetry breaking
      Abstract: I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalisation of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.
    • Colloquium
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 04.03.2023

      Colloquium

      Speaker: Luca Iliesiu, Stanford

      Title: Black hole microstate counting from the gravitational path integral

      Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Swampland Seminar 04.10.23

      Swampland Seminar

      Speaker: Seung-Joo Lee (IBS Daejeon)

      Title: Swampland bounds on the abelian gauge sectors

      Abstract: In this talk we will derive various bounds on the 0-form and the 1-form abelian gauge sectors of gravitational effective theories in 6 dimensions with minimal supersymmetry. We will start by considering 6-dimensional F-theory vacua with at least one tensor multiplets, to bound for them the number of the (0-form) U(1) gauge factors as well as the cyclic orders of the 1-form discrete gauge factors. While the two abelian gauge sectors may look rather independent, we will observe that both are heavily constrained by the solitonic heterotic strings present in the spectrum, which provide a common intuition for the derived bounds. Building upon the heterotic intuition, we will also try extending the arena to address analogous bounds for all F-theory vacua in 6 dimensions and even beyond. If time permits, several applications and future directions of research will be discussed at the end of the talk.

    • Math Science Literature Lecture Series
      11:00 am-12:30 pm
      12/01/2024

      Sergiu Klainerman (Princeton University)

      Title: Nonlinear stability of Kerr black holes for small angular momentum

      Abstract: According to a well-known conjecture,  initial data sets,  for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon)   which approaches  (globally)  a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $|a|/m $ sufficiently small. The work, ArXiv:2104.11857v1,  also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr,  with Szeftel and Elena Giorgi,  which I will also describe.

      Talk chair: Lydia Bieri 

      Video

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin

      Title: Explicit Ramsey Graphs and Two Source Extractors

      Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      Jefferson Hall Room 368, 17 Oxford St, Cambridge, MA 02138

      Swampland Seminar

      Speaker: Thomas Grimm (Utrecht U.)

      Title: The Tameness of Quantum Field Theories

      Abstract: Tameness is a generalized notion of finiteness that is restricting the geometric complexity of sets and functions. The underlying mathematical foundation lies in tame geometry, which is built from o-minimal structures introduced in mathematical logic. In this talk I formalize the connection between quantum field theories and logical structures and argue that the tameness of a quantum field theory relies on its UV definition. I quantify our expectations on the tameness of effective theories that can be coupled to quantum gravity and on CFTs. In particular, I present tameness conjectures about CFT observables and propose universal constraints that render spaces of CFTs to be tame sets. I then highlight the relation of these conjectures to other swampland conjectures, e.g., by arguing that the tameness of CFT observables restricts having parametrical gaps in the operator spectrum.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Swampland Seminar 03.27.23

      Swampland Seminar

      Speaker: Valerio De Luca (UPenn)

      Title: Recent developments on the tidal Love numbers of black holes

      Abstract: Tidal Love numbers describe the deformability of compact objects under the presence of external tidal perturbations, and are found to be exactly zero for black holes in pure General Relativity. This property is however fragile, since they receive corrections from higher-order derivative terms in the theory. We show that the tidal deformability of neutral black holes is constrained by the Weak Gravity Conjecture.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Alvaro Herraez (Saclay)

      Title: The Emergence Proposal in Quantum Gravity and the Species Scale

      Abstract: The Emergence Proposal claims that in Quantum Gravity the kinetic terms of the fields in the IR emerge from integrating out (infinite) towers of particles up to the QG cutoff. After introducing this proposal in the context of the Swampland Program, I will explain why it is natural to identify this QG cutoff with the Species Scale, motivating it by direct computation in the presence of the relevant towers. Then, I will present evidence for this proposal by directly studying how it is realized in different string theory setups, where the kinetic terms of scalars, p-forms and even scalar potentials can be shown to emerge after integrating out such towers.

       

       

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024

      General Relativity Seminar

      Speaker: Daniel Kolb (Max Planck Institute)

      Title: Quasi-Local Mass in a Binary Black Hole Merger

      Abstract: One of the major open problems in classical general relativity is how one should define the mass of a finite region of space. In this talk, we will investigate a promising definition proposed by Wang and Yau in 2009. A closed 2-surface bounding the region of interest is embedded isometrically into Minkowski space. The mass is then calculated by comparing the extrinsic geometries. The Wang-Yau mass has many desirable properties, but it has previously not been calculated for surfaces in dynamical spacetimes. To remedy this, we will discuss how the Wang-Yau mass can be computed in practice and extend the definition to surfaces important in black hole dynamics: their quasi-local horizons. Finally, we look at how this mass behaves in a merger of black holes.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: David Kubiznak (Charles University)

      Title: Remarkable symmetries of rotating black holes

      Abstract: It is well known that the Kerr geometry admits a non-trivial Killing tensor and its ‘square root’ known as the Killing-Yano tensor. These two objects stand behind Carter’s constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object — the principal Killing-Yano tensor — generates a tower of explicit and hidden symmetries responsible for integrability of geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes described by the `magic square’ version of the Lense-Thirring solution, giving rise to a geometrically preferred spacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.

    • General Relativity Seminar
    • General Relativity Seminar
    • General Relativity Seminar
    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Leo Stein (Mississippi)

      Title: Resolving memory in numerical relativity, and fixing BMS frames for modeling

      Abstract: Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE), and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames, we can extract well-defined remnant quantities, perform precision ringdown modeling, and build complete surrogate waveform models that capture memory effects.

    • Seminars
      Seminars Colloquia & Seminar
      3-2-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      12/01/2024-03/03/2018
    • Seminars
      Seminars Colloquia & Seminar
      2-16-2018 Mirror Symmetry Seminar
      11:00 am
      12/01/2024
    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge MA 02138

      General Relativity Seminar

      Speaker: David Fajman (Vienna)

      Title: Fluid stabilization in slowly expanding cosmological spacetime

      Abstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.

       

      Talk via Zoom, broadcast in G10

       

    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      4-13-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      12/01/2024-04/14/2018
    • Seminars
      Seminars Colloquia & Seminar
      10/19/2018 Mirror Symmetry Seminar
      11:00 am-11:00 pm
      12/01/2024
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      02-09-2018 Mirror Symmetry Seminar
      11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2-23-2018 Mirror Symmetry Seminar
      11:00 am
      12/01/2024
    • Member Seminar
      11:01 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-21-16 Mathematical Physics Seminar
      11:02 am
      12/01/2024

      No additional detail for this event.

    • Algebraic Geometry in String Theory Seminar
      11:02 am-12:02 pm
      12/01/2024

      Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      11:03 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:03 am-11:04 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:04 am
      12/01/2024

      The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

      Spring 2020

      DateSpeakerTitle/Abstract
      1/29/2020David Yang (Harvard)

      Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

      2/5/2020Scott Aaronson (UT Austin)

      Video

      Title: Gentle Measurement of Quantum States and Differential Privacy

      Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
      of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

      Based on joint work with Guy Rothblum (arXiv:1904.08747)

      2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

      Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

      2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

      Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

      2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

      Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
      3/4/2020

      4:45 – 5:45pm

      Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

      Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

      In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

      3/11/2020

      Postponed

      Jose Scheinkman

      (Columbia)

      This colloquium will be rescheduled at a later date. 

      Title: Menu Costs and the Volatility of Inflation

      Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

      3/12/2020

      4:00 – 5:00pm

      Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

      Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

      Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

      Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

      3/25/2020Cancelled
      4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

      Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

      Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

      4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

      Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

      Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
      explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
      fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

      4/15/2020
      Lars Andersson (Max-Planck Institute for Gravitational Physics)
      This meeting will be taking place virtually on Zoom.

      Title: Stability of spacetimes with supersymmetric compactifications

      Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

      4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow in high codimension

      Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

      4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

      Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

      5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

      Title: Energy, Mass and Radiation in General Spacetimes

      Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

      5/13/2020Mikhail Lukin (Harvard)

      Video

      This meeting will be taking place virtually on Zoom.

      Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

      Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

      5/20/2020This meeting will be taking place virtually on Zoom.

      Fall 2019

      DateSpeakerTitle/Abstract
      9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

      Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

      ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

      ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

      ◦ The natural Nullstellensatz are falling into place.

      The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

      9/25/2019Pavel Etingof (MIT)

       

      Title: Double affine Hecke algebras

      Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

      10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

      Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

      10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

       

      Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

       

      Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

      John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

      Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

      Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

      Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

      10/16/2019Aram Harrow (MIT)

      Video

      Title: Monogamy of entanglement and convex geometry

      Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

      10/23/2019No talk
      10/30/2019Nima Arkani-Hamed (IAS)

      Video

      Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
      11/6/2019Kevin Costello (Perimeter Institute)

      Video

      Title: A unified perspective on integrability

       

      Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

      11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

      Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

      11/20/2019Xi Yin (Harvard)

      Video

      Title: An Introduction to the Non-Perturbative Bootstrap

      Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

      11/25/2019

      Monday

      Madhu Sudan (Harvard)
      Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

      In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

      Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

      12/4/2019Xiao-Gang Wen (MIT)
      Video
      Title: Emergence of graviton-like excitations from a lattice model

      Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

      2018-2019

      DateSpeakerTitle/Abstract
      9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

      Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

      10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

      Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

      10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

      Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

      10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

      Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

      In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

      10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

      Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

      11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

      Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

      11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

      Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

      11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

      Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

      12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

      Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

      Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

      12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

      Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

      1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

      Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

      2/7/2019

      *Thursday*

      Ulrich Mueller (Princeton)Title: Inference for the Mean

      Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

      2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

      Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

      2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

      Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

      [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

      2/27/2019

      2:30pm

      Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

      Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

      3/6/2019

      2:30pm

      Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

      Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

      3/13/2019

      5:15pm

      Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

      Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

      3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

      Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

      3/27/2019

      5:15pm

      Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      4/3/2019

      2:30pm

      Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

      Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

      4/10/2019

      2:30pm

      Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

      Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

      Paper

      Online Appendix

      4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

      Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

      .

      [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

      [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

      [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

      4/24/2019Shengwu Li (Harvard)
      Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
      Date…………SpeakerTitle
      02-09-2018 *Friday       Fan Chung

      (UCSD)

      Sequences: random, structured or something in between

      There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

      testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

      02-14-2018Zhengwei Liu

      (Harvard Physics)

      A new program on quantum subgroups

      Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

      02-21-2018Don Rubin

      (Harvard)

      Essential concepts of causal inference — a remarkable history

      Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

      02-26-2018 *MondayTom Hou

      (Caltech)

      Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

      Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

      03-07-2018Richard Kenyon

      (Brown)

      Harmonic functions and the chromatic polynomial

      Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

      03-14-2018
      03-21-2018
      03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

      Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

      We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
      [Based on joint work with Song Mei and Phan-Minh Nguyen]

      03-30-2018
      04-04-2018Ramesh Narayan 

      (Harvard)

      Black Holes and Naked Singularities

      Abstract: Black Hole solutions in General Relativity contain Event Horizons and
      Singularities. Astrophysicists have discovered two populations of
      black hole candidates in the Universe: stellar-mass objects with
      masses in the range 5 to 30 solar masses, and supermassive objects
      with masses in the range million to several billion solar
      masses. There is considerable evidence that these objects have Event
      Horizons. It thus appears that astronomical black hole candidates are
      true Black Holes. Direct evidence for Singularities is much harder to
      obtain since, at least in the case of Black Holes, the Singularities
      are hidden inside the Event Horizon. However, General Relativity also
      permits Naked Singularities which are visible to external
      observers. Toy Naked Singularity models have been constructed, and
      some observational features of accretion flows in these spacetimes
      have been worked out.

      04-11-2018Pablo Parrilo

      (MIT)

      Graph Structure in Polynomial Systems: Chordal Networks

      Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

      04-18-2018Washington Taylor

      (MIT)

      On the fibration structure of known Calabi-Yau threefolds

      Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

      04-25-2018 Xi Yin

      (Harvard)

      How we can learn what we need to know about M-theory

      Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

      05-02-2018
      05-09-2018

      2016-2017

      DateNameTitle/Abstract
      01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

      Title: Spectral graph theory of cognitive maps

      Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

      02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

      Sean_Eddy

      Title: Biological sequence homology searches: the future of deciphering the past 

      Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

      02-08-17Matthew Headrick, Brandeis University

      matthew_headrick

      Title: Quantum entanglement, classical gravity, and convex programming: New connections

      Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

      02-15-17Masahito Yamazaki, IMPU

      Masahito Yamazaki

       Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

      Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

      Video

      02-22-17Steven Rayan, University of Saskatchewan

      Title: Higgs bundles and the Hitchin system

      Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

      Video

      03-01-17Jun Liu, Harvard University

      Jun liu

      Title: Expansion of biological pathways by integrative Genomics

      Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

      Based on the joint work with Yang Li and the Vamsi Mootha lab.

      Video

      03-08-17Gabor Lippner, Northeastern University

      ---

      Title: Evolution of cooperation in structured populations

      Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

      In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
      03-15-17 Spring Break: No session
      03-22-17Gunther Uhlmann, University of Washington

      guntherUhlman

      Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
      waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
      The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
      We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
      03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

      Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

      NOTE: This talk will begin at 4:00pm

      04-05-17Gongjie Li, Harvard University

      GongjieLi

      Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

      Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

      Video

      04-12-17Shlomo Razamat, Israel Institute of Technology

      ShlomoRazamat

      Title: Complicated four-dimensional physics and simple mathematics

      Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

      Video

      04-19-17Cumrun Vafa, Harvard University

      CumrunVafa

      Title: String Swampland

      Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

      04-27-17Mehran Kardar, MIT

      MehranKardar

      Title: Levitation by Casimir forces in and out of equilibrium

      Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

      Note: This talk will begin at 3:00pm

      05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

      Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
      similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
      have led to substantial progress in protein structural and functional
      predictions.

      Note:  This talk will begin at 4:00pm

      05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

      Abstract: A deterministic or random system with a conservation law is often used to
      approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

      Note: This talk will be held in the Science Center, Room 507

      05-10-17
      05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

      Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

      05-24-17 NO COLLOQUIUM
      05-31-17Peter Michor, University of Vienna

       Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

      Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

      DateNameTitle
      09-09-16

      Bong Lian, Brandeis

      portrait

      Title: Riemann-Hilbert Problem and Period Integrals

      Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

      09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

      Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

      09-21-16Prof. L. Mahadevan, Harvard SEAS

      Mahadevan_200x300

      Title: “Morphogenesis: Biology, Physics and Mathematics”

      Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

      09-28-16Hong Liu, MIT

      liu_hong

      Title: A new theory of fluctuating hydrodynamics

      Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

      We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

      Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

      10-05-16

      Alexander LogunovTel-Aviv University

      alex

      Title: Zeroes of harmonic functions and Laplace eigenfunctions

       Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

      10-12-16 Conan Nai Chung Leung, CUHK

      conan_profile

      Title:  Coisotropic A-branes and their SYZ transform

      Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

      10-19-16Vaughan Jones, UC Berkeley

      vj6

      Title: Are the Thompson groups any good as a model for Diff(S^1)?

      Abstract. The Thompson groups are by definition groups of piecewise linear
      diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
      be conjugated to a group of smooth diffeomorphisms. That’s the good news.
      The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
      procedure analogous to the constructions of the central extension of Diff(S^1)?
      I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

       10-26-16

      Henry Cohn, Microsoft

      ????????????????????????????????????

      Sums of squares, correlation functions, and exceptional geometric structures

      Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

      11-02-16

      Christian Borgs, Microsoft

      Borgs

      Title:  Graphon processes and limits of   sparse graph sequences

      Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

      In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

      11-09-16

      TIME CHANGE: 4PM

      Norden E. HuangNational Central University, (Taiwan)

      member1_clip_image003

      Title: On Holo-Hilbert Spectral Analysis

      Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

      11-16-16Tristan Collins, Harvard University

      image

      TIME CHANGE: 3:30PM

      Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

      Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

      11-22-16 TUESDAY

      TIME CHANGE: 4-5PM

      Xiangfeng Gu, Stonybrook

      Title: Differential Geometric Methods for Engineering Applications

      Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

      11-30-16

      TIME CHANGE: 4:20PM

      Sharad Ramanathan, Harvard MCB & SEAS

      Ramanathan.Sharad_200x300

      Title: Finding co-ordinate systems to monitor the development of mammalian embryos
       12-07-16

      Valentino Tosatti, Northwestern

      Title: Metric limits of hyperkahler manifolds

      Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

       12-14-16

      2015-2016

      DateNameTitle
      09-02-2015Madhu SudanRobust low-degree testing
      09-09-2015Mithat Unsal
      What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
      09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
      09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
      09-30-2015Leslie ValiantHolographic Algorithms
      10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
      10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
      10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
      10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
      11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
      11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
      11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
      11-25-2015ThanksgivingNo seminar
      12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
      12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
      01-27-2016Conan LeungSome modern aspects of Morse theory 
      02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
      02-10-2016Chun Peng Wang
      02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
      02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
      03-02-2016Lydia BieriMathematical General Relativity
      03-09-2016Piotr ChruscielThe mathematics of gravitation
      03-16-2016Spring BreakNo Talk
      03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
      03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
      04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
      04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
      04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
      04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
      04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
      05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
      05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
    • Colloquium
      11:05 am-11:06 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:07 am-11:08 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:08 am-11:09 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-22-2016 Random Matrix & Probability Theory Seminar
      11:12 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-07-2016 Random Matrix & Probability Theory Seminar
      11:16 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-05-16 Mathematical Physics Seminar
      11:17 am
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
      11:19 am
      12/01/2024-11/14/2019
      Dynamics-12-x-18-683x1024

      On November 12-14, 2019 the CMSA will be hosting a workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Biological cells are the fundamental units of life, and predictive modeling of cellular dynamics is essential for understanding a myriad of biological processes and functions. Rapid advances in technologies have made it possible for biologists to measure many variables and outputs from complex molecular and cellular networks with various inputs and environmental conditions. However, such advances are far ahead of the development of mathematical theory, models and methods needed to secure a deep understanding of how high-level robust behaviors emerge from the interactions in complex structures, especially in dynamic and stochastic environments. This workshop will bring together mathematicians and biological scientists involved in developing mathematical theories and methods for understanding, predicting and controlling dynamic behavior of molecular and cellular networks. Particular emphasis will be placed on efforts directed towards discovering underlying biological principles that govern function, adaptation and evolution, and on the development of associated mathematical theories.

      Organizers: Jeremy Gunawardena (Harvard) and Ruth Williams (University of California, San Diego)

      A limited amount of funding is available to help in defraying the travel costs of early career researchers, women, and underrepresented minorities, participating the workshop. Early career researchers are researchers who received their Ph.D. in 2014 or later, or who are Ph.D. students expecting to complete their Ph.D. by the end of 2020.

      To apply, please send a CV, a statement of why you wish to attend, and, if you are a grad student, a letter of support from your advisor to Sarah LaBauve at slabauve@math.harvard.edu

      All applications received by 5pm, EDT, October 28, 2019 will receive full consideration.

      Speakers: 

      Videos from the workshop can be found in the Youtube playlist.

    • Seminars
      11:21 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:21 am-11:22 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-14-2016 Random Matrix & Probability Theory Seminar
      11:22 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      11:24 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      11:25 am
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Learning from health data in the million genome era
      11:26 am
      12/01/2024

      On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

      Speakers: 

      • Heidi Rehm, Ph.D.
        Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
      • Saiju Pyarajan, Ph.D.
        Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
      • Tianxi Cai, Sci.D
        John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
      • Susan Redline, M.D., M.P.H
        Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
      • Avinash Sahu, Ph.D.
        Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
      • Peter J. Park, Ph.D.
        Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
      • David Roberson
        Community Engagement Manager, Seven Bridges

      Registration & Schedule

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      9/29/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      4/20/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      12/15/2020 Computer Science for Math
      11:30 am-12:30 pm
      12/01/2024
    • Quantum Matter
      11:30 am-1:00 pm
      12/01/2024

      Quantum Matter Seminar

      Speaker: Daniel S. Freed (U Texas)

      Title: Topological symmetry in field theory

      Abstract: Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries,” “higher symmetries,” “noninvertible symmetries,” etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory. This is joint work with Constantin Teleman and Greg Moore.

       

      https://www.youtube.com/watch?v=y5uHfqVGunA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=26

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Quantum Field Theory Seminar
      11:30 am-12:00 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/24/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Quantum Oscillations of Electrical Resistivity in an Insulator
      11:30 am-1:00 pm
      12/01/2024
      CMSA-QMMP-02.03.2022

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      9/22/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      9/15/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      10/6/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      Rank-Based Independence Testing in Near Linear Time
      11:30 am-12:30 pm
      12/01/2024

      Speaker: Chaim Even-Zohar (Alan Turing Institute, London)

      Title: Rank-Based Independence Testing in Near Linear Time

      Abstract: In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.
      We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.

      Joint work with Calvin Leng.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      10/20/2020 Computer Science for Math
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      5/11/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/3/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      4/6/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      10/27/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      01-30-2017 Mathematical Physics Seminar
      11:30 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/23/2020 Mathematical Physics Seminar
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/17/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/2/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/23/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      3/2/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Quantum Matter
      11:30 am-1:00 pm
      12/01/2024

      Speaker: Lu Li (U Michigan)

      Title: Quantum Oscillations of Electrical Resistivity in an Insulator

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/10/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      3/9/2021 Computer Science for Mathematicians
      11:30 am-12:30 am
      12/01/2024-03/10/2021
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      3/23/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/9/2021 Computer Science for Math
      11:30 am-12:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-07-2017 Social Sciences Applications Forum
      11:32 am
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      11:33 am-1:33 pm
      12/01/2024

      Title: Symmetry types in QFT and the CRT theorem

      Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-06-2017 Mathematical Physics Seminar
      11:33 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-13-2017, Mathematical Physics Seminar
      11:34 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      11:35 am
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
      11:36 am
      12/01/2024-10/30/2019
      Space-Time-poster-5

      As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

      Everyone is welcome to attend the lectures.

      The master class workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Photos of the event

      Organizers:

    • Member Seminar
      11:37 am
      12/01/2024

      Hansol Hong, Harvard

      Title: Homological Mirror Functors

      Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

    • Colloquium
      11:39 am-11:40 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:40 am-11:41 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-14-2017 Social Science Applications Forum
      11:42 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:43 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:45 am
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      11:47 am-1:47 pm
      12/01/2024

      Title: Applications of instantons, sphalerons and instanton-dyons in QCD

      Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

      Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

    • Quantum Matter
      11:48 am-1:48 pm
      12/01/2024

      Title: Oscillations in the thermal conductivity of a spin liquid*

      Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

      *Czajka et al., Nature Physics 17, 915 (2021).

      Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

    • Quantum Matter
      11:49 am-1:49 pm
      12/01/2024

      Title: Line defects in CFTs: Renormalization group flows and semiclassical limits

      Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

    • Seminars
      Seminars Colloquia & Seminar
      10/24/2019 Quantum Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/21/2019 Condensed Matter seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/5/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/12/2019 Quantum Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/7/2019 Quantum Matter Seminar
      11:50 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/31/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • CMSA EVENT: Quantum Information Workshop
      11:52 am-11:53 am
      12/01/2024
      Asset-6-600x338

      Please note, this workshop has been postponed to a later date. Details will be posted to this page when they are available.

      The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

      The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

      More information to follow.

    • Quantum Matter
      11:54 am-1:54 pm
      12/01/2024

      Title: A tour of categorical symmetry

      Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-12-2017 Random Matrix & Probability Theory Seminar
      11:56 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:56 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-22-2017 Random Matrix & Probability Theory Seminar
      11:58 am
      12/01/2024

      No additional detail for this event.

    • Algebraic Geometry in String Theory Seminar
      11:58 am-12:58 pm
      12/01/2024

      Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.

    • Colloquium
      11:58 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-21-2017 Social Science Applications Forum
      11:59 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4/1/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Chuck Doran

      Title: Modularity of Landau-Ginzburg Models

      Abstract:  Fano varieties are the basic building blocks of algebraic varieties.  Smooth Fano varieties have been classified in dimensions one (the projective line), two (del Pezzo surfaces), and three (Mori-Mukai classification).  What does Mirror Symmetry have to say about such classifications?  By studying the Landau-Ginzburg models mirror to smooth Fano threefolds we can transform the Mori-Mukai classification into an effective uniruledness result for moduli spaces of certain K3 and abelian surfaces.  This is joint work with Andrew Harder, Ludmil Katzarkov, Mikhail Ovcharenko, and Victor Przjalkowski (arXiv:2307.15607).

       

       

    • Seminars
      Seminars Colloquia & Seminar
      3/02/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/19/2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/9/2020 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Samy Jelassi

      Title: An introduction to mixture of experts in deep learning

      Abstract: Scale has opened new frontiers in natural language processing – but at a high cost. Mixture-of-Experts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By doing so, the parameter count is decoupled from the compute per example leading to very large, but efficient models. In this talk, I will review the concept of mixture of experts, provide a basic description of the Switch Transformers model, characterize some of their behaviors and conclude by highlighting some open problems in the field. This talk is mainly based on the following papers: https://arxiv.org/pdf/2101.03961.pdfhttps://arxiv.org/pdf/2209.01667.pdf .

    • Seminars
      Seminars Colloquia & Seminar
      1/28/2018 Mathematical Physics Seminar
      12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/24/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/22/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Mike Douglas

      Title: AI and Theorem Proving

      Abstract: We survey interactive theorem proving and the Lean theorem prover, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.

    • Seminars
      Seminars Colloquia & Seminar
      3/23/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/4/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Zi Yang Kang

      Title: Deformations of Landau-Ginzburg models and their fibers

      Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

    • Seminars
      Seminars Colloquia & Seminar
      4/25/2019 Fluid Dynamics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/25/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Kai Xu (CMSA)

      Title: Moduli of vector bundles on curve and semiorthogonal decomposition

      Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived Θ-stratification.

       

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      9/24/2020 Strongly Correlated Quantum Materials
      12:00 pm-1:30 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Juven Wang

      Title: Categorical Symmetry of the Standard Model from Gravitational Anomaly

      Abstract: In the Standard Model, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.147652204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ16 respectively. For this construction, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, or the 3d boundary topological order of 4d ℤTF4-time-reversal symmetric topological superconductor [2302.14862].

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Benjamin McKenna

      Title: Random matrices and large deviations

      Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson.

       

    • Seminars
      Seminars Colloquia & Seminar
      3/4/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Daniel Kapec (CMSA)

      Title: Black Holes as Quantum Systems

      Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles.

       

    • Seminars
      Seminars Colloquia & Seminar
      12/18/2019 Quantum Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/25/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/8/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/11/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Max Wiesner

      Title: Quantum Gravity constraints beyond asymptotic regimes

      Abstract: Not every effective field theory that is consistent in the absence of gravity can be completed to a consistent theory of quantum gravity. The goal of the Swampland program is to find general criteria that distinguish effective field theories, that can be obtained as a low-energy approximation of quantum gravity, from those that are inconsistent in the presence of gravity. These criteria are oftentimes motivated by patterns observed in explicit compactifications of perturbative string theory and have passed many non-trivial tests in asymptotic regions of the field space such as, e.g., weak coupling limits. Still, the Swampland criteria should equally apply to effective theories that do not arise in asymptotic regions of the field space of string theory compactifications. In this talk I will summarize some of my recent works that studies the interior of regions of the field space of string theory in the context of the Swampland program.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/3/2020 Math-Physics
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/2/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/3/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/4/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/13/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024-04/22/2020
    • Seminars
      Seminars Colloquia & Seminar
      4/15/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/10/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/29/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Sunghyuk Park

      Title: Quantum UV-IR map and curve counts in skeins

      Abstract: Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong.

      In this talk, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules, using skein-valued curve counts of Ekholm and Shende.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/29/2018 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Farzan Vafa

      Title: Dynamics of active nematic defects on cones

      Abstract: In the first part of the talk, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge, which in analogy to electrostatics, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle, which is determined by charged defects screening the effective apex charge: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk, we investigate the dynamics of an active nematic on a cone, and via simulations find long-time circular orbits of either one or two flank defects, with transitions between these states mediated by the apex via defect absorption, emission, or defect pair creation.

    • Probability Seminar
      12:00 pm-1:00 pm
      12/01/2024

      Probability Seminar

      Speaker: Jun Yin (UCLA)

      Title: A random matrix model towards the quantum chaos transition conjecture

      Abstract: The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE.

      This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of the same phenomenon, shedding light on the intricacies of this long-standing conjecture.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/5/2018 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Dan Kapec

      Title: Hints of Flat Space Holography

      Abstract: Despite our detailed understanding of holography in Anti-de Sitter space, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space, bulk gravitons produce a boundary stress tensor, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Changji Xu

      Title: Spectral gap and two-point functions in spin glasses

      Abstract: Many have worked on spin glass models over the past 50 years, including physicists, mathematicians, and computers. A question that arises is whether computers yield dependable simulation results. In this talk, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.

    • Algebraic Geometry in String Theory Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Oliver Schlotterer (Uppsala University)

      Title: Modular graph forms and iterated integrals in string amplitudes

      Abstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful cross-talk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress in clarifying their connection with modular graph forms.

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Faidra Monachou

      Title: Optimal Dynamic Allocation: Simplicity through Information Design

      Abstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that, when the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the information disclosed about each object is an interval containing the object quality, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases, these intervals become coarser, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality, in terms of the Lorenz order.

    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Freid Tong

      Title: On complete Calabi-Yau metrics and some related Monge-Ampere equations

      Abstract: We will give a basic introduction to constructions for complete Calabi-Yau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of Tian-Yau in the 90s and have attracted a lot of attention in recent years. I will discuss some joint work with B. Guo and T. Collins on a singular version of such a construction, as well as some ongoing work with Prof. Yau on some related boundary value problems.

       

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Jue Liu

      Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds

      Abstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass, we define a new quasilocal mass using the Hamilton method. With this definition, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture, that is under what conditions there will be a static extension to the given Bartnik data.

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Barak Weiss  

      Title: New bounds on lattice covering volumes, and nearly uniform covers

      Abstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK, such that L+rK = R^n, normalized by the covolume of L. Pairs (L,K) with small covering volume correspond to efficient coverings of space by translates of K, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE, Hebrew University) and Oded Regev (CS, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.

    • Math Science Literature Lecture Series
      12:00 pm-1:30 pm
      12/01/2024

      Ralph Cohen (Stanford University)

      Title: Immersions of manifolds and homotopy theory

      Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest dimension Euclidean space into which every n-manifold embeds or immerses. The embedding question is still very much unsolved, and the immersion question was solved in the 1980’s. I will discuss the homotopy theoretic techniques involved in the solution of this problem, and contributions in the 60’s, 70’s and 80’s of Massey, Brown, Peterson, and myself. I will also discuss questions regarding the best embedding and immersion dimensions of specific manifolds, such has projective spaces. Finally, I will end by discussing more modern approaches to studying spaces of embeddings due to Goodwillie, Weiss, and others. This talk will be geared toward a general mathematical audience.

      Talk chair: Michael Hopkins

      Video

    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Quantum Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/30/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4-17-2018 Special Algebraic Geometry Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Puskar Mondal

      Title: Recent progress on coupled Einstein-Yang-Mills dynamics

      Abstract: I will discuss my recent work with prof. S.T. Yau on Einstein-Yang-Mills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gauge-gravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a double-null framework play an important role. I’ll sketch how the special structure of the Einstein and Yang-Mills nonlinearities play a crucial role in obtaining the stability result of non-expanding spacetimes in particular AF spacetimes.

    • Seminars
      Seminars Colloquia & Seminar
      9/16/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/20/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/6/2019 Math Physics
      12:00 pm-1:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/2/2020 Strongly Correlated Quantum Materials
      12:00 pm-1:30 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-5-2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/27/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Puskar Mondal (CMSA)

      Title: On the Breakdown of Einstein’s Gravity

      Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-26-2018 Math Physics Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/3/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Aghil Alaee

      Title: A quasi-local mass in general relativity

      Abstract: One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime, which can include a star, black hole, or galaxy. We define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition.  Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau.

       

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Chuck Doran

      Title: Motivic Geometry of Two-Loop Feynman Integrals

      Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/19/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Gabriel Wong

      Title: Quantum information and extended topological quantum field theory

      Abstract: Recently, ideas from quantum information theory have played an important role in condensed matter and quantum gravity research. Most of these applications focus on the entanglement structure of quantum states, and the computation of entanglement measures such as entanglement entropy has been an essential part of the story. In this talk, we will address some subtleties that arise when trying to define entanglement entropy in quantum field theory and quantum gravity. In particular, we will explain why extended topological field theory provides a useful framework to define and compute entanglement entropy in a continuous system. Time permitting, we will explain some recent applications of these ideas in low dimensional quantum gravity and to topological string theory.

       

       

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-2-2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/28/2019 Math Physics
      12:00 pm-1:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/26/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Aghil Alaee

      Title: Toroidal Positive Mass Theorem

      Abstract: In this talk, we review the positive mass conjecture in general relativity and prove a toroidal version of this conjecture in an asymptotically hyperbolic setting.

    • Seminars
      Seminars Colloquia & Seminar
      10/7/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Iacopo Brivio (CMSA)

      Title: Extension of pluricanonical forms in positive and mixed characteristics

      Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{times m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring.

       

    • Seminars
      Seminars Colloquia & Seminar
      9/9/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Michael Simkin

      Title: Randomized algorithms in combinatorics

      Abstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples:

      1. Enumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other?
      2. Constructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In 1973 Erdos conjectured that there exist STSs with arbitrary large girth (informally, no small set of vertices spans many triples). I will discuss the use of randomized algorithms to prove this conjecture. Joint work with Kwan, Sah, and Sawhney.
      3. Thresholds in random graphs and hypergraphs: I will discuss how randomized algorithms can be combined with the recent resolution of the Kahn–Kalai conjecture to determine thresholds in random (hyper) graph theory. Joint work with Pham, Sah, and Sawhney.
    • Seminars
      Seminars Colloquia & Seminar
      3/25/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Quantum Matter
      12:00 pm-1:30 pm
      12/01/2024
    • Seminars
      12:00 pm-1:00 pm
      12/01/2024
      Raymarching and the Thurston Geometries

      On Wednesday, December 16 at 12:00 p.m. EST, WAM and CMSA will host a holiday seminar featuring Sabetta Matsumoto, Georgia Institute of Technology who will present The Inside View: Raymarching and the Thurston Geometries.

      The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon, Henry Segerman and Steve Trettel.

      Visit the event page

      Register to access this event here

       

    • Quantum Matter
      12:00 pm-1:00 pm
      12/01/2024

      Speaker: Eric Sharpe (Virginia Tech)

      Title: Anomaly resolution via decomposition

      Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

    • Quantum Matter
      12:00 pm-1:00 pm
      12/01/2024

      Speaker: Biao Lian (Princeton)

      Title: Integrability and chaos of 1+1d chiral edge states

      Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

    • General Relativity Seminar
      12:00 pm-1:00 pm
      12/01/2024

      The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
      04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
      04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
      04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
      05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
      05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
      05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
      05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Juven Wang

      Title: Open Problems in Physics and Novel Solutions from Math

       

      Abstract: (1) How do neutrinos obtain tiny mass and oscillate between e, \mu, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis?

      (2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions?

      (3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry?

      (4) Family/Generation problem: Why are there three families/generations of quarks and leptons?

      In my talk, I will sketch and propose novel solutions to these challenging open problems in physics based on my own work (available on arXiv, some jointly with my collaborators).

      I will show that the eclectic cross-disciplinary fertilization of ideas between the Math-Physics geometry and topology, Quantum Condensed Matter, and High-Energy Physics (theory, pheno, lattice) can help solving these big problems.

      The (1) answer relates to Ultra Unification: a Z_{16} class Atiyah-Patodi-Singer eta invariant (Baryon – Lepton)-protected topological superconductor and a symmetry-extended anomalous topological quantum field theory.

      The (2) and (3) answers relate to a trivial cobordism class and Symmetric Mass Generation, and disordering and removing the Pecci-Quinn axions.

      The (4) answer has to do with the Hirzebruch signature and Atiyah-Singer index theorem, gravitational Chern-Simons theory, and 3 E8 quantum Hall states.

       

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Title: Duality in Einstein’s Gravity

      Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/8/2021 Interdisciplinary Science Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Alejandro Poveda

      Title: On compactness phenomena

      Abstract: In this presentation I shall be preoccupied with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behavior. This phenomenon is intrinsic to the very architecture of the mathematical universe and manifests to us in a cornucopia of forms. Over the past fifty years, the study of compactness phenomena has been a cornerstone of research in set theory. This talk will present recent discoveries regarding compactness principles, spanning classical themes like the tree property and stationary reflection, while also forging novel connections with other topics, such as Woodin’s HOD Conjecture.

    • Active Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 10.20.22
      Active Matter Seminar
      Speaker: Sharad Ramanathan, Harvard
      Title: Attempts at understanding human axial elongation and patterning
      Abstract: Some of the most dramatic events during human development is the axial elongation of the embryo with concomitant changes in the geometry and composition of the underlying tissues. The posterior part of the embryo gives rise to the spinal cord, vertebral column, ribcage, back muscles, and dermis.  In this talk, I will present our attempts at coaxing human embryonic stem cells to form these structures of the early human embryo that closely recapitulate the geometry, relative arrangements, composition, and dynamics of development of the early spinal cord flanked progenitors of the musculoskeletal system. Our goal was to do so, such that we could build hundreds of these organoids at a time. I will also present preliminary results for the use of this system to understand key events during early human development through imaging and genetic perturbations.
    • Colloquium
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      colloquium

      Colloquium

      Speaker: Yannai Gonczarowski (Harvard)

      Title: Strategyproof-Exposing Mechanisms Descriptions

      Abstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.

      By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.

      Joint work with Ori Heffetz and Clayton Thomas.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-22-2017 Random Matrix & Probability Theory Seminar
      12:01 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:03 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Cosmic Road to New Physics
      12:04 pm
      12/01/2024
      The colourful star cluster NGC 3532

      The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

      The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

      Organizers:

      Scientific Advisory:

      Speakers: 

      CosmicRoad_Poster

    • Colloquium
      12:05 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:06 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:08 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:09 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      12:10 pm-1:10 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

       

      Speaker: Man-Wai Cheung

      Title: Compactification for cluster varieties without frozen variables of finite type

      Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

    • CMSA EVENT: 2019 Ding Shum Lecture
      12:11 pm
      12/01/2024
      DingShum-2019

      DSC_0468-e1568985499370

      On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

      Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

      Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

      Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

      This event is made possible by the generous funding of Ding Lei and Harry Shum.

      DingShum-2019

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-1-2017 Random Matrix & Probability Seminar
      12:11 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
      12:11 pm
      12/01/2024-04/19/2017

      From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

    • Colloquium
      12:12 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:13 pm-12:14 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-27-2017 Mathematical Physics Seminar
      12:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-7-2017 Social Science Applications Forum
      12:15 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:15 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/13/2019 Special Seminar
      12:15 pm-1:05 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3-8-2017 CMSA Special Lecture Series
      12:16 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
      12:19 pm
      12/01/2024-10/18/2019
      Noncommutative-Analysis-Poster-3

      On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

      This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

      Please register here

      Speakers:

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-8-2017 Random Matrix & Probability Theory Seminar
      12:21 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-6-2017 Mathematical Physics Seminar
      12:24 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      12:25 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-10-2017 Special Lecture Series
      12:27 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-21-2017 Social Science Applications Forum
      12:28 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
      12:28 pm
      12/01/2024-05/05/2019
      1 Oxford Street, Cambridge MA 02138
      Differential Geometry, Calabi-Yau theory and General Relativity

      Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

      On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

      Organizers:

      • Horng-Tzer Yau (Harvard)
      • Wilfried Schmid (Harvard)
      • Clifford Taubes (Harvard)
      • Cumrun Vafa (Harvard)

      Speakers:

      • Lydia Bieri, University of Michigan
      • Tristan Collins, MIT
      • Simon Donaldson, Imperial College
      • Fan Chung Graham, UC San Diego
      • Nigel Hitchin, Oxford University
      • Jun Li, Stanford University
      • Kefeng Liu, UCLA
      • Chiu-Chu Melissa Liu, Columbia University
      • Alina Marian, Northeastern University
      • Xenia de la Ossa, Oxford University
      • Duong H. Phong, Columbia University
      • Richard Schoen, UC Irvine
      • Andrew Strominger, Harvard University
      • Nike Sun, MIT
      • Clifford Taubes, Harvard University
      • Chuu-Lian Terng, UC Irvine
      • Valentino Tosatti, Northwestern University
      • Karen Uhlenbeck, University of Texas
      • Cumrun Vafa, Harvard University
      • Mu Tao Wang, Columbia University
      • Edward Witten, IAS
      • Stephen Yau, Tsinghua University, P.R. China
    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 03.22.2023

      Speaker: Mete Soner (Princeton University)

      Title: Synchronization in a Kuramoto Mean Field Game

      Abstract:  Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a  key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  We explore this system in the mean field formalism.  We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium.  The mean field game also exhibits a bifurcation from incoherence to self-organization.  This approach has found interesting applications including circadian rhythms and jet-lag recovery.  This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Tim Adamo, University of Edinburgh

      Title: An invitation to strong-field scattering

      Abstract: Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to all-multiplicity twistor and string methods.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Xi Yin (Harvard Physics) and Peter Kronheimer (Harvard Math)
      Topics:
      Xi Yin: What is string field theory?
      Peter Kronheimer: What is Seiberg-Witten theory?
    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Four-dimensional topology
      12:30 pm-1:30 pm
      12/01/2024
      Lecture_Manolescu-pdf

      Ciprian Manolescu (Stanford)

      Title: Four-dimensional topology

      Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to four-manifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience.

      Video

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 05.03.2023

      Speaker: Xin Guo, UC Berkeley

      Title: Generative Adversarial Networks (GANs): An Analytical Perspective

      Abstract: Generative models have attracted intense interests recently. In this talk, I will discuss one class of generative models, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis.

       

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)
      Topics:
      Dan Freed: What is framing anomaly? How is it different from other anomalies?
      Dan Berwick-Evans: What is Atiyah-Singer index theorem?
    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Speakers: Dan Freed (Harvard Math and CMSA), Denis Auroux (Harvard Math)

    • Math Science Literature Lecture Series
      12:30 pm-2:00 pm
      12/01/2024
      Lecture_Freedman-1-pdf

      Michael Freedman (Microsoft – Station Q)

      Title: A personal story of the 4D Poincare conjecture

      Abstract:  The proof of PC4 involved the convergence of several historical streams.  To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.

      Talk Chair: Peter Kronheimer

      Video

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 03.08.2023

      Speaker: Ning Su, University of Pisa

      Title: Conformal symmetry, Optimization algorithms and the Critical Phenomena

      Abstract: In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid phase transition and Heisenberg magnet to very high precision.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 03.29.2023

      Speaker: Ruth Britto (Trinity College Dublin)

      Title: Scattering amplitudes in quantum field theory

      Abstract: Particle collider experiments require a detailed description of scattering events, traditionally computed through sums of Feynman diagrams. However, it is not practical to evaluate Feynman diagrams directly for all significant scattering processes. Moreover, adding all diagrams reveals many cancellations: scattering amplitudes in theories such as QCD take remarkably simple forms. This simplicity is a clue that the perturbative theory is perhaps best understood without reference to Feynman diagrams. In fact, it has recently become possible to explain some of this simplicity. I will show how to derive many amplitudes efficiently and elegantly, and propose taming the remaining complexity with ideas drawn from combinatorics and geometry.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 04.26.2023.rev2

      Speaker: Max Metlitski (MIT)

      Title: Boundary behavior at classical and quantum phase transitions

      Abstract: There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter, where exotic protected boundary states are ubiquitous. In this talk, I’ll ask: what happens at a boundary of a system, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field, as well as some extensions to quantum phase transitions.

       

    • Colloquium
      12:30 pm
      12/01/2024

      No additional detail for this event.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University)

      Topics:

      Michael Douglas: “What is non-commutative field theory?”
      Mayuko Yamashita: “What is differential cohomology?”
    • Topological Quantum Matter Seminar
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Hart Goldman, University of Chicago

      Title: Composite fermions and the fractional quantum anomalous Hall effect

      Abstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk, I will argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new zero-field context. In particular, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end, I will present exact diagonalization evidence for such composite Fermi liquid states at zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs), I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 04.12.2023
      Speaker: James Halverson (Northeastern University)
       
      Title: Unexpected Uses of Neural Networks: Field Theory and Metric Flows

      Abstract:  We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics, sometimes leading to rigorous results. In this talk, however, I will argue that breakthroughs in deep learning theory are also useful for making progress, focusing on applications to field theory and metric flows. Specifically, I will introduce a neural network approach to field theory with a different statistical origin, that exhibits generalized free field behavior at infinite width and interactions at finite width, and that allows for the study of symmetries via the study of correlation functions in a different duality frame. Then, I will review recent progress in approximating Calabi-Yau metrics as neural networks and cast that story into the language of neural tangent kernel theory, yielding a theoretical understanding of neural network metric flows induced by gradient descent and recovering famous metric flows, such as Perelman’s formulation of Ricci flow, in particular limits.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 11.16.22 - 2

      Colloquium

      Speaker: Hidenori Tanaka (NTT Research at Harvard)

      Title: Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks

      Abstract: In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle, but the role of symmetry breaking is not well understood. Here, we develop a Lagrangian formulation to study the geometry of learning dynamics in neural networks and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. Then, we generalize Noether’s theorem known in physics to describe a unique symmetry breaking mechanism in learning and derive the resulting motion of the Noether charge: Noether’s Learning Dynamics (NLD). Finally, we apply NLD to neural networks with normalization layers and discuss practical insights. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      A tale of two balloons
      12:30 pm-1:30 pm
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-11.16.21

      Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
      Joint work with Omer Angel and Gourab Ray.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-20-2017 Mathematical Physics Seminar
      12:30 pm
      12/01/2024

      No additional detail for this event.

    • Math Science Literature Lecture Series
      12:30 pm-1:30 pm
      12/01/2024
      Lecture_Lian-pdf

      Bong Lian (Brandeis)

      Title: From string theory and Moonshine to vertex algebras

      Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed at a general audience.

      Slides | Video

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium
      Colloquium
      Speaker: Melody Chan
      Title: Moduli spaces of graphs
      Abstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.
    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.13.2023

      Title: Complete Calabi-Yau metrics: Recent progress and open problems

      Abstract: Complete Calabi-Yau metrics are fundamental objects in Kahler geometry arising as singularity models or “bubbles” in degenerations of compact Calabi-Yau manifolds.  The existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to Yau and Tian-Yau. I will describe some recent progress towards the question of existence, and explain some future directions, highlighting connections with notions of algebro-geometric stability.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Mike Douglas (Harvard CMSA) and Anurag Anshu (Harvard Computer Science)

      Topics:

      Mike Douglas: What are scaling laws in deep learning?

      Anurag Anshu: What’s the difference between classical information theory and quantum information theory (or classical computation vs quantum computation)?

       

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.02.2023

      Speaker: Max Reppen (Boston University)

      Title: Neural Optimal Stopping Boundary

      Abstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.12.22 (1)

      Colloquium

      Title: Complete disorder is impossible: Some topics in Ramsey theory

      Speaker: James Cummings, Carnegie Mellon University

      Abstract: The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory, which touches on many areas of mathematics including graph theory, set theory and dynamics. I will give an overview of Ramsey theory, emphasizing the diverse ideas which are at play in this area.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA)

      Topics:

      Dan Freed: What is Dijkgraaf-Witten theory?

      Sunghyuk Park: What happened at the Clay Math Institute Workshop?

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.19.22

      Colloquium

      Speaker: Patrick Lopatto (Brown)

      Title: The Mobility Edge of Lévy Matrices

      Abstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness, these models have been broadly applied in physics, finance, and statistics. When the entries have infinite mean, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/6/2020 Strongly Correlated Quantum Materials Lecture
      12:30 pm-3:00 pm
      12/01/2024
    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.08.2023

      Speaker: David Gamarnik (MIT)

      Title: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property

      Abstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph, the problem of finding a near ground state in a spin glass model, the problem of finding a satisfying assignment in a random constraint satisfaction problem, and many many more. Unfortunately, at the same time no formal computational hardness results exist which  explains this persistent algorithmic gap.

      In the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms which exhibit a form of stability/noise insensitivity.

      We will specifically show how to use this property to obtain stronger (stretched exponential) than the state of the art (quasi-polynomial) lower bounds on the size of constant depth Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph, and the problem of finding a near ground state of a p-spin model.

      Joint work with Aukosh Jagannath and Alex Wein

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math)

      Topics:

      Mike Hopkins: What are topological modular forms?

      Mihnea Popa: What is the abundance conjecture and why should it to be true?

       

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 09.28.22

      Colloquium

      Speaker: Dima Sinapova (Rutgers University)

      Title: The Tree Property and uncountable cardinals

      Abstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes.

      We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.

       

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.26.22

      Speaker: Virginia Vassilevska Williams (MIT)

      Title: Clique listing algorithms

      Abstract: A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history.

      A fundamental question, with many applications, is “How fast can one list all k-cliques in a given graph?”.

      Even just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant, such as 3 or 4 (independent of n), even the brute-force algorithm runs in polynomial time, O(n^k), and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k), the brute-force algorithm is in some sense optimal, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques, with running times depending on the number of vertices n, the number of edges m, the number of k-cliques T and more. We will focus on the case when k=3, but we will note some extensions.

      (Based on joint work with Andreas Bjorklund, Rasmus Pagh, Uri Zwick, Mina Dalirrooyfard, Surya Mathialagan and Yinzhan Xu)

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.22.2023

      Speaker: Netta Engelhardt (MIT)

      Title: The Black Hole Information Paradox: A Resolution on the Horizon?

      Abstract: The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary, and in particular its application to entanglement and complexity, however, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-5-2017 Random Matrix & Probability Theory Seminar
      12:31 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:32 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
      12:33 pm
      12/01/2024-05/01/2019

      From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Videos

      Speakers: 

       

      Monday, April 29

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

      Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

      10:00 – 10:30amBreak
      10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

      Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

      11:30 – 1:30pmLunch
      1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

      Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

      2:30 – 3:00pmBreak
      3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

      Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

      4:00 – 4:30pmBreak
      4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

      Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

       

      Tuesday, April 30

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

      Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

      10:00 – 10:30amBreak
      10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

      Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

      11:30 – 1:00pmLunch
      1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

      Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

      2:00 – 2:15pmBreak
      2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

      Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

      Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

      We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

      This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

      3:15 – 3:30pmBreak
      3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

      Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

      4:30 – 4:45pmBreak
      4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

      Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

       

      Wednesday, May 1

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

      Abstract: PDF

      This is joint work with Eric Rains and Douglas Stryker.

      10:00 – 10:30amBreak
      10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

      Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
      and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
      to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

      11:30 – 11:45amBreak
      11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

      Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

      In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

      This is a joint work with Felix Janda and Yongbin Ruan.

      12:45 – 2:30pmLunch
      2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

      Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

      3:30 – 4:00pmBreak
      4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

      Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-29-2017 Random Matrix & Probability Theory Seminar
      12:35 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-24-2017 Random Matrix & Probability Theory Seminar
      12:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-30-2017 CMSA Special Seminar
      12:38 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-27-2017 Mathematical Physics Seminar
      12:40 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:41 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-5-2017 Special Lecture Series
      12:42 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-7-2017 Special Lecture Series
      12:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Special Lecture Series
      12:44 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:45 pm-1:45 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 11.02.22

      Speaker: Liang Fu (MIT)

      Title: Doping and inverting Mott insulators on semiconductor moire superlattices

      Abstract: Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First, in an intermediate range of magnetic fields, doping this Mott insulator gives rise to a dilute gas of spin polarons, which form a pseudogap metal. Second, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.

    • Colloquium
      12:45 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-14-2017 Special Lecture Series
      12:46 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-3-2017 Mathematical Physics Seminar
      12:50 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      12:51 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Social Science Applications Forum
      12:53 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Mirror Symmetry and Stability
      12:55 pm
      12/01/2024-03/20/2019
      HMS-2019-1

      This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

      Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

      Speakers:

      Dylan Allegretti (Sheffield)
      Tristan Collins (MIT)
      Naoki Koseki (Tokyo)
      Chunyi Li (Warwick)
      Jason Lo (CSU Northridge)
      Emanuele Macrì (NEU & IHES)
      Genki Ouchi (Riken iTHEMS)
      Pranav Pandit (ICTS)
      Laura Pertusi (Edinburgh)
      Jacopo Stoppa (SISSA)
      Alex Takeda (UC Berkeley)
      Xiaolei Zhao (UC Santa Barbara)

      More details will be added later.

      Visit the event page for more information. 

       

      HMS-2019-1

    • Colloquium
      12:55 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:57 pm
      12/01/2024

      No additional detail for this event.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Active crystals are highly ordered structures that emerge from the nonequilibrium self-organization of motile objects, and have been widely studied in synthetic and bacterial active matter. In this talk, I will describe how swimming sea star embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiment, hydrodynamic theory, and simulations, we demonstrate that the formation, dynamics, and dissolution of these living crystals are controlled by the natural development of the embryos. Remarkably, due to nonreciprocal force and torque exchange between the embryos, the living chiral crystals exhibit self-sustained oscillations with dynamic signatures recently predicted to emerge in materials with odd elasticity.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character \theta of G, and a G-invariant function w on V.  This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient.  GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM, very few computations of these invariants have been carried out.  In this talk I will describe a new method for computing generating functions of GLSM invariants.  I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.

    • Math Science Literature Lecture Series
      1:00 pm-2:00 pm
      12/01/2024
      Lecture_Harris_updated-pdf

      Joe Harris (Harvard)

      Title: Rationality questions in algebraic geometry

      Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension two) and Hodge theory (dimension 3). But there remained much we didn’t understand about the condition of rationality, such as how it behaves in families. However, there has been recent progress: work of Hassett, Tschinkel, Pirutka and others, working with examples in dimension 4, showed that it is in general neither an open condition nor a closed one, but does behave well with respect to specialization. In this talk I’ll try to give an overview of the history of rationality and the current state of our knowledge.

      Video

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack), there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk, we first show that these three definitions are equivalent. Second, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third, we apply these results to various moduli situations, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      No additional detail for this event.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-01.27.2022

      Abstract: Fluids pervade complex systems, ranging from fish schools, to bacterial colonies and nanoparticles in drug delivery. Despite its importance, little is known about the role of fluid mechanics in such applications. Is schooling the result of vortex dynamics synthesized by individual fish wakes or the result of behavioral traits? Is fish schooling energetically favorable?  I will present multifidelity computational studies of collective swimming in 2D and 3D flows. Our studies demonstrate that classical models of collective swimming (like the Reynolds model) fail to maintain coherence in the presence of long-range hydrodynamic interactions. We demonstrate in turn that collective swimming can be achieved through reinforcement learning. We extend these studies to 2D and 3D viscous flows governed by the Navier Stokes equations. We examine various hydrodynamic benefits with a progressive increase of the school size and demonstrate the importance of controlling the vorticity field generated by up to 300 synchronized swimmers.

    • Seminars
      Seminars Colloquia & Seminar
      11/13/2019 General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024
    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar
      Speaker: Herbert Levine (Northeastern)
      Title: Frustration-free states of cell fate networks: the case of the epithelial-mesenchymal transition

      Abstract: Cell fate decisions are made by allowing external signals to govern the steady-state pattern adopted by networks of interacting regulatory factors governing transcription and translation. One of these decisions, of importance for both developmental processes and for cancer metastasis, is the epithelial-mesenchymal transition (EMT). In this talk, we will argue that these biological networks have highly non-generic interaction structures such that they allow for phenotypic states with very low frustration, i.e. where most interactions are satisfied. This property has important consequences for the allowed dynamics of these systems.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA-GR-Seminar-03.10.22

      Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Gromov-Witten invariants count pseudo-holomorphic curves on a symplectic manifold passing through some fixed points and submanifolds. Similarly, open Gromov-Witten invariants are supposed to count disks with boundary on a Lagrangian, but in most cases such counts are not independent of some choices as we would wish. Motivated by Fukaya’11, J. Solomon and S. Tukachinsky constructed open Gromov-Witten invariants in their 2016 papers from an algebraic perspective of $A_{\infty}$-algebras of differential forms, utilizing the idea of bounding chains in Fukaya-Oh-Ohta-Ono’06. On the other hand, Welschinger defined open invariants on sixfolds in 2012 that count multi-disks weighted by the linking numbers between their boundaries. We present a geometric translation of Solomon-Tukachinsky’s construction. From this geometric perspective, their invariants readily reduce to Welschinger’s.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Max Lavrentovich, Worcester State University

      Title: Strongly driven mixtures and membranes: Out of equilibrium surprises

      Abstract: The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phase-separating colloidal mixture and a lipid membrane, which demonstrate counterintuitive properties when driven out of equilibrium. We will see that the phase separating mixture, when driven by a uniform force, develops (in simulations) an intriguing pattern with a characteristic length scale set by the magnitude of the drive. We will look at some theoretical approaches to understanding the pattern formation and possible experimental realizations. The membrane, when driven by an oscillatory electric field, develops (in experiments) a long-lived metastable state with a decreased capacitance and increased dissipation. This state may have implications for neuronal processing and memory formation.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.

      1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.

      2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-02.24.22

      Abstract: The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological
      disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes: (i) to explain the tortoise & hare story in bacterial competition: how motility of Pseudomonas aeruginosa bacteria leads to a slower invasion of bacteria colonies, which are individually faster, and
      (ii) how self-propelled defects lead to finding an unanticipated mechanism for cell death.

      I will then discuss various strategies to tame, otherwise chaotic, active flows, showing how hydrodynamic screening of active flows can act as a robust way of controlling and guiding active particles into dynamically ordered coherent structures. I will also explain how combining hydrodynamics with topological constraints can lead to further control of exotic morphologies of active shells.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      No additional detail for this event.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

    • Seminars
      Seminars Colloquia & Seminar
      12/6/2019 Special Seminar
      1:00 pm-2:00 pm
      12/01/2024
    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I will present a four-term exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations, the Hodge, weight, and perverse Leray filtrations, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the Clemens-Schmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      9/28/2021 Combinatorics, Physics and Probability Seminar
      1:00 pm
      12/01/2024

      Title: The hypersimplex and the m=2 amplituhedron

      Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.

    • Math Science Literature Lecture Series
      1:00 pm-2:00 pm
      12/01/2024

      Robert Griess (University of Michigan)

      Title: My life and times with the sporadic simple groups

      Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad school at University of Chicago,  I became fascinated with the unfolding story of sporadic simple groups. It involved theory, detective work and experiments. During this lecture, I will describe some of the people, important ideas and evolution of thinking about sporadic simple groups. Most should be accessible to a general mathematical audience.

      Video | Slides

    • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
      1:00 pm-6:00 pm
      12/01/2024-04/07/2018
      banner-image-1

      The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

      Confirmed Speakers:

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 11.17.22
      Active Matter Seminar

      Speaker: Max Prigozhin (Harvard)

      Title: Dynamic and multicolor electron microscopy

      Abstract: My lab is developing biophysical methods to achieve multicolor and dynamic biological imaging at the molecular scale. Our approach to capturing the dynamics of cellular processes involves cryo-vitrifying samples after known time delays following stimulation using custom cryo- plunging and high-pressure freezing instruments. To achieve multicolor electron imaging, we are exploring the property of cathodoluminescence—optical emission induced by the electron beam. We are developing nanoprobes (“cathodophores”) that will be used as luminescent protein tags in electron microscopy. We are applying these new methods to study G-protein- coupled receptor signaling and to visualize the formation of biomolecular condensates.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem, and new results in this direction, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-02.10.22

      Abstract: My lab is interested in the active and adaptive materials that underlie control of cell shape.  This has centered around understanding force transmission and sensing within the actin cytoskeleton.  I will first review our current understanding of the types of active matter that can be constructed by actin polymers.  I will then turn to our recent experiments to understand how Cell shape changes in epithelial tissue.  I will describe the two sources of active stresses within these tissues, one driven by the cell cycle and controlling cell-cell stresses and the other controlled by cell-matrix signaling controlling motility.  I will then briefly describe how we are using optogenetics to locally control active stresses to reveal adaptive and force-sensitive mechanics of the cytoskeletal machinery. Hopefully, I will convince you that recent experimental and theoretical advances make this a very promising time to study this quite complicated form of active matter.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: During development, organisms interact with their natural habitats while undergoing morphological changes, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria, a basal animal lineage that includes sea anemones, corals, hydras, and jellyfish, offers unique insight into the development and evolution of morphological complexity.  In my talk, I will introduce our research on “ethology of morphogenesis,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels, opening new perspectives about the design principle of soft-bodied animals. In addition, I will discuss a fascinating feature of cnidarian biology. For humans, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule.

      References
      Anniek Stokkermans, Aditi Chakrabarti, Ling Wang, Prachiti Moghe, Kaushikaram Subramanian, Petrus Steenbergen, Gregor Mönke, Takashi Hiiragi, Robert Prevedel, L. Mahadevan, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976

      Ikmi A, Steenbergen P, Anzo M, McMullen M, Stokkermans M, Ellington L, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensisNature communications, Sept 02; 11:4399

      He S, Del Viso F, Chen C, Ikmi A, Kroesen A, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensisScience, Vol. 361, Issue 6409, pp. 1377-1380.
      Ikmi A, McKinney SA, Delventhal KM, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensisNature communications. Nov 24; 5:5486.

    • Seminars
      Seminars Colloquia & Seminar
      Combinatorics & Complexity Seminar, Fridays
      1:00 pm-4:00 pm
      12/01/2024

      The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

      Additional information on CMSA’s Combinatorics and Complexity program can be found here.

       

      DateNameTitle/Abstract
      09-08-17TBA
      09-15-2017TBA
      09-22-17TBA
      09-29-17TBA
      10-06-17 TBA
      10-13-2017TBA
      10-20-2017TBA
      10-27-2017TBA
      11-03-2017TBA
      11-10-2017TBA
      11-17-2017TBA
      11-24-2017TBA
      12-01-2017TBA
      12-08-2017 TBA
    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 11.03.22

      Active Matter Seminar

      Speaker: Siavash Monfared, Niels Bohr Institute, Copenhagen

      Title: Force transmission informs the collective behavior of active cell layers

      Abstract: Collective cell migration drives numerous physiological processes such as tissue morphogenesis, wound healing, tumor progression and cancer invasion. However, how the interplay of mechanical interactions and the modes of collective self-organization among cells informs such processes is yet to be established. In this talk, I will focus on the role of three-dimensional force transmission, from a theoretical and computational perspective, on two phenomena: (1) cell extrusion from a cellular monolayer and (2) density-independent solid-like to fluid-like transition of active cell layers. For the first topic, I will focus on how increasing cell-cell adhesion relative to cell-substrate adhesion enables cells to collectively exploit distinct mechanical pathways – leveraging defects in nematic and hexatic phases associated with cellular arrangement – to eliminate an unwanted cell. For the second topic, I will show how solid-like to fluid-like transition in active cell layers is linked to the percolation of isotropic stresses. This is achieved via two distinct and independent paths to model this transition by increasing (a) cell-cell adhesion and (b) active traction forces. Additionally, using finite-size scaling analyses, the phase transition associated with each path is mapped onto the 2D site percolation universality class. Our results highlight the importance of force transmission in informing the collective behavior of living cells and opens the door to new sets of questions for those interested in connecting the physics of cellular self-organization to the dynamics of biological systems.

       

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will illustrate how this challenge can be overcome by elucidating the probabilistic connections between models of different levels of detail. These connections explain how stochastic partial differential equations (SPDE) arise naturally from particle models.

      I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.

    • Colloquium
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane. The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

       

       

      Speaker: Achilleas Porfyriadis, Harvard Black Hole Initiative

      Title: Extreme Black Holes: Anabasis and Accidental Symmetry

      Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of  AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Fred MacKintosh (Rice University)

      Title: Contractility, structure formation and fluctuations in active gels, with and without molecular motors

      Abstract: Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence, however, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified, reconstituted systems also point to contractility and structure formation in disordered, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this, as well as possible evidence for non-motor force generation.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Michael Shelley (Flatiron)

      Title: Active structures and flows in living cells

      Abstract: Flows in the fluidic interior of living cells can serve biological function or act as signatures of how intracellular forces are exerted. I’ll discuss examples of each. One is understanding the emergence of cell-spanning vortical flows in large developing egg cells, while the other arises in studying the nature of force transduction in single cell embryos moving towards their first cell division. Both involve the cytoskeleton, that set of polymers, cross-linkers, and molecular motors that underlie much of the active mechanics within cells, and has led to the development of new coarse-grained active matter models and novel instabilities.

    • Seminars
      Seminars Colloquia & Seminar
      4-11-2017 Social Science Applications Forum
      1:00 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

      In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

      This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

    • Active Matter Seminar
      1:00 pm-2:26 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-04.07.22

      Abstract: The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.

    • Math Science Literature Lecture Series
      1:00 pm-2:30 pm
      12/01/2024
      Lecture_Ma-1-pdf
      Yi Ma
      Photo Copyright Noah Berger / 2019

       

      Yi Ma (University of California, Berkeley)

      Title: Deep Networks from First Principles

      Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation, both for optimizing the same objective. This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.

      Talk chair: Harry Shum

      Slides | Video

    • Quantum Matter
      1:00 pm-2:30 pm
      12/01/2024
    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review  another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a self-organizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

    • Active Matter Seminar
      1:00 pm-2:20 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-03.24.22

      Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes and second layers within a base monolayer of M xanthus cells. We find that cells align with each other over the majority of the monolayer forming an active nematic liquid crystal with defect point where cell alignment is undefined. We find that new layers and holes form at positive and negative topological defects respectively. We model the cell layer using hydrodynamic modeling and find that this layer and hole formation process is driven by active nematic forces through cell motility and anisotropic substrate friction.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar
      Speaker: Alexander Grosberg (NYU)

      Title: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell

      Abstract: Nucleus of a living cell houses a cell genome – a polymer called chromatin, which is a functional form of DNA.  It is very long, e.g., 2 meters long for every human cell.  Nucleus is also an arena of incessant energy-driven activity.  Experiments show that chromatin undergoes large scale motions sustained over long times of order seconds.  In the talk, after reviewing the phenomenology, I will show how these flows may arise due to a phase transition in which chromatin-driving motors, such as RNA polymerase, form a polar (“ferromagnetic”) order controlled by hydrodynamic interactions.  The talk is based on the joint work with I.Eshghi and A.Zidovska.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-04.28.22
      Speaker: Guillaume Duclos (Brandeis)
      Title: Building active nematic and active polar liquids out of biological machines

      Abstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium, leading to emergent collective behaviors not found in passive materials. In this talk, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics, as well as shine light on the physical mechanisms that regulate self-organization in living matter.

       

      Video (Youtube)

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Active Matter Seminar

       

      Speaker:  Jonathan Bauermann, Max Planck Institute for the Physics of Complex Systems

      Title: Active chemical reactions in phase-separating systems

      Abstract: Motivated by the existence of membrane-less compartments in the chemically active environment of living cells, I will discuss the dynamics of droplets in the presence of active chemical reactions. Therefore, I will first introduce the underlying interplay between phase separation and active reactions, which can alter the droplet dynamics compared to equilibrium systems. A key feature of such systems is the emergence of concentration gradients even at steady states. In the second part of this talk, I will discuss how these gradients can trigger instabilities in the core of chemically active droplets, giving rise to a new non-equilibrium steady state of liquid spherical shells. Finally, I will present experimental and theoretical results discussing the existence and energetic cost of this non-equilibrium steady state in a coacervate system.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Shane McInally, Brandeis

      Title: Control of actin cable length by decelerated growth and network geometry

      Abstract: The sizes of many subcellular structures are coordinated with cell size to ensure that these structures meet the functional demands of the cell. In eukaryotic cells, these subcellular structures are often membrane-bound organelles, whose volume is the physiologically important aspect of their size. Scaling organelle volume with cell volume can be explained by limiting pool mechanisms, wherein a constant concentration of molecular building blocks enables subcellular structures to increase in size proportionally with cell volume. However, limiting pool mechanisms cannot explain how the size of linear subcellular structures, such as cytoskeletal filaments, scale with the linear dimensions of the cell. Recently, we discovered that the length of actin cables in budding yeast (used for intracellular transport) precisely matches the length of the cell in which they are assembled. Using mathematical modeling and quantitative imaging of actin cable growth dynamics, we found that as the actin cables grow longer, their extension rates slow (or decelerate), enabling cable length to match cell length. Importantly, this deceleration behavior is cell-length dependent, allowing cables in longer cells to grow faster, and therefore reach a longer length before growth stops at the back of the cell. In addition, we have unexpectedly found that cable length is specified by cable shape. Our imaging analysis reveals that cables progressively taper as they extend from the bud neck into the mother cell, and further, this tapering scales with cell length. Integrating observations made for tapering actin networks in other systems, we have developed a novel mathematical model for cable length control that recapitulates our quantitative experimental observations. Unlike other models of size control, this model does not require length-dependent rates of assembly or disassembly. Instead, feedback control over the length of the cable is an emergent property due to the cross-linked and bundled architecture of the actin filaments within the cable. This work reveals a new strategy that cells use to coordinate the size of their internal parts with their linear dimensions. Similar design principles may control the size and scaling of other subcellular structures whose physiologically important dimension is their length.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Open mic Swampland Discussion

      Topic: Cobordism

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Nicolas Romeo (UChicago)

      Title: Scaling behavior and control of nuclear wrinkling

      Abstract: The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. We characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behaviour. A spectral analysis of three-dimensional high-resolution live-imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing the mechanical properties of the nuclear envelope, highlighting in passing the importance of nonlinear response to biological robustness.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Mehran Kardar, MIT

      Title: Competition at the front of expanding populations

      Abstract: When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that  integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar

      Speaker: Josef Käs, Leipzig University

      Title: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

      Abstract: Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.

      Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.

      We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.

      Video (Youtube)

    • Quantum Matter
      1:00 pm-2:30 pm
      12/01/2024
    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Open Mic Discussion
      Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 02.02.23
      Active Matter Seminar

      Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen

      Title: Interacting Active Matter

      Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      Jefferson Hal Room 256, 17 Oxford Street, Cambridge MA 02138
      Active Matter Seminar
      Speaker: Sahand Hormoz, Harvard Medical School, Dana-Farber Cancer Institute
      Title: Insights from single cell lineage trees
      Abstract: In this talk, I will discuss two recent projects from my lab that involve lineage trees of cells (the branching diagram that represents the ancestry and division history of individual cells). In the first project, we reconstructed the lineage trees of individual cancer cells from the patterns of randomly occurring mutations in these cells. We then inferred the age at which the cancer mutation first occurred and the rate of expansion of the population of cancer cells within each patient. To our surprise, we discovered that the cancer mutation occurs decades before diagnosis. For the second project, we developed microfluidic ‘mother machines’ that allow us to observe mammalian cells dividing across tens of generations. Using our observations, we calculated the correlation between the duration of cell cycle phases in pairs of cells, as a function of their lineage distance. These correlations revealed many surprises that we are trying to understand using hidden Markov models on trees. For both projects, I will discuss the mathematical challenges that we have faced and open problems related to inference from lineage trees.
    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

    • Seminars
      Seminars Colloquia & Seminar
      5/15/2020 Math Physics Seminar
      1:00 pm-2:00 pm
      12/01/2024
    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Mark Bowick, Kavli Institute for Theoretical Physics, UCSB

      Title: The Role of Orientational Order in Development

      Abstract: Morphogenesis, the process through which genes generate form, establishes tissue scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fueled by cell proliferation, which, naively, should disrupt order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order remains an outstanding question in animal development. I will review the statistical mechanics of orientational order and discuss the observation of a fourfold orientationally ordered phase (tetratic) in the model organism Parhyale hawaiensis. I will also discuss theoretical mechanisms for the formation of orientational order that require both motility and cell division, with support from self-propelled vertex models of tissue. The aim is to uncover a robust, active mechanism for generating global orientational order in a non-equilibrium system that then sets the stage for the development of shape and form.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be “Swampland constraints, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      Lyman Lab, 17 Oxford Street, Cambridge MA 02138
      CMSA Active Matter Seminar 12.08.22
      Active Matter Seminar

      Speaker: Julien Tailleur (MIT)

      Title: Self-organization of motile cells by quorum-sensing or chemotactic interactions

      Abstract: Equilibrium statistical mechanics tells us how to control the self-assembly of passive materials by tuning the competition between energy and entropy to achieve desired states of organization. Out of equilibrium, no such principles apply and self-organization principles are scarce. Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Dissipation and injection of energy are then disconnected at the microscopic scale, hence driving the system strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases in the absence of cohesive attractive forces, but it also leaves us without guiding principles to understand the self-organization of active matter. In this talk, I will review the progress which has been made over the past ten years to control the organization of self-propelled agents using motility control, either externally or through interactions. I will show that generic principles apply and illustrate the theoretical developments presented in the talk using recent experiments on the motility-induced self-organization of bacterial mixtures.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 02.16.23
      Active Matter Seminar

      Speaker: Jörn Dunkel, MIT

      Title: Towards programmable living materials and quantitative models of active matter

      Abstract: Over the last two decades, major progress has been made in understanding the self-organization principles of active matter.  A wide variety of experimental model systems, from self-driven colloids to active elastic materials, has been established, and an extensive theoretical framework has been developed to explain many of the experimentally observed non-equilibrium pattern formation phenomena. Two key challenges for the coming years will be to translate this foundational knowledge into functional active materials, and to identify quantitative mathematical models that can inform and guide the design and production of such materials. Here, I will describe joint efforts with our experimental collaborators to realize self-growing bacterial materials [1], and to implement computational model inference schemes for active and living systems dynamics [2,3].

      [1] Nature 608: 324, 2022
      [2] PNAS 120: e2206994120, 2023
      [3] eLife 10: e68679, 2021

    • CMSA EVENT: Second Annual STAR Lab Conference
      1:01 pm-1:02 pm
      12/01/2024

      The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

      For more information, please consult the event’s website.

    • Colloquium
      1:02 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-10-2017 Mathematical Physics Seminar
      1:07 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:07 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:09 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      1:10 pm-3:00 pm
      12/01/2024
    • Colloquium
      1:10 pm-3:10 pm
      12/01/2024

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    • Colloquium
      1:10 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-31-2015 Mathematical Physics Seminar
      1:10 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:11 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Differential Geometry Seminar
      1:12 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-12-2017 Random Matrix & Probability Theory Seminar
      1:12 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Evolution Equation Seminar
      1:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-14-2015 Mathematical Physics Seminar
      1:14 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-17-2017 Mathematical Physics Seminar
      1:14 pm
      12/01/2024

      No additional detail for this event.

    • Active Matter Seminar
      1:15 pm-2:30 pm
      12/01/2024

      Abstract: In this talk I will review our ongoing theoretical and experimental efforts toward deciphering the hydrodynamic behavior of confluent epithelia. The ability of epithelial cells to collectively flow lies at the heart of a myriad of processes that are instrumental for life, such as embryonic morphogenesis and wound healing, but also of life-threatening conditions, such as metastatic cancer. Understanding the physical origin of these mechanisms requires going beyond the current hydrodynamic theories of complex fluids and introducing a new theoretical framework, able to account for biomechanical activity as well as for scale-dependent liquid crystalline order.

    • Quantum Matter
      1:15 pm-2:45 pm
      12/01/2024
      CMSA QMMP 1.24.23

      Quantum Matter Seminar

      Speakers: Jacob McNamara (Caltech) and Matthew Reece (Harvard)

      Title: Reflections on Parity Breaking

      Abstract: One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we will describe the formal meaning of parity as a gauge symmetry, and argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. We will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity, as well as their relationship with the Swampland Cobordism Conjecture.

       

      https://www.youtube.com/watch?v=hTeaVGRG3LA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=19

    • Seminars
      Seminars Colloquia & Seminar
      4-18-2017 Social Science Applications Forum
      1:15 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-08-2015 Geometric Analysis Seminar
      1:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-06-2015 Geometric Analysis Seminar
      1:17 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-08-2015 Evolution Equations Seminar
      1:18 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:18 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:20 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:21 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      1:21 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:22 pm-2:22 pm
      12/01/2024

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-19-2017 Random Matrix & Probability Theory Seminar
      1:22 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-13-2015 Geometric Analysis Seminar
      1:22 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-10-2015 Evolution Equations Seminar
      1:23 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: 2016 Big Data Conference & Workshop
      1:24 pm
      12/01/2024-08/23/2016
      1 Oxford Street, Cambridge MA 02138

      ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

      Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

      The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

      The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

      Conference Speakers:

      1. Jörn Boehnke, Harvard CMSA
      2. Joan Bruna, UC Berkeley [Video]
      3. Tamara Broderick, MIT [Video]
      4. Justin Chen, MIT [Video]
      5. Yiling Chen, Harvard University [Video]
      6. Amir Farbin, UT Arlington [Video]
      7. Doug Finkbeiner, Harvard University [Video]
      8. Andrew Gelman, Columbia University [Video]
      9. Nina Holden, MIT [Video]
      10. Elchanan Mossel, MIT
      11. Alex Peysakhovich, Facebook
      12. Alexander Rakhlin, University of Pennsylvania [Video]
      13. Neal Wadhwa, MIT [Video]
      14. Jun Yin, University of Wisconsin
      15. Harry Zhou, Yale University [Video]

      Please click Conference Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Please click here for registration.

      Conference Schedule:

      August 22 – Day 1
      8:30amBreakfast
      8:55amOpening remarks
      9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
      9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
      2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
      4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
      August 23 – Day 2
      8:45amBreakfast
      9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
      9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
      2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

      Workshop Participants:

      Richard Freeman’s Group:

      1. Sen Chai, ESSEC
      2. Brock Mendel, Harvard University
      3. Raviv Muriciano-Goroff, Stanford University
      4. Sifan Zhou, CMSA

      Scott Kominer’s Group:

      1. Bradly Stadie, UC Berkeley
      2. Neal Wadhwa, MIT [Video]
      3. Justin Chen

      Christopher Rogan’s Group:

      1. Amir Farbin, UT Arlington [Video]
      2. Paul Jackson, University of Adelaide

      For more information about the workshops, please reach out directly to the individual group leaders.

      This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

    • Seminars
      Seminars Colloquia & Seminar
      10-01-2015 Evolution Equations Seminar
      1:25 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-15-2015 Geometric Analysis Seminar
      1:26 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-16-2015 Random Matrix & Probability Theory Seminar
      1:27 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5-3-2017 Random Matrix & Probability Theory Seminar
      1:29 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-23-2015 Random Matrix & Probability Theory Seminar
      1:29 pm
      12/01/2024

      No additional detail for this event.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/16/2021 Computer Science for Mathematicians
      1:30 pm-2:30 pm
      12/01/2024

      Speaker: Michael P. Kim (UC Berkeley)

      Title: Outcome Indistinguishability

      Abstract: Prediction algorithms assign numbers to individuals that are popularly understood as individual “probabilities” — e.g., what is the probability of 5-year survival after cancer diagnosis? — and which increasingly form the basis for life-altering decisions. The understanding of individual probabilities in the context of such unrepeatable events has been the focus of intense study for decades within probability theory, statistics, and philosophy. Building off of notions developed in complexity theory and cryptography, we introduce and study Outcome Indistinguishability (OI). OI predictors yield a model of probabilities that cannot be efficiently refuted on the basis of the real-life observations produced by Nature.

      We investigate a hierarchy of OI definitions, whose stringency increases with the degree to which distinguishers may access the predictor in question.  Our findings reveal that OI behaves qualitatively differently than previously studied notions of indistinguishability.  First, we provide constructions at all levels of the hierarchy.  Then, leveraging recently-developed machinery for proving average-case fine-grained hardness, we obtain lower bounds on the complexity of the more stringent forms of OI.  The hardness result provides scientific grounds for the political argument that, when inspecting algorithmic risk prediction instruments, auditors should be granted oracle access to the algorithm, not simply historical predictions.

      Joint work with Cynthia Dwork, Omer Reingold, Guy N. Rothblum, Gal Yona; to appear at STOC 2021.

    • Probability Seminar
      1:30 pm-2:30 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 05.11.23

      Probability Seminar

      Speaker: Giorgio Cipolloni (Princeton)

      Title: How do the eigenvalues of a large non-Hermitian random matrix behave?

      Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues. Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X.

      Location: Science Center Room 232

    • Seminars
      Seminars Colloquia & Seminar
      11/14/2018 Hodge Seminar
      1:30 pm
      12/01/2024
    • Probability Seminar
      1:30 pm-2:30 pm
      12/01/2024
      Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

      Probability Seminar

      Speaker: Arka Adhikari (Stanford)

      Title: Correlation decay for finite lattice gauge theories

      Abstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.

       

    • Seminars
      1:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5-2-2017 Social Sciences Application Forum
      1:30 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA GR Seminar 05.11.23

      General Relativity Seminar

      Speaker: Aghil Alaee, Clark University

      Title: Positivity of Static quasi-local Mass in general relativity

      Abstract: In this talk, we review results on the PMT of quasi-local masses and prove the positivity of static quasi-local masses with respect to the AdS and AdS Schwarzschild spacetimes.

    • Seminars
      1:30 pm-3:00 pm
      12/01/2024
    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 04.24.23 (1)

      General Relativity Seminar

      Speaker: Tin Yau Tsang, University of California Irvine

      Title: Recent advances in scalar curvature and positive mass theorems
      Abstract:  First, we have a review of classical tools for studying scalar curvature and positive mass theorem. Then we are going to discuss some advances and new perspectives on these tools which lead to a deeper understanding of geometry and initial data sets.
    • CMSA EVENT: Current Developments in Mathematics 2019
      1:30 pm-5:00 pm
      12/01/2024-11/23/2019
      CDM-POSTER-2019.email_-662x1024

       

      cdmFriday, Nov. 22, 2019 1:30 pm – 5:20 pm

      Saturday, Nov. 23, 2019  9:00 am – 5:00 pm

      Harvard University Science Center, Hall C

      Speakers:

      ·      Svetlana Jitomirskaya (UC Irvine)

      ·      Subash Khot (NYU)

      ·      Jun Li (Stanford)

      ·      André Neves (Chicago)

      ·      Geordie Williamson (U Sidney)

      Free and open to the public – registration is required.
      Please register in advance online at www.math.harvard.edu/cdm

      CDM_2019-agenda-791x1024

    • Special Seminar
      Special Seminar
      4/30/2018 Special Seminar
      1:30 pm-2:30 pm
      12/01/2024
    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 02.09.23

      General Relativity Seminar

      Speaker: Maciej Zworski, UC Berkeley

      Title: Quasinormal modes and Ruelle resonances: mathematician’s perspective

      Abstract: Quasinormal modes of gravitational waves and Ruelle resonances in hyperbolic classical dynamics share many general properties and can be considered “scattering resonances”: they appear in expansions of correlations, as poles of Green functions and are associated to trapping of trajectories (and are both notoriously hard to observe in nature, unlike, say, quantum resonances in chemistry or scattering poles in acoustical scattering). I will present a mathematical perspective that also includes zeros of the Riemann zeta function (scattering resonances for the Hamiltonian given by the Laplacian on the modular surface) and stresses the importance of different kinds of trapping phenomena, resulting, for instance, in fractal counting laws for resonances.

    • Seminars
      Seminars Colloquia & Seminar
      11/21/2018 Hodge Seminar
      1:30 pm
      12/01/2024
    • Special Seminar
      1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/23/2019 Hodge Seminar
      1:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/5/2018 Hodge Seminar
      1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/28/2018 Hodge Lecture
      1:30 pm
      12/01/2024
    • Special Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Random Matrix & Probability Theory Seminar
      Speaker: Minh-Binh TRAN (SMU & MIT)

      Location: CMSA, Room G02

      Title: On the wave turbulence theory for a stochastic KdV type equation

      Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic  Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave  kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is  $d\ge 2$, the smallness of the nonlinearity $\lambda$ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation.  Unlike the cubic nonlinear Schrodinger equation, for which such a general result is commonly expected without the noise, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen  as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.

    • Seminars
      Seminars Colloquia & Seminar
      5/27/2020 Quantum Matter Seminar
      1:30 pm-3:00 pm
      12/01/2024
    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 02.16.23

      General Relativity Seminar

      Speaker: Kwinten Fransen (UC Santa Barbara)

      Title: Quasinormal Modes from Penrose Limits

      Abstract: In this talk, I will explain how to describe quasinormal modes with large real frequencies using Penrose limits. To do so, I first recall relevant aspects of the Penrose limit, and its resulting plane wave spacetimes, as well as quasinormal modes to subsequently tie these together. Having established the main principle, I will illustrate the usefulness of this point of view with the geometric realization of the emergent symmetry algebra underlying the quasinormal modes in the large real frequency limit and present its application to the astrophysically important example of Kerr black holes. Based on arXiv:2301.06999.

    • Colloquium
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 04.20.2023

      Speaker: Julio Parra Martinez, Caltech

      Title: Black hole collider physics

      Abstract: Despite more than a century since the development of Einstein’s theory, the general relativistic two-body problem remains unsolved. A precise description of its solution is now essential, as it is necessary for understanding the strong-gravity dynamics of compact binaries observed at LIGO/VIRGO/KAGRA and in future gravitational wave observatories. In this talk, I will describe how considering the scattering of black holes and gravitons can shed new light on this problem. I will explain how using modern ideas from collider and particle physics we can calculate scattering observables in classical gravity, and extract the basic ingredients that describe the bound binary dynamics. Such calculations have produced state-of-art predictions for current and future gravitational wave observatories, which open the door for further discovery as we enter this new era of precision gravitational physics.

    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 03.23.23

      General Relativity Seminar

      Speaker: Prahar Mitra (University of Cambridge)

      Title: New Phases of N=4 SYM

      Abstract: We construct new static solutions to gauged supergravity that, via the AdS/CFT correspondence, are dual to thermal phases in N=4 SYM at finite chemical potential. These solutions dominate the micro-canonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. These are constructed in two distinct truncations of gauged supergravity and can be uplifted to solutions of type IIB supergravity. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials. We will also discuss the status of hairy supersymmetric black hole solutions in this theory.

      Based on: https://arxiv.org/pdf/2207.07134.pdf [hep-th]

    • Seminars
      Seminars Colloquia & Seminar
      09-28-2015 Mathematical Physics Seminar
      1:31 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-24-2017 Mathematical Physics Seminar
      1:31 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:31 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      1:32 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:33 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
      1:34 pm
      12/01/2024-04/10/2016

      The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Speakers:

      1. Lydia Bieri (University of Michigan)
      2. Luis Caffarelli (University of Texas at Austin)
      3. Mihalis Dafermos (Princeton University)
      4. Camillo De Lellis (Universität Zürich)
      5. Pengfei Guan (McGill University)
      6. Slawomir Kolodziej (Jagiellonian University)
      7. Melissa Liu (Columbia University)
      8. Duong H. Phong (Columbia University)
      9. Richard Schoen (UC Irvine)
      10. Cliff Taubes (Harvard University)
      11. Blake Temple (UC Davis)
      12. Valentino Tosatti (Northwestern University)
      13. Tai-Peng Tsai (University of British Columbia)
      14. Mu-Tao Wang (Columbia University)
      15. Xu-jia Wang (Australian National University)

      Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Schedule:

      April 8 – Day 1
      8:30amBreakfast
      8:45amOpening remarks
      9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
      10:00am – 10:15amBreak
      10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
      11:15am – 11:30amBreak
      11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
      April 9 – Day 2
      8:45amBreakfast
      9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
      10:00am – 10:15amBreak
      10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
      11:15am – 11:30amBreak
      11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
      April 10 – Day 3
      8:45amBreakfast
      9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
      10:00am – 10:15amBreak
      10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
      11:15am – 11:30amBreak
      11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      10-22-2015 Evolution Equations Seminar
      1:37 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/11/2017 Mathematical Physics Seminar
      1:38 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-18-17 Mathematical Physics Seminar
      1:39 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-17-2015 Evolution Equations Seminar
      1:39 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      9-27-17 RM&PT Seminar
      1:41 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-27-17 Mathematical Physics Seminar
      1:42 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-23-17 Mathematical Physics Seminar
      1:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/11/2019 Random Matrix
      1:45 pm-2:45 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-25-17 RMPT Seminars
      1:45 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:47 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-10-2017 RM & PT Seminar
      1:48 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:51 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-22-2015 Geometric Analysis Seminar
      1:52 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:52 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-30-2015 Random Matrix & Probability Theory Seminar
      1:53 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-13-2017 Mathematical Physics Seminar
      1:53 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:54 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:54 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-15-17 RM & PT Seminar
      1:55 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      1:56 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:58 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      9/9/2020 RMPT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/18/2020 RMPT
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02/26/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
      2:00 pm-7:00 pm
      12/01/2024-09/17/2014

      The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      12.07.2022

      New Technologies in Mathematics Seminar

      Speaker: Cyril Zhang, Microsoft Research

      Title: How do Transformers reason? First principles via automata, semigroups, and circuits

      Abstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models, leading to dramatic advances in natural language understanding, program synthesis, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses, given that they resist interpretation? In this work, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure.

      Specifically, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory, we characterize shortcut solutions, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore, in synthetic experiments, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness, and discuss mitigations.

      Joint work with Bingbin Liu, Jordan Ash, Surbhi Goel, and Akshay Krishnamurthy.

    • Seminars
      2:00 pm-4:00 pm
      12/01/2024

      References: 

      • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
      • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
      • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
      • Nick Sheridan’s IAS and Jussieu lectures. 
      • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA NTM Seminar 10.26.2022

      New Technologies in Mathematics Seminar

      Speakers: João Araújo, Mathematics Department, Universidade Nova de Lisboa and Michael Kinyon, Department of Mathematics, University of Denver

      Title: From Engine to Auto

      Abstract: Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type, etc.
      In this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups, loops, semigroups, logic algebras, lattices and generalizations, quandles, and many more.
    • Seminars
      Seminars Colloquia & Seminar
      Homological Mirror Symmetry Seminar
      2:00 pm-4:00 pm
      12/01/2024-09/15/2017

      The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      09-15-16
      09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

      Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

      Lecture Slides

      09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

      Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

      Lecture Slides

      10-06-16

      Hansol Hong, CMSAhong

      Title: Homological mirror symmetry for elliptic curves

      Abstract:
      We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
      which use homological algebra techniques and formal deformation theory of Lagrangians etc.

      Notes

      Notes (Baris)

      10-13-16

      Yu-Wei Fan, Harvard

      s_yuwei_fan

      Title: Semi-flat mirror symmetry and Fourier-Mukai transform

      Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

       10-20-16

      Tim Large, MIT

      Title: “Symplectic cohomology and wrapped Fukaya categories”

      Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

      Notes

       10-27-16

      Philip Engel, Columbia

      picture

      Title: Mirror symmetry in the complement of an anticanonical divisor”

      According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

      Notes

      11-03-16

      Yusuf Baris Kartal, MIT

      HMS for Del Pezzo surfaces

      I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

      11-10-16No seminar this week
       12-08-16

      Lino Amorim, Boston University

      Title: The Fukaya category of a compact toric manifold

      Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

      Video

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      12/2/2020 Random Matrix and Probability Theory
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024

      New Technologies in Mathematics Seminar

      Speaker: Timo Schick, Meta AI

      Title: Toolformer: Language Models Can Teach Themselves to Use Tools

      Abstract: Language models exhibit remarkable abilities to solve new tasks from just a few examples or textual instructions, especially at scale. They also, paradoxically, struggle with basic functionality, such as arithmetic or factual lookup, where much simpler and smaller models excel. In this talk, we show how these limitations can be overcome by letting language models teach themselves to use external tools via simple APIs. We discuss Toolformer, a model trained to independently decide which APIs to call, when to call them, what arguments to pass, and how to best incorporate the results into future token prediction. Through this, it achieves substantially improved zero-shot performance across a variety of downstream tasks without sacrificing its core language modeling abilities.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5/20/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024

      New Technologies in Mathematics Seminar

      Speaker: Dmitry Krotov, IBM Research – Cambridge

      Title: Modern Hopfield Networks for Novel Transformer Architectures

      Abstract: Modern Hopfield Networks or Dense Associative Memories are recurrent neural networks with fixed point attractor states that are described by an energy function. In contrast to conventional Hopfield Networks, which were popular in the 1980s, their modern versions have a very large memory storage capacity, which makes them appealing tools for many problems in machine learning and cognitive and neurosciences. In this talk, I will introduce an intuition and a mathematical formulation of this class of models and will give examples of problems in AI that can be tackled using these new ideas. Particularly, I will introduce an architecture called Energy Transformer, which replaces the conventional attention mechanism with a recurrent Dense Associative Memory model. I will explain the theoretical principles behind this architectural choice and show promising empirical results on challenging computer vision and graph network tasks.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speakers: Katherine Collins and Albert Jiang, Department of Computer Science and Technology, University of Cambridge

      Title: Evaluating Language Models for Mathematics through Interactions

      Abstract: There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs based on static pairs of inputs and outputs is insufficient to be able to make an informed decision about which LLMs, and under what assistive settings they can be sensibly utilised. Static assessment fails to take into account the essential interactive element in their deployment, and therefore limits how we understand language model capabilities. In this talk, we present our recent work introducing CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We discuss our study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we identify useful scenarios and existing issues of GPT-4 in mathematical reasoning through a series of case studies contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models which communicate uncertainty, respond well to user corrections, and are more interpretable and concise may constitute better assistants; interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models’ algebraic fallibility and discern where they are appropriate to use.

       

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Jimmy Ba, University of Toronto

      Title: How to steer foundation models?

      Abstract: By conditioning on natural language instructions, foundation models and large language models (LLMs) have displayed impressive capabilities as general-purpose computers. However, task performance depends significantly on the quality of the prompt used to steer the model. Due to the lack of knowledge of how foundation models work, most effective prompts have been handcrafted by humans through a demanding trial-and-error process. To reduce the human effort in this alignment process, I will discuss a few approaches to steer these powerful models to excel in various downstream language and image tasks.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/21/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/04/2020 RMPT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/16/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/14/2020 RM&PT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/8/2019 Topology Seminar
      2:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/7/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/22/2019 Social Science Applications Forum
      2:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Johan Commelin, Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

      Title: Breaking the one-mind-barrier in mathematics using formal verification

      Abstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.

      I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.

      Video
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024

      Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

      In the 2020-2021 AY, the Random Matrix and Probability Theory Seminar will take place on select Wednesdays from 2:00 – 3:00pm virtually. This seminar is organized by Christian Brennecke (brennecke@math.harvard.edu ).

      To learn how to attend this seminar, please fill out this form.

      The schedule below will be updated as the details are confirmed.

      Spring 2021:

      DateSpeakerTitle/Abstract
      3/31/2021Philippe Sosoe, Cornell UniversityTitle:  Fluctuation bounds for O’Connell-Yor type systems

      Abstract: The O’Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about this model thanks to remarkable algebraic structure uncovered by O’Connell, Yor and others, basic estimates for the behavior of the tails of the centered partition function for finite N that are available for zero temperature models are missing. I will present an iterative estimate to obtain strong concentration and localization bounds  for the O’Connell-Yor polymer on an almost optimal scale N^{1/3+\epsilon}.

      In the second part of the talk, I will introduce a system of interacting diffusions describing the successive increments of partition functions of different sizes. For this system, the N^{2/3} variance upper bound known for the OY polymer can be proved for a general class of interactions which are not expected to correspond to integrable models.

      Joint work with Christian Noack and Benjamin Landon.

      4/7/2021Yue M. Lu, HarvardTitleHouseholder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Random Matrices

      Abstract: In many problems in statistical learning, random matrix theory, and statistical physics, one needs to simulate dynamics on random matrix ensembles. A classical example is to use iterative methods to compute the extremal eigenvalues/eigenvectors of a (spiked) random matrix. Other examples include approximate message passing on dense random graphs, and gradient descent algorithms for solving learning and estimation problems with random initialization. We will show that all such dynamics can be simulated by an efficient matrix-free scheme, if the random matrix is drawn from an ensemble with translation-invariant properties. Examples of such ensembles include the i.i.d. Gaussian (i.e. the rectangular Ginibre) ensemble, the Haar-distributed random orthogonal ensemble, the Gaussian orthogonal ensemble, and their complex-valued counterparts.A “direct” approach to the simulation, where one first generates a dense n × n matrix from the ensemble, requires at least O(n^2) resource in space and time. The new algorithm, named Householder Dice (HD), overcomes this O(n^2) bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are O(nT) and O(n T^2), respectively, with T being the number of iterations. When T ≪ n, which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint.Finally, the HD algorithm is not just a computational trick. I will show how its construction can serve as a simple proof technique for several problems in high-dimensional estimation
      4/14/2021Canceled
      4/16/2021
      Friday
      Patrick Lopatto (IAS)Title: Fluctuations in local quantum unique ergodicity for generalized Wigner matrices

      Abstract: In a disordered quantum system, delocalization can be understood in many ways. One of these is quantum unique ergodicity, which was proven in the random matrix context by Bourgade and Yau. It states that for a given eigenvector and set of coordinates J, the mass placed on J by the eigenvector tends to N^{-1}|J|, the mass placed on those coordinates by the uniform distribution. Notably, this convergence holds for any size of J, showing that the eigenvectors distribute evenly on all scales.

      I will present a result which establishes that the fluctuations of these averages are Gaussian on scales where |J| is asymptotically less than N, for generalized Wigner matrices with smooth entries. The proof uses new eigenvector observables, which are analyzed dynamically using the eigenvector moment flow and the maximum principle.

      This is joint work with Lucas Benigni.

      4/21/2021Jean-Christophe Mourrat, Courant Institute, NYUTitleMean-field spin glasses: beyond Parisi’s formula?

      Abstract: Spin glasses are models of statistical mechanics encoding disordered interactions between many simple units. One of the fundamental quantities of interest is the free energy of the model, in the limit when the number of units tends to infinity. For a restricted class of models, this limit was predicted by Parisi, and later rigorously proved by Guerra and Talagrand. I will first show how to rephrase this result using an infinite-dimensional Hamilton-Jacobi equation. I will then present partial results suggesting that this new point of view may allow to understand limit free energies for a larger class of models, focusing in particular on the case in which the units are organized over two layers, and only interact across layers.

      Fall 2020:

      DateSpeakerTitle/Abstract
      9/9/2020Yukun He (Zurich)Title: Single eigenvalue fluctuations of sparse Erdős–Rényi graphs

      Abstract: I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdös-Rényi graph $G(N,p)$. I show that if $N^{-1}\ll p \ll N^{-2/3}, then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. The main technical tool of the proof is a rigidity bound of accuracy $N^{-1-\varepsilon}p^{-1/2}$ for the extreme eigenvalues, which avoids the $(Np)^{-1}$-expansions from previous works. Joint work with Antti Knowles.

      10/14/2020David Belius (University of Basel)TitleThe TAP approach to mean field spin glasses

      Abstract: The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated methods  in theoretical physics and mathematics, such as the replica method, which are largely orthogonal to the TAP approach. The TAP approach has the advantage of being interpretable as a variational principle optimizing an energy/entropy trade-off, as commonly encountered in statistical physics and large deviations theory, and potentially allowing for a more direct characterization of the Gibbs measure and its “pure states”. In this talk I will recall the TAP approach, and present preliminary steps towards a solution of mean field spin glass models entirely within a TAP framework.

      10/28/2020Giuseppe Genovese (University of Basel)TitleNon-convex variational principles for the RS free energy of restricted Boltzmann machines

      Abstract: From the viewpoint of spin glass theory, restricted Boltzmann machines represent a veritable challenge, as to the lack of convexity prevents us to use Guerra’s bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will present old and new results around the topic along with some open problems.

      11/4/2020Benjamin Landon (MIT)Title:  Fluctuations of the spherical Sherrington-Kirkpatrick model

      Abstract:  The SSK model was introduced by Kosterlitz, Thouless and Jones as a simplification of the usual SK model with Ising spins. Fluctuations of its observables may be related to quantities from random matrix theory using integral representations.  In this informal talk we discuss some results on fluctuations of this model at critical temperature and with a magnetic field

      11/11/2020
      3:00 – 4:00pm
      Lucas Benigni (University of Chicago)Title:  Optimal delocalization for generalized Wigner matrices

      Abstract: We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result, known as delocalization, to more general entry distributions. After giving a brief overview of the previous results going in this direction, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.

      11/18/2020Simone Warzel (Technical University of Munich)Title:  Hierarchical quantum spin glasses

      Abstract: Hierarchical spin glasses such as the generalised random energy model are known to faithfully model typical energy landscapes in the classical theory of mean-field spin glasses. Their built-in hierarchical structure is known to emerge spontaneously in the spin-glass phase of, e.g., the Sherrington-Kirkpatrick model. In this talk, I will review recent results on the effects of a transversal magnetic field on such hierarchical quantum spin glasses.
      In particular, I will present a formula of Parisi-type for their free energy which allows to make predictions about the phase diagram.
      12/2/2020Sabine Jansen (LMU Munich)TitleThermodynamics of a hierarchical mixture of cubes

      Abstract: The talk discusses a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes of side-lengths 2^j, j\in \N_0. Cubes belong to an admissible set such that if two cubes overlap, then one cube is contained in the other, a picture reminiscent of Mandelbrot’s fractal percolation model. I will present exact formulas for the entropy and pressure, discuss phase transitions from a fluid phase with small cubes towards a condensed phase with a macroscopic cube, and briefly sketch some broader questions on renormalization and cluster expansions that motivate the model. Based on arXiv:1909.09546 (J. Stat. Phys. 179 (2020), 309-340).

      For information on previous seminars, click here

      The schedule will be updated as details are confirmed.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Gabriel Poesia, Dept. of Computer Science, Stanford University

      Title: Peano: Learning Formal Mathematical Reasoning Without Human Data

      Abstract: Peano is a theorem proving environment in which a computational agent can start tabula rasa in a new domain, learn to solve problems through curiosity-driven exploration, and create its own higher level actions. Gabriel will describe the system, present case studies on learning to solve simple algebra problems from the Khan Academy platform, and describe work on progress on learning the Natural Number Game, a popular introduction to theorem proving in Lean for mathematicians.

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      10.19.2022

      New Technologies in Mathematics Seminar

      Speaker: Antonia Creswell, DeepMind

      Title: Towards Faithful Reasoning Using Language Models

      Abstract: Language models are showing impressive performance on many natural language tasks, including question-answering. However, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this, we will introduce Selection-Inference, a faithful reasoning model, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy.

       

       

    • New Technologies in Mathematics Seminar
      2:00 pm-4:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      10.05.2022

      New Technologies in Mathematics Seminar

      Speaker: Guy Gur-Ari, Google Research

      Title: Minerva: Solving Quantitative Reasoning Problems with Language Models

      Abstract: Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA NTM Seminar 09.28.2022

      New Technologies in Mathematics

      Speaker: Surya Ganguli, Stanford University

      Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
      Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size, sometimes achieving exponential scaling, by collecting small carefully curated datasets rather than large random ones.
      References: Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
      Sorscher, Ben, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/31/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/28/2020 RM&PT seminar
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Sean Welleck, CMU, Language Technologies Institute

      Title: Llemma: an open language model for mathematics

      Abstract: We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of mathematical web data, code, and scientific papers. The resulting models show improved mathematical capabilities, and can be adapted to various tasks. For instance, Llemma outperforms the unreleased Minerva model suite on an equi-parameter basis, and is capable of tool use and formal theorem proving without any further fine-tuning. We openly release all artifacts, including the Llemma models, the Proof-Pile II, and code to replicate our experiments. We hope that Llemma serves as a platform for new research and tools at the intersection of generative models and mathematics.

       

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/29/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5/13/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Quantum Matter
      2:00 pm-3:30 pm
      12/01/2024

      Speaker: Clay Cordova (U Chicago)

      Title: Non-Invertible Duality Defects in 3+1 Dimensions

      Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

    • Topological Quantum Matter Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Ceren Dag, Harvard

      Title: Breaking ergodicity: quantum scars and regular eigenstates

      Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411, in peer review.

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo
      2:00 pm-5:00 pm
      12/01/2024-04/03/2018
      1 Oxford Street, Cambridge MA 02138
      Math Science Lectures in Honor of Raoul Bott

      DSC_0170-e1525711590120

      On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

      The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

       

      Cachazo-e1519325938458

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-20-2017 RM & PT Seminar
      2:00 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Special Seminar

      Speaker: Mayuko Yamashita, Kyoto University

      Title: Topological modular forms and heretoric string theory

      Abstract: In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF.

      Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

       

    • Topological Quantum Matter Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker:  Ken K. W. Ma (Northeastern University)

      Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future

      Abstract: The discovery of fractional quantum Hall (FQH) states started a new chapter in modern physics. Nowadays, more than 70 FQH states at different filling factors have been observed. Among them, the FQH state at the filling factor ν=5/2 in GaAs (or the 5/2 state) remains one of the most special and attractive states. Since its discovery in 1987, different possible topological orders have been proposed to describe the 5/2 state. Some of them can host an exotic type of particles, known as non-Abelian anyons. Recent experiments have provided more insights into the understanding of the 5/2 state, but its underlying nature is still under debate.

      In this talk, I will review the basics of the 5/2 state [1] and a more unified theoretical description of different possible topological orders of the 5/2 state that we have recently proposed [2]. I will also review the groundbreaking thermal Hall conductance experiment [3] and the follow-up quantum Hall interface experiments by the Weizmann Institute group [4, 5], and discuss what possible lessons that we can learn from the experimental results. Lastly, I will talk about some possible directions and related topics for future investigations.

      References:

      [1] K. K. W. Ma, M. R. Peterson, V. W. Scarola, and K. Yang, “Fractional quantum Hall effect at the filling factor ν = 5/2” in Encyclopedia of Condensed Matter Physics (Second Edition), edited by T. Chakraborty, Academic Press (2024).
      [2] K. K. W. Ma and D. E. Feldman, “The sixteenfold way and the quantum Hall effect at half-integer filling factors”, Phys. Rev. B 100, 035302 (2019).
      [3] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern, “Observation of half-integer thermal Hall conductance”, Nature (London) 559, 205 (2018).
      [4] B. Dutta, W. Yang, R. Melcer, H. K. Kundu, M. Heiblum, V. Umansky, Y. Oreg, A. Stern, D. Mross, “Distinguishing between non-Abelian topological orders in a quantum Hall system”, Science 375, 193 (2021).
      [5] B. Dutta, V. Umansky, M. Banerjee, and M. Heiblum, “Isolated ballistic non-Abelian interface channel”, Science 377, 1198 (2022).

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Yuanzhi Li, CMU Dept. of Machine Learning and Microsoft Research

      Title: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation

      Abstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking results about this question. Using a synthetic biography dataset, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence, can mitigate this issue. Using linear probing, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations.

      We then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset, so that it could answer “What is the birthday of XXX” with 100% accuracy.  Even so, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly.  Even using Chain of Thought training data only helps the model answer such questions in a CoT manner, not directly.

      We will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example, is a 1B parameter language model enough to store all the knowledge of a middle school student?

       

       

    • Topological Quantum Matter Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Prashant Kumar, University of Chicago

      Title: Emergent composite-fermion Luttinger liquid at the half-filled Landau level

      Abstract: The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, I will present our numerical calculations of the excitation spectrum of this state on infinite cylinders. By comparing our results with a quasi-1D theory of CFs, we show compelling quantitative evidence for the emergence of a Luttinger liquid of composite-fermions at low energies, distinct from that of electrons. I will comment on some future directions.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5/6/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Abhishek Panigrahi, Dept. of Computer Science, Princeton University

      Title: On the Power of Forward pass through Transformer Architectures

      Abstract: Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of study. This talk studies two interesting phenomena.

      In the first half, we explore how and why pre-trained language models, specifically BERT of moderate sizes, can effectively learn linguistic structures like parse trees during pre-training. Specifically, using synthetic data through PCFGs, we show how moderate-sized transformers can perform forward-backward parsing, also known as the inside-outside algorithm, during inference. We further understand the role of the pre-training loss for the model to learn to parse during pre-training.

      In the second half, we consider in-context learning of large language models, where they learn to reason on the fly. An ongoing hypothesis is that transformers simulate gradient descent at inference to perform in-context learning. We propose the Transformer in Transformer (TinT) framework, which creates explicit transformer architectures that can simulate and fine-tune a small pre-trained transformer model during inference. E.g. a 1.3B parameter TINT model can simulate and fine-tune a 125 million parameter model in a single forward pass. This framework suggests that large transformers might execute intricate sub-routines during inference, and provides insights for enhancing their capabilities through intelligent design considerations.

       

    • Math Science Literature Lecture Series
      2:00 pm-3:00 pm
      12/01/2024

      Shing-Tung Yau (Harvard)

      Title: Shiing-Shen Chern as a Great Geometer of 20th Century

      Video | Slides | Article

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024

      New Technologies in Mathematics Seminar

      Speaker: Ronen Eldan, Microsoft Research

      Title: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent

      Abstract: While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity?

      In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4-year-olds typically understand, generated by GPT-3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the state-of-the-art models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for low-resource or specialized domains, and shed light on the emergence of language capabilities in LMs.

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: François Charton, Meta AI

      Title:  Transformers for maths, and maths for transformers

      Abstract: Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics.

      Problems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic, I show that model predictions can be explained, that trained models do not confabulate, and that carefully choosing the training distributions can help achieve better, and more robust, performance.

       

       

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/1/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • General Relativity Seminar
      2:00 pm-3:00 pm
      12/01/2024
      17 Oxford St, Cambridge, MA 02138

      General Relativity Seminar

      Speaker: Suman Kundu (Weizmann Institute)

      Title: ‘Grey Galaxy’ as the endpoint of the Kerr-AdS super radiant blackhole

      Abstract: Kerr AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses near extremality. We conjecture that these instabilities settle down into Grey Galaxies (GG)s – a new class of solutions to Einstein’s equations which we construct for $d=3$. Grey Galaxies consist of an $mega=1$ black hole in the `centre’ of $AdS$, surrounded by a uniformly thick and very large disk of thermal bulk matter that revolves around the centre of AdS at the speed of light. The parametrically low energy density and parametrically large radius of the gas disk are inversely related; as a consequence, the gas carries a finite fraction of the total energy. Grey Galaxy saddles exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr AdS black holes and the gas. In addition to a smooth piece, the boundary stress tensor of these solutions includes a contribution from a delta function localized at the `equator’ of the boundary sphere, a term which may be used as an order parameter that sharply distinguishes GG solutions from ordinary Kerr-Black hole saddles. We also construct `Revolving Black Hole (RBH) saddles’,  macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, that describe black holes revolving around the centre of $AdS$, at the fixed radial location but in a quantum wave function in the angular directions. RBH saddles turn out to be (marginally) entropically subdominant to GG saddles. We argue that supersymmetric versions of RBH saddles exist and have interesting consequences for the spectrum of SUSY states in, e.g.  ${\cal N}=4$ Yang-Mills theory.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Alex Gu, MIT Dept. of EE&CS

      Title: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models

      Abstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

       

    • Seminars
      Seminars Colloquia & Seminar
      4/22/2020 RM&PT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-29-17 RM & PT Seminar
      2:03 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      09-24-2015 Evolution Equations Seminar
      2:03 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2015 Special Random Matrix & Probability Theory Seminar
      2:05 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-18-2015 Random Matrix & Probability Theory Seminar
      2:07 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:08 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 RM&PT Seminar
      2:08 pm
      12/01/2024
    • Colloquium
      2:10 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-29-2017 Mathematical Physics Seminar
      2:11 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      2:11 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-29-2015 Geometric Analysis Seminar
      2:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-28-2015 CMSA Special Seminar
      2:15 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:15 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      2:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-05-2015 Mathematical Physics Seminar
      2:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-15-2015 Evolution Equations Seminar
      2:17 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-6-2017 Mathematical Physics Seminar
      2:17 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-07-2015 Random Matrix & Probability Theory Seminar
      2:19 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:20 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-29-2015 Evolution Equations Seminar
      2:20 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-14-2015 Random Matrix & Probability Theory Seminar
      2:21 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:21 pm
      12/01/2024-03/06/2018

      During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

      You can watch Prof. Sheshmani describe the series here.

      The Syllabus is as follows:

      Date………..TopicVideo/Audio
      1-25-2018Gromov-Witten invariants 

      Definition, examples via algebraic geometry I

      Video / Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture.

       2-01-2018Gromov-Witten invariants 

      Virtual Fundamental Class I (definition)

      Video Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture

      2-13-2018Gromov-Witten invariants 

      Virtual Fundamental Class II (computation in some cases)

       2-15-2018Computing GW invariants 

      Three level GW classes

      Genus zero invariants of the projective plane

       2-20-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) I

      2-22-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) II

      2-27-2018Quantum Cohomology 

      Big Quantum Cohomology I

       3-1-2018Quantum Cohomology 

      Big Quantum Cohomology II

      GW potential

      WDVV equation

      3-6-2018GW invariants via Quantum Cohomology 

      The Quintic threefold case

      The P^2 case

      GW invariants via Quantum Cohomology 

      Dubrovin (quantum) connection

      Nakajima varieties 

      -Algebraic and symplectic reduction

      Nakajima varieties 

      Quasi maps to Nakajima varieties

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) I

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) I

       
      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) IV

       
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      11/11/21 Interdisciplinary Science Seminar
      2:22 pm-3:22 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-11.11.21

      Title: The Kervaire conjecture and the minimal complexity of surfaces

      Abstract: We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture.
      The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/<<w>> is still nontrivial. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of surfaces in HNN extensions. This gives a conceptually simple proof of Klyachko’s theorem that confirms the Kervaire conjecture for any G torsion-free. I will also explain new results obtained using this approach.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-21-2015 Random Matrix & Probability Theory Seminar
      2:22 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Existence of Canonical Metrics on Non-Kähler Geometry
      2:23 pm-2:24 pm
      12/01/2024

      On Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on “Existence of Canonical Metrics on Non-Kähler Geometry.

      In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses works by Jun Li of Fudan University in Shanghai, Ji-Xiang Fu of Fudan University, Ivan Smith of the University of Cambridge, Richard P. Thomas of Imperial College London, Tristan C. Collins of the Massachusetts Institute of Technology, French mathematician Émile Picard, Teng Fei of Rutgers University in Newark, New Jersey, Adam Jacob of the University of California, Davis, and Duong H. Phong of Columbia University.

      More information about this talk can be found on the Simons Foundation website.

    • Colloquium
      2:23 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:24 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      11/18/2021 Interdisciplinary Science Seminar
      2:25 pm-3:25 pm
      12/01/2024

      Title: Amplituhedra, Scattering Amplitudes and Triangulations

      Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      12/2/2021 Interdisciplinary Science Seminar
      2:28 pm-3:28 pm
      12/01/2024

      Title: Polyhomogeneous expansions and Z/2-harmonic spinors branching along graphs

      Abstract: In this talk, we will first reformulate the linearization of the moduli space of Z/2-harmonic spinorsv branching along a knot. This formula tells us that the kernel and cokernel of the linearization are isomorphic to the kernel and cokernel of the Dirac equation with a polyhomogeneous boundary condition. In the second part of this talk, I will describe the polyhomogenous expansions for the Z/2-harmonic spinors branching along graphs and formulate the Dirac equation with a suitable boundary condition that can describe the perturbation of graphs with some restrictions. This is joint work with Andriy Haydys and Rafe Mazzeo.

    • Colloquium
      2:29 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      12/9/21 Interdisciplinary Science Seminar
      2:29 pm-3:29 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-12.09.21-1583x2048

      Title: Numerical Higher Dimensional Geometry

      Abstract: In 1977, Yau proved that a Kahler manifold with zero first Chern class admits a Ricci flat metric, which is uniquely determined by certain “moduli” data. These metrics have been very important in mathematics and in theoretical physics, but despite much subsequent work we have no analytical expressions for them. But significant progress has been made on computing numerical approximations. We give an introduction (not assuming knowledge of complex geometry) to these problems and describe these methods.

    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-Quantum-Matter-in-Mathematics-and-Physics-11.18.21-1583x2048

      Speaker: B. Andrei Bernevig (Princeton University)

      Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

      Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

    • Seminars
      Seminars Colloquia & Seminar
      9/19/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/12/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-28-2015 Random Matrix & Probability Theory Seminar
      2:30 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      2:30 pm-3:30 pm
      12/01/2024-04/26/2020
    • Seminars
      Seminars Colloquia & Seminar
      12/10/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-QMMP-1.18.22-1544x2048-1

      Speaker: Aavishkar Patel (UC Berkeley)

      Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

      Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

    • Seminars
      Seminars Colloquia & Seminar
      11/26/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024

      Speaker: Jeongwan Haah (Microsoft)

      Title: A degeneracy bound for homogeneous topological order

    • Seminars
      Seminars Colloquia & Seminar
      11/21/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      2/27/2019 Colloquium
      2:30 pm-4:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-QMMP-1.28.2022-1544x2048-1

      Speaker: Maria Tikhanovskaya (Harvard)

      Title: Maximal quantum chaos of the critical Fermi surface

      Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

    • Seminars
      Seminars Colloquia & Seminar
      11/14/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Colloquium
      2:30 pm-3:00 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      4/10/2019 Colloquium
      2:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/3/2019 Colloquium
      2:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/31/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Social Science Applications Forum
      2:30 pm-4:00 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-QMMP-12.10.21-1544x2048

      Speaker: Lukasz Fidkowski (U Washington)

      Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

      Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

    • Seminars
      Seminars Colloquia & Seminar
      3/7/2019 Social Science Applications Forum
      2:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/18/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      12/01/2024
    • Colloquium
      2:32 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-19-2015 Mathematical Physics Seminar
      2:33 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-20-2015 Geometric Analysis Seminar
      2:35 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-26-2015 Mathematical Physics Seminar
      2:36 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-02-2015 Mathematical Physics Seminar
      2:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      01-26-2018 Mirror Symmetry Seminar
      2:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-03-2015 Geometric Analysis Seminar
      2:39 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-04-2015 Random Matrix & Probability Theory Seminar
      2:40 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-29-2018 Mathematical Physics Seminar
      2:42 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      1-30-2018 Special Seminar
      2:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2-2-2018 Mirror Symmetry Seminar
      2:44 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:44 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:45 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      12/16/2021 Interdisciplinary Science Seminar
      2:46 pm-3:46 pm
      12/01/2024

      Title: Quadratic reciprocity from a family of adelic conformal field theories

      Abstract: We consider a deformation of the 2d free scalar field action by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it’s no longer invariant under the local conformal symmetry algebra. Furthermore, there is an adelic version of this family of global conformal field theories, parametrized by the choice of a number field, together with a Hecke character. Tate’s thesis plays an important role here in calculating Green’s functions of these theories, and in ensuring the adelic compatibility of these theories. In particular, the local L-factors contribute to prefactors of these Green’s functions. We shall try to see quadratic reciprocity from this context, as a consequence of an adelic version of holomorphic factorization of these theories. This is work in progress with B. Stoica and X. Zhong.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/6/2022 Interdisciplinary Science Seminar
      2:47 pm-3:47 pm
      12/01/2024

      Title: The smooth closing lemma for area-preserving surface diffeomorphisms

      Abstract: In this talk, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing result of twisted Seiberg- Witten Floer homology. This is joint work with Dan Cristofaro-Gardiner and Rohil Prasad.

    • Colloquium
      2:47 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:48 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/13/2022 Interdisciplinary Science Seminar
      2:48 pm-3:48 pm
      12/01/2024

      Title: A universal triangulation for flat tori

      Abstract: A celebrated theorem of Nash completed by Kuiper implies that every smooth Riemannian surface has a C¹ isometric embedding in the Euclidean 3-space E³. An analogous result, due to Burago and Zalgaller, states that every polyhedral surface, obtained by gluing Euclidean triangles, has an isometric PL embedding in E³. In particular, this provides PL isometric embeddings for every flat torus (a quotient of E² by a rank 2 lattice). However, the proof of Burago and Zalgaller is partially constructive, relying on the Nash-Kuiper theorem. In practice, it produces PL embeddings with a huge number of vertices, moreover distinct for every flat torus. Based on a construction of Zalgaller and on recent works by Arnoux et al. we exhibit a universal triangulation with less than 10.000 vertices, admitting for any flat torus an isometric embedding that is linear on each triangle. Based on joint work with Florent Tallerie.

    • Seminars
      Seminars Colloquia & Seminar
      11-19-2015 Evolution Equations Seminar
      2:50 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 CMSA Special Lecture
      2:51 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/20/2022 – Interdisciplinary Science Seminar
      2:52 pm-4:52 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-01.20.22-1577x2048

      Title: Markov chains, optimal control, and reinforcement learning

      Abstract: Markov decision processes are a model for several artificial intelligence problems, such as games (chess, Go…) or robotics. At each timestep, an agent has to choose an action, then receives a reward, and then the agent’s environment changes (deterministically or stochastically) in response to the agent’s action. The agent’s goal is to adjust its actions to maximize its total reward. In principle, the optimal behavior can be obtained by dynamic programming or optimal control techniques, although practice is another story.

      Here we consider a more complex problem: learn all optimal behaviors for all possible reward functions in a given environment. Ideally, such a “controllable agent” could be given a description of a task (reward function, such as “you get +10 for reaching here but -1 for going through there”) and immediately perform the optimal behavior for that task. This requires a good understanding of the mapping from a reward function to the associated optimal behavior.

      We prove that there exists a particular “map” of a Markov decision process, on which near-optimal behaviors for all reward functions can be read directly by an algebraic formula. Moreover, this “map” is learnable by standard deep learning techniques from random interactions with the environment. We will present our recent theoretical and empirical results in this direction.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/27/2022 – Interdisciplinary Science Seminar
      2:54 pm-4:54 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-1.27.2022-1583x2048

      Title: Polynomials vanishing at lattice points in convex sets

      Abstract: Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number, which we compute for many (but maybe not all) triangles P.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 Mathematical Physics Seminar
      2:54 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:54 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:55 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:56 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-19-2015 Random Matrix and Probability Theory Seminar
      2:57 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:57 pm
      12/01/2024

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      2/3/2022 – Interdisciplinary Science Seminar
      2:57 pm-4:57 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.03.2022-1583x2048-1

      Title:Quasiperiodic prints from triply periodic blocks

      Abstract: Slice a triply periodic wooden sculpture along an irrational plane. If you ink the cut surface and press it against a page, the pattern you print will be quasiperiodic. Patterns like these help physicists see how metals conduct electricity in strong magnetic fields. I’ll show you some block prints that imitate the printing process described above, and I’ll point out the visual features that reveal conductivity properties.

      Interactive slides:https://www.ihes.fr/~fenyes/seeing/slices/

    • Colloquium
      2:59 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-16-2015 Mathematical Physics Seminar
      2:59 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/31/2020 Quantum Matter Seminar
      3:00 pm-4:30 pm
      12/01/2024
    • Special Seminar
      Special Seminar
      3-28-2018 Special Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11-17-2015 Geometric Analysis Seminar
      3:00 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2/25/2020 Fluid Dynamics
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2-27-2018 HMS Lecture
      3:00 pm-4:00 pm
      12/01/2024-03/01/2018
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024

      Speaker: Jason Rute, CIBO Technologies

      Title: Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models

      Abstract: Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.

    • New Technologies in Mathematics Seminar
    • Seminars
      Seminars Colloquia & Seminar
      Algebraic Geometry Seminar, Thursdays
      3:00 pm-4:00 pm
      12/01/2024

      This seminar will not be held in the Spring 2018 Semester.

      The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated as details are confirmed.

       

       

      DateNameTitle/Abstract
      09-14-17 Yu-Wei Fan (Harvard Math)

      Entropy of an autoequivalence on Calami-Yau manifolds

      Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

      11-1-17

      *5:00pm, G10*

       Shamil Shakirov, Harvard Math

      Undulation invariants of plane curves

      Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

      11-2-17

       

      Alexander Moll, IHES

      Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

      ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

      11-9-17  TBD  TBD
      11-16-17 TBD TBD
      11-23-17  TBD  TBD
      11-30-17  TBD  TBD
      12-7-17  TBD  TBD
      12-15-17  TBD  TBD
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/4/2019 Special Seminar
      3:00 pm
      12/01/2024
    • Math Science Literature Lecture Series
      3:00 pm-4:00 pm
      12/01/2024
      Lecture_Donaldson-pdf

      Simon Donaldson (Stony Brook)

      Title: The ADHM construction of Yang-Mills instantons

      Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the Yang-Mills instanton equations over the 4-sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics,  and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof,  using Penrose’s twistor theory and results on algebraic vector bundles over projective 3-space. As time permits, we will also discuss some further developments, for example, the work of Nahm on monopoles and connections to Mukai duality for bundles over complex tori.

      Video | Slides

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Quantum Groups
      3:00 pm-4:00 pm
      12/01/2024-05/05/2020
      Lecture_Etingof-pdf

      Pavel Etingof (MIT)

      Title: Quantum Groups

      Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum Yang-Baxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as representation theory, the Langlands program, low-dimensional topology, category theory, enumerative geometry, quantum computation, algebraic combinatorics, conformal field theory, integrable systems, integrable probability, and others. I will review some of the main ideas and examples of quantum groups and try to briefly describe some of the applications.

      Video | Slides

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      10/9/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Probability Seminar
      3:00 pm-4:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 04.10.23

      Probability Seminar

      *Please note room change: Science Center 232*

      Speaker: Ron Peled (Tel Aviv University)

      Title: Localization for random band matrices

      Abstract: I will explain an approach via “an adaptive Mermin-Wagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}.

      Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/03/2018 RMPT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Dmytro Shklyrov HMS Focused Lecture Series
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/25/2019 Math Physics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Fluid Dynamics Seminar
      3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • CMSA EVENT: 2018 Ding Shum Lecture
      3:00 pm-4:00 pm
      12/01/2024
      ding-shum-2018

       

      Screen-Shot-2018-06-14-at-1.41.25-PM

      On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

      This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

      Pictures of the event can be found here.

    • Seminars
      Seminars Colloquia & Seminar
      2/14/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/17/2019 Fluid Dynamics Seminar
      3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/31/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Special Seminar
      3:00 pm-4:30 pm
      12/01/2024-05/09/2019

      In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

      Click here for reference material

      Click here for a syllabus

      Schedule:

      Section 1: Basic setting of derived geometry

      The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

      2/05/2019Lecture 1: Model and с-categoriesVideo
      2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
      2/12/2019Lecture 3: Derived Artin stacksVideo 
      2/14/2019Lecture 4: Cotangent complexes

      Section 2: Loop spaces and differential forms

      The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

      2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
      2/21/2019Lecture 6: Chern characterVideo
      2/26/2019

      Room G02

      Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
      2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
      3/05/2019Lecture 9: Cyclic homologyVideo

      Section 3: Shifted symplectic structures
      Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

      3/07/2019Lecture 10: Definition and existence resultsVideo
      3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
      3/14/2019

      Room G02

      Lecture 12: Lagrangians and Lagrangian fibrationsVideo
      3/26/2019Lecture 13: Intersections of LagrangiansVideo
      3/28/2019

      Room G02

      Lecture 14: Examples and applications 2 (Part I)Video
      4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

      Section 4: Uhlenbeck–Yau construction and correspondence

      4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
      4/09/2019

      Room G02

      Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/7/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/11/2020 RM&PT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/13/2019 Special Algebraic Geometry Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Quantum Matter
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/24/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Quantum Matter
      3:00 pm-4:30 pm
      12/01/2024

      Speaker: Jie Wang (Simons Foundation)

      Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

      Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

      [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
      [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
      [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

    • Seminars
      Seminars Colloquia & Seminar
      2/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Probability Seminar
      3:00 pm-4:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 11.30.22

      Probability Seminar

      Title: Lipschitz properties of transport maps under a log-Lipschitz condition

      Abstract: Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting, for applications, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition.

      I will present a construction of a transport map, constructed infinitesimally along the Langevin flow, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds, and which, at the moment, seem to be out of reach of the classically studied optimal transport theory.

      Joint work with Max Fathi and Yair Shenfeld.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/6/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/8/2019 Special Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024

      Speaker: Josef Urban, Czech Technical University

      Title: AI and Theorem Proving

      Abstract: The talk will discuss the main approaches that combine machine learning with automated theorem proving and automated formalization. This includes learning to choose relevant facts for “hammer” systems, guiding the proof search of tableaux and superposition automated provers by interleaving learning and proving (reinforcement learning) over large ITP libraries, guiding the application of tactics in interactive tactical systems, and various forms of lemmatization and conjecturing. I will also show some demos of the systems, and discuss autoformalization approaches such as learning probabilistic grammars from aligned informal/formal corpora, combining them with semantic pruning, and using neural methods to learn direct translation from Latex to formal mathematics.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/28/2018 Random Matrix and Probability Theory Seminar
      3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/7/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024

      Speaker: Thomas Hales, Univ. of Pittsburgh Dept. of Mathematics

      Title: A Mathematical Language

      Abstract: A controlled natural language for mathematics is an artificial language that is designed in an explicit way with precise computer-readable syntax and semantics.  It is based on a single natural language (which for us is English) and can be broadly understood by mathematically literate English speakers.  This talk will describe the design of a controlled natural language for mathematics that has been influenced by the Lean theorem prover, by TeX, and by earlier controlled natural languages. The semantics are provided by dependent type theory.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/14/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/22/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12/5/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/15/2019 Fluid Dynamics
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/1/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      2/10/2022 – Interdisciplinary Science Seminar
      3:00 pm-4:00 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.10.2022-1

      Title: Metric Algebraic Geometry

      Abstract: A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a distance metric. In this talk, we introduce metric algebraic geometry through a discussion of Voronoi cells, bottlenecks, and the reach of an algebraic variety. We also show applications to the computational study of the geometry of data with nonlinear models.

    • Seminars
      Seminars Colloquia & Seminar
      11-23-2015 Mathematical Physics Seminar
      3:01 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar (2016-2017)
      3:01 pm
      12/01/2024-12/14/2017
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      DSC_0025-768x512

      The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    • Member Seminar
      3:02 pm
      12/01/2024-01/01/2021

      The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below.

      Previous seminars can be found here.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/29/2021Cancelled
      2/5/2021Itamar ShamirTitle: Boundary CFT and conformal anomalies

      Abstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.

      2/12/2021Louis FanTitle:  Joint distribution of Busemann functions in corner growth models

      Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.

      2/19/2021Daniel JunghansTitle: Control issues of the KKLT scenario in string theory

      Abstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular, we show that, generically, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.

      2/26/2021Tsung-Ju LeeTitle: SYZ fibrations and complex affine structures

      Abstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.

      3/5/2021Cancelled
      3/11/2021

      9:00pm ET

      Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification

      Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

      3/18/2021

      9:00pm ET

      Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification
      Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.
      3/26/2021

      8:30am ET

      Aghil AlaeeTitle:  Rich extra dimensions are hidden inside black holes

      Abstract: In this talk, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.

      4/2/2021
      8:30am ET
      Enno KeßlerTitle: Super Stable Maps of Genus Zero

      Abstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.

      4/9/2021Juven Wang

      Video

      Title: Ultra Unification

      Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate more on the nonperturbative global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.

      4/16/2021Sergiy VerstyukTitle: Deep learning methods for economics

      Abstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way, interpretability of neural networks features prominently.

      4/23/2021Yifan WangTitle: Virtues of Defects in Quantum Field Theories

      Abstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra, precision studies of defect observables, and the implications thereof for strongly coupled dynamics. In this talk, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics, and that open new windows to nonperturbative effects in quantum gravity.

      4/30/2021Yun ShiTitle: D-critical locus structure for local toric Calabi-Yau 3-fold

      Abstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.

      5/7/2021Thérèse Yingying WuTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2

      Abstract: In this talk, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.

      5/14/2021Du PeiTitle: Three applications of TQFTs

      Abstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds, and 3) smooth structures on 4-manifolds.

      5/21/2021Farzan VafaTitle: Active nematic defects and epithelial morphogenesis

      Abstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/11/2020Moran KorenTitle:  Observational Learning and Inefficiencies in Waitlists

      Abstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents, upon receiving an offer, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.

      9/18/2020Michael DouglasTitle: A talk in two parts, on strings and on computers and math

      Abstract: I am dividing my time between two broad topics. The first is string theory, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert,GPT) which have led to breakthroughs on natural language processing, describe their potential for helping us do math, and sketch some related theoretical problems.

      9/25/2020Cancelled – Math Science Lecture
      10/2/2020Cancelled – Math Science Lecture
      10/9/2020Wai Tong (Louis) FanTitle: Stochastic PDE as scaling limits of interacting particle systems

      Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
      In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.

      10/16/2020Tianqi WuTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

      Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.

      10/23/2020Changji XuTitle: Random Walk Among Bernoulli Obstacles

      Abstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk, we will discuss some recent results about the behaviors of the conditional random walk, in quenched, annealed, and biased settings.

      10/30/2020Michael SimkinTitle: The differential equation method in Banach spaces and the $n$-queens problem

      Abstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
      We apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.

      11/6/2020Kenji KawaguchiTitle: Deep learning: theoretical results on optimization and mixup

      Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization, robustness, and generalization, during the optimization process of a neural network. In this talk, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.

      11/13/2020Omri Ben-EliezerTitle: Sampling in an adversarial environment

      Abstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations, the existing statistical literature does not apply.

      We propose a new sequential adversarial model capturing these situations, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results, techniques, and applications reveal close connections to various areas in mathematics and computer science, including VC theory, discrepancy theory, online learning, streaming algorithms, and computational geometry.

      Based on joint works with Noga Alon, Yuval Dagan, Shay Moran, Moni Naor, and Eylon Yogev.

      11/20/2020Charles DoranTitle: The Calabi-Yau Geometry of Feynman Integrals

      Abstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.

      Colloquia & Seminars,Seminars

    • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
      3:02 pm-3:03 pm
      12/01/2024-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Participants:

      Gerard Ben Arous, Courant Institute of Mathematical Sciences

      Alex Bloemendal, Broad Institute

      Arup Chakraburty, MIT

      Zhou Fan, Stanford University

      Alpha Lee, Harvard University

      Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

      David R. Nelson, Harvard University

      Nick Patterson, Broad Institute

      Marc Potters, Capital Fund management

      Yasser Roudi, IAS

      Tom Trogdon, UC Irvine

      Organizers:

      Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

      Please click Program for a downloadable schedule with talk abstracts.

      Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

      Schedule:

      January 9 – Day 1
      9:30am – 10:00amBreakfast & Opening remarks
      10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
      11:00am – 12:00pmYasser Roudi
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 10 – Day 2
      8:30am – 9:00amBreakfast
      9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
      10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
      11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 11 – Day 3
      8:30am – 9:00amBreakfast
      9:00am – 10:00amNick Patterson
      10:00am – 11:00amLucy Colwell
      11:00am – 12:00pmAlpha Lee
      12:00pm – 2:00pmLunch
      2:00pm-4:00pmAfternoon Discussion
      4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
      January 12 – Day 4
      8:30am – 9:00amBreakfast
      9:00am – 10:00amGovind Menon
      10:00am – 11:00amAlex Bloemendal
      11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 13 – Day 5
      8:30am – 9:00amBreakfast
      9:00am – 12:00pmFree for Working
      12:00pm – 2:00pmLunch
      2:00pmFree for Working

      * This event is sponsored by CMSA Harvard University.

    • Colloquium
      3:03 pm-4:00 pm
      12/01/2024

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    • Colloquium
      3:03 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      3:03 pm-4:03 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.11.22-1583x2048

      Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.

    • Seminars
      Seminars Colloquia & Seminar
      11-24-2015 Geometric Analysis Seminar
      3:03 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-04-2016 Evolution Equations Seminar
      3:04 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      3:05 pm-4:05 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.12.22-1583x2048-1

      Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Sparse Markov Models for High-dimensional Inference
      3:05 pm-4:05 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.17.2022-1-1583x2048-1

      Abstract: Finite order Markov models are theoretically well-studied models for dependent data.  Despite their generality, application in empirical work when the order is larger than one is quite rare.  Practitioners avoid using higher order Markov models because (1) the number of parameters grow exponentially with the order, (2) the interpretation is often difficult. Mixture of transition distribution models (MTD)  were introduced to overcome both limitations. MTD represent higher order Markov models as a convex mixture of single step Markov chains, reducing the number of parameters and increasing the interpretability. Nevertheless, in practice, estimation of MTD models with large orders are still limited because of curse of dimensionality and high algorithm complexity. Here, we prove that if only few lags are relevant we can consistently and efficiently recover the lags and estimate the transition probabilities of high order MTD models. Furthermore, we show that using the selected lags we can construct non-asymptotic confidence intervals for the transition probabilities of the model. The key innovation is a recursive procedure for the selection of the relevant lags of the model.  Our results are  based on (1) a new structural result of the MTD and (2) an improved martingale concentration inequality. Our theoretical results are illustrated through simulations.

    • Colloquium
      3:06 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-02-2016 Geometric Analysis Seminar
      3:06 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Hodge and Noether-Lefschetz Loci Seminar
      3:06 pm
      12/01/2024

      In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

      The schedule below will be updated as talks are confirmed.

      DateTitle/Abstract
      11/7/2018

      Video

      Title: Hodge and Noether-Lefschetz loci

      Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

      In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

      11/14/2018

      Video

      Title:  Integral Hodge conjecture for Fermat varieties

      Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

      11/21/2018

      Video

      Title:  Periods of algebraic cycles

      Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

      11/28/2018

      Video

      Title: Periods of Complete Intersection Algebraic Cycles

      Speaker: Roberto Villaflor

      Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

      12/05/2018

      Room G02

      Title: Some explicit Hodge cycles

      Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

      12/12/2018

      Video

      Title: A conjectural Hodge locus for cubic tenfold

      Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

      1/16/2019Title: Algebraic BCOV anomaly equation

      Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

      1/23/2019

      Video

      Title: A new model for modular curves

      Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

      The talk is based on the article arXiv:1808.01689.

      1/30/2019

      Video

      Title: Constant Yukawa couplings

      Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

      2/6/2019

      Video

      Title: Integrality properties of CY modular forms

      Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

      We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

      2/13/2019Title: Foliations and Hodge loci

      Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

       

      References:

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Singular Set in Obstacle Problems
      3:08 pm-4:08 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.24.2022-1583x2048

      Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.

    • Colloquium
      3:09 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
      3:09 pm-3:10 pm
      12/01/2024-04/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

      Workshop Locations:

      April 4 – 7 (Monday ~ Thursday)

      Room G10,
      20 Garden Street, Cambridge, MA 02138 

      April 8 (Friday)

      EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
      20 Oxford Street, Cambridge, MA 02138

       Participants:

      • Peter Hubyers (Harvard University)
      • Eli Tziperman (Harvard University)
      • Andrew Rhines (University of Washington)
      • Karen McKinnon (UCAR)
      • Douglas MacMartin (Caltech)
      • Thomas Laepple (Alfred Wegener Institute)
      • Yossi Ashkenazy (Ben-Gurion University)
      • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
      • Natesh Pillai (Harvard University)
      • Judah Cohen (Atmospheric and Environmental Research)
      • Cristian Proistosescu (Harvard University)

      Please click Workshop Agenda for a downloadable agenda.

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      02-11-2016 Evolution Equations Seminar
      3:09 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-16-2018 RM & PT Seminar
      3:09 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      3:11 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-03-2016 Random Matrix & Probability Theory Seminar
      3:11 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:11 pm-4:11 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.03.2022-1583x2048-1

      Abstract: While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573.

      Bio: Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research, New England. In 2019, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text, images, and other forms of data, using techniques such as non-convex optimization and tensor decompositions.

    • Colloquium
      3:12 pm-4:12 pm
      12/01/2024

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    • Interdisciplinary Science Seminar
      3:13 pm-4:13 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.10.2022-1583x2048-1

      Abstract: The gig economy provides workers with the benefits of autonomy and flexibility, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms, an unexplored aspect is the organization identity. In a series of studies, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach, combining methodologies from randomized field experiments, recommender systems, and counterfactual machine learning. Together, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy.

      Bio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning, causal inference, and field experiments in his research, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences, including PNAS, ACM TOIS, WWW, and ICWSM.

    • Colloquium
      3:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 RM & PT Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 RM & PT Seminar
      3:15 pm
      12/01/2024
    • Colloquium
      3:15 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2019 Random Matrix and Probability Theory Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Interdisciplinary Science Seminar
      3:15 pm-4:15 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048

      Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization, during the optimization process. In this talk, I will discuss some mathematical properties of optimization and generalization for deep neural networks.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/6/2019 Random Matrix and Probability Theory Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 RMPT Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-16-2016 Geometric Analysis Seminar
      3:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-15-2016 Mathematical Physics Seminar
      3:17 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      An operadic structure on supermoduli spaces
      3:17 pm-5:17 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048 (1)

      Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin. Based joint work with Yu. I. Manin and Y. Wu. https://arxiv.org/abs/2202.10321

    • Seminars
      Seminars Colloquia & Seminar
      02-18-2016 Evolution Equations Seminar
      3:19 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:20 pm-5:20 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.231.2022-1583x2048-1

      Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space.  Many fundamental questions have been open for these classical objects.  We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry.  Key objects involve compactifications of embedded vector spaces, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector bundles and the cohomology ring of stellahedral varieties.

    • Seminars
      Seminars Colloquia & Seminar
      02-22-2016 Mathematical Physics Seminar
      3:20 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:22 pm-5:22 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.07.2022-1583x2048-1

      Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson, as well as joint work with (separately) Larson and Jim Bryan.

    • Seminars
      Seminars Colloquia & Seminar
      02-23-2016 Geometric Analysis Seminar
      3:22 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-24-2016 Random Matrix & Probability Theory
      3:23 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
      3:23 pm
      12/01/2024-12/02/2016

      The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

      Organizers:

      Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

      Speakers:

      1. Conan Leung, Chinese University of Hong Kong
      2. Junwu Tu, University of Missouri
      3. Jingyu Zhao, Columbia University
      4. David Treumann, Boston College
      5. Hiro Lee Tanaka, Harvard University
      6. Fabian Haiden, Harvard University
      7. Hansol Hong, Harvard CMSA/Brandeis University
      8. Netanel Blaier, Harvard CMSA/Brandeis University
      9. Garret Alston, The University of Oklahoma

      Please click Workshop Program for a downloadable schedule with talk abstracts.

      Conference Schedule:

      Monday, November 28 – Day 1
      10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
      Lunch
      1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
      4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
      Tuesday, November 29 – Day 2
      10:30am –11:30amConan Leung, “Remarks on SYZ”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
      4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
      Wednesday, November 30 – Day 3
      10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30-2:45pm Break
      2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
      Thursday, December 1 – Day 4
      10:30am –11:30amDavid Treumann“Some examples in three dimensions”
      Lunch
      1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
       2:30-2:45pm Break
      2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

      * This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      02-25-2016 Evolution Equations Seminar
      3:25 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      3:25 pm
      12/01/2024

      During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

      The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

      To learn how to attend, please fill out this form.

      Information on previous colloquia can be found here.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

      Slides

      Video

      Title: Topology protects chiral edge currents in stochastic systems

      Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

      2/3/2021André Luiz de Gouvêa (Northwestern)

      Video

      Title: The Brave Nu World

      Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

      2/10/2021Mykhaylo Shkolnikov (Princeton)

      Video

      Title: Probabilistic approach to free boundary problems and applications

      Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

      2/17/2021
      9:00 – 10:00PM ET
      C. Seshadhri (UC Santa Cruz)

      Video

      Title: Studying the (in)effectiveness of low dimensional graph embeddings

      Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

      2/24/2021David Ben-Zvi (U Texas)

      Video

      Title: Electric-Magnetic Duality for Periods and L-functions

      Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
      A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
      We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

      3/3/2021

      9:00pm ET

      Omer Tamuz (Caltech)Title: Monotone Additive Statistics

      Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

      (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

      3/10/2021

      9:00pm ET

      Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

      Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

      3/17/2021
      9:00pm ET
      Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

      Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

      3/24/2021Weinan E (Princeton)

      Video

      Title: Machine Learning and PDEs

      Abstract: I will discuss two topics:
      (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
      (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

      3/31/2021Thore Graepel (DeepMind/UCL)

      Video

      Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

      Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

      4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

      Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

      4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

      Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

      4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
      Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
      4/28/2021

      9:00 – 10:00pm ET

      Shamit Kachru (Stanford)

      Slides

      Title: K3 Metrics from String Theory

      Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

      Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

      10/7/2020

      10:00am

      Mariangela Lisanti (Princeton University)

      Video

      Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

      Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

      10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

      Video

      Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

      Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
      a) My general argument “against” quantum computers,
      b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
      Relevant papers:
      Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
      wordpress.com/2019/11/stat-quantum2.pdf

      Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
      wordpress.com/2020/08/laws-blog2.pdf

      Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
      wordpress.com/2019/09/main-pr.pdf

      10/21/2020Marta Lewicka (University of Pittsburgh)

      Video

      Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

      Abstract: We propose results that relate the following two contexts:
      (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
      (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
      For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
      geometry and mechanics of materials in the prediction of patterns and shape formation.

      10/28/2020Jonathan Heckman (University of Pennsylvania)

      Video

      Title: Top Down Approach to Quantum Fields

      Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

      11/4/2020
      9:00pm ET
      Surya Ganguli (Stanford)

      Video

      Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

      Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
      Selected References:
      M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
      M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
      A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
      H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
      S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
      B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
      Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
      S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

      11/11/2020Kevin Buzzard (Imperial College London)

      Video

      Title: Teaching proofs to computers

      Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
      I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

      11/18/2020Jose A. Scheinkman (Columbia)

      Video

      Title: Re-pricing avalanches

      Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

      11/25/2020

      10:45am

      Eric J. Heller (Harvard)

      Video

      Title: Branched Flow

      Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

      12/2/2020Douglas Arnold (U of Minnesota)

      Video

      Title: Preserving geometry in numerical discretization

      Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

      12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

      Video

      Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

      Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
      After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

    • Seminars
      Seminars Colloquia & Seminar
      03-03-2016 Evolution Equations Seminar
      3:26 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-5-2018 Mathematical Physics Seminar
      3:27 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      03-29-2016 Geometric Analysis Seminar
      3:27 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      3:28 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
      3:29 pm
      12/01/2024-05/02/2017

      In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

      Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

      Confirmed Speakers

      * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Tomas Berggren (MIT)

      Title: Geometry of the doubly periodic Aztec dimer model

      Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions — known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.

       

       

    • Colloquium
      3:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 05.03.23

      Probability Seminar

      Speaker: Boris Hanin (Princeton)

      Title: Random Neural Networks

      Abstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially L) are large. The first set of results are for deep linear networks, which are simply products of L random matrices of size N x N. I’ll explain how the setting where the ratio L / N is fixed with both N and L large reveals a number of phenomena not present when only one of them is large. I will then state several results about non-linear networks in which this depth-to-width ratio L / N again plays a crucial role and gives an effective notion of depth for a random neural network.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 04.26.23

      Probability Seminar

      Speaker: Jimmy He (MIT)

      Title: Boundary current fluctuations for the half space ASEP

      Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

    • Seminars
      Seminars Colloquia & Seminar
      11/12/2019 Spacetime Seminar
      3:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Spacetime Seminar
      3:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      Harvard Science Center, 1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 04.19.23

      Probability Seminar

      Speaker: Evita Nestoridi (Stonybrook)

      Title: Diagonalizing Transition Matrices of Card Shuffles

      Abstract: In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 04.12.23

      Probability Seminar

      Speaker: Emma Bailey (CUNY)

      Title: Large deviations of Selberg’s central limit theorem

      Abstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance.  It is natural to investigate how far into the tails this Gaussianity persists, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials.  It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations, as well as certain maxima and moments. In this talk I will focus more on the techniques we apply to approach this problem and I will assume no number theoretic knowledge. This is joint work with Louis-Pierre Arguin.

    • Seminars
      Seminars Colloquia & Seminar
      7/29/2020 Quantum Matter Seminar
      3:30 pm-5:00 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 04.05.23

      Probability Seminar

      Speaker: Ahmed El Alaoui (Cornell)

      Title: Sampling from the SK and mixed p-spin measures with stochastic localization

      Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model. This is based on a joint work with Andrea Montanari and Mark Sellke.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/17/2018 RM & PT Seminar
      3:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA Probability Seminar 03.22.23

      Probability Seminar

      Speaker: Wei-Kuo Chen (Minnesota)

      Title: Some rigorous results on the Lévy spin glass model

      Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024

      Probability Seminar

      Speaker: Benjamin Landon (University of Toronto)

      Title: Tail estimates for stationary KPZ models

      Abstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size, including the stochastic six vertex model, the ASEP and a class of non-integrable interacting diffusions.

      Joint work with Christian Noack and Phil Sosoe.

       

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main)

      Title: Solving spin systems, the Babylonian way

      Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues, but quite astonishingly, evidence is mounting that Parisi’s ultrametricity assumption, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024

      Probability Seminar

      Speaker: Vishesh Jain (University of Illinois Chicago)
      Title: Thresholds for edge colorings
      Abstract: We show that if each edge of the complete bipartite graph K_{n,n} is given a random list of C(\log n) colors from [n], then with high probability, there is a proper edge coloring where the color of each edge comes from the corresponding list. We also prove analogous results for Latin squares and Steiner triple systems. This resolves several related conjectures of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-Osthus. I will discuss some of the main ingredients which go into the proof: the Kahn-Kalai conjecture, absorption, and the Lovasz Local Lemma distribution. Based on joint work with Huy Tuan Pham.
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 02.15.23

      Probability Seminar

      Speaker: Zhigang Yao (Harvard CMSA/National University of Singapore)

      Title: Manifold Fitting: An Invitation to Statistics

      Abstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference: https://arxiv.org/abs/1909.10228

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Youngtak Sohn (MIT)

      Title: Universality of max-margin classifiers

      Abstract: Many modern learning methods, such as deep neural networks, are so complex that they perfectly fit the training data. Despite this, they generalize well to the unseen data. Motivated by this phenomenon, we consider high-dimensional binary classification with linearly separable data. First, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule, namely the max-margin classification, has near-optimal prediction accuracy. Then, we discuss universality of max-margin classification. In particular, we characterize the prediction accuracy of the non-linear random features model, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally, we consider the wide-network limit, where the number of neurons tends to infinity, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective.

      Joint work with Andrea Montanari, Feng Ruan, Jun Yan, and Basil Saeed.

    • Quantum Matter
      3:30 pm-5:00 pm
      12/01/2024

      Title: Electric-magnetic duality and the Geometric Langlands duality

      Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      Virtual and in 20 Garden Street, Room G10
      CMSA Probability Seminar 02.08.23

      Probability Seminar

      Speaker: Roland Bauerschmidt (Cambridge)

      Title: Bakry-Emery theory and renormalisation

      Abstract: I will discuss an approach to log-Sobolev inequalities that
      combines the Bakry-Emery theory with renormalisation and present several
      applications. These include log-Sobolev inequalities with polynomial
      dependence for critical Ising models on Z^d when d>4 and singular SPDEs
      with uniform dependence of the log-Sobolev constant on both the
      regularisation and the volume. The talk is based on joint works with
      Thierry Bodineau and Benoit Dagallier.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024

      Probability Seminar

      Speaker: Antoine Maillard (ETH Zürich)

      Title: Fitting ellipsoids to random points

      Abstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science, and is conjectured to undergo a sharp transition: with high probability, it has a solution if n < d^2/4, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture, and highlight some recent progress, in three different directions:

      • A proof that the problem is feasible for n < d^2 / C, for some (large) constant C, significantly improving over previously-known bounds.
      • A non-rigorous characterization of the conjecture, as well as significant generalizations, using analytical methods of statistical physics.
      • A rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.

      This talk is based on the three manuscripts: arXiv:2307.01181, arXiv:2310.01169, arXiv:2310.05787, which are joint works with A. Bandeira, Tim Kunisky, Shahar Mendelson and Elliot Paquette.

    • Seminars
      Seminars Colloquia & Seminar
      4/4/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 12.07.22

      Probability Seminar

      Note location change: Science Center Room 300H

      Speaker: Lior Alon (MIT)

      Title: Fourier quasicrystals and stable polynomials

      Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A, such that the sum of exp(iat), over a in A, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial, and the measures associated with each irreducible factor is either supported on an arithmetic progression, or its support has a bounded intersection with any arithmetic progression. Finally, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix.

      Based on joint work with Pravesh Kothari.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 11.16.22

      Probability Seminar

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 11.09.22 (1)

      Probability Seminar

      Speaker: Hugo Falconet (Courant Institute, NYU)

      Title: Liouville quantum gravity from random matrix dynamics

      Abstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary group at equilibrium, then the measures $|det(U_t – e^{i theta}|^gamma dt dtheta$ converge to the 2d LQG measure with parameter $gamma$, in the limit of large dimension. This extends results from Webb, Nikula and Saksman for fixed time. The proof relies on a new method for Fisher-Hartwig asymptotics of Toeplitz determinants with real symbols, which extends to multi-time settings. I will explain this method and how to obtain multi-time loop equations by stochastic analysis on Lie groups.

      Based on a joint work with Paul Bourgade.

       

    • Seminars
      Seminars Colloquia & Seminar
      3/14/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Social Science Application Forum
      3:30 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-23-2018 RM & PT Seminar
      3:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Quantum Matter
      3:30 pm-5:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-04.22.22-1583x2048-1

      Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Jinyoung Park (NYU)

      Title: Thresholds

      Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a “threshold.” Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Catherine Wolfram (MIT)

      Title: Large deviations for the 3D dimer model

      Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is different from two, explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.

       

    • Seminars
      Seminars Colloquia & Seminar
      10/15/2019 Spacetime Seminar
      3:30 pm-5:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Mathematical Physics Seminar
      3:31 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-01-2016 Geometric Analysis Seminar
      3:32 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:33 pm-5:33 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.28.22-1583x2048-1

      Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole,  length of the shortest closed geodesic on X.

    • Seminars
      Seminars Colloquia & Seminar
      03-10-2016 Evolution Equations Seminar
      3:34 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
      3:34 pm
      12/01/2024-03/30/2017

      The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Photos of the event can be found on CMSA’s Blog.

       Participants:

      Organizers:

      * This event is sponsored by CMSA Harvard University.

      Schedule:

      Monday, March 27

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
      10:00am – 11:00amKieron Burke, University of California, Irvine

      The density functionals machines can learn

      11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

      Tuesday, March 28

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amRyan Adams, HarvardTBA
      10:00am – 11:00amGábor Csányi, University of Cambridge

      Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

       Wednesday, March 29 

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
      10:00am – 11:00amJörg Behler, University of GöttingenTBA
      11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
      4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

      CMSA Colloquium

      Thursday, March 30

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
      10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-09-2016 Random Matrix & Probability Theory
      3:35 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      3:35 pm-4:35 pm
      12/01/2024

      Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Fluid Dynamics Seminar
      3:35 pm
      12/01/2024
    • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
      3:35 pm-3:36 pm
      12/01/2024-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Participants:

      Dan Freed, UT Austin

      Anton Kapustin, California Institute of Technology

      Alexei Y. Kitaev, California Institute of Technology

      Greg Moore, Rutgers University

      Constantin Teleman, University of Oxford

      Organizers:

      Mike Hopkins, Shing-Tung Yau

      * This event is sponsored by CMSA Harvard University.

    • Interdisciplinary Science Seminar
      3:36 pm-5:36 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.05.2022-1583x2048

      Abstract: Although everyone talks about AI + healthcare, many people were unaware of the fact that there are two possible outcomes of the collaboration, due to the inherent dissimilarity between the two giant subjects. The first possibility is healthcare-leads, and AI is for building new tools to make steps in healthcare easier, better, more effective or more accurate. The other possibility is AI-leads, and therefore the protocols of healthcare can be redesigned or redefined to make sure that the whole infrastructure and pipelines are ideal for running AI algorithms.

      Our system Qianfang belongs to the second category. We have designed a new kind of clinic for the doctors and patients, so that it will be able to collect high quality data for AI algorithms. Interestingly, the clinic is based on Traditional Chinese Medicine (TCM) instead of modern medicine, because we believe that TCM is more suitable for AI algorithms as the starting point.

      In this talk, I will elaborate on how we convert TCM knowledge into a modern type-safe large-scale system, the mini-language that we have designed for the doctors and patients, the interpretability of AI decisions, and our feedback loop for collecting data.

      Our project is still on-going, not finished yet.Bio: Yang Yuan is now an assistant professor at IIIS, Tsinghua. He finished his undergraduate study at Peking University in 2012. Afterwards, he received his PhD at Cornell University in 2018, advised by Professor Robert Kleinberg. During his PhD, he was a visiting student at MIT/Microsoft New England (2014-2015) and Princeton University (2016 Fall). Before joining Tsinghua, he spent one year at MIT Institute for Foundations of Data Science (MIFODS) as a postdoc researcher. He now works on AI+Healthcare, AI Interpretability and AI system.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-23-2016 Random Matrix & Probability Theory
      3:37 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Geometric Models for Sets of Probability Measures
      3:38 pm-5:38 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.12.22-1583x2048

      Abstract: Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models.  In this setting, we often are unable to match individual data points but rather need to deduce relationships between entire weighted and unweighted point sets. In this talk, I will summarize our team’s recent efforts to apply geometric techniques to problems in this space, using tools from optimal transport and spectral geometry. Motivated by applications in dataset comparison, time series analysis, and robust learning, our work reveals how to apply geometric reasoning to data expressed as probability measures without sacrificing computational efficiency.

    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Social Science Applications Forum
      3:38 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
      3:40 pm-3:41 pm
      12/01/2024-05/02/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Speakers:

      Orr Ashenberg, Fred Hutchinson Cancer Research Center

      John Barton, Massachusetts Institute of Technology

      Simona Cocco, Laboratoire de Physique Statistique de l’ENS

      Sean Eddy, Harvard University

      Efthimios Kaxiras, Harvard University

      Michael Laub, Massachusetts Institute of Technology

      Debora S. Marks, Harvard University

      Govind Menon, Brown University

      Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

      Andrew Murray, Harvard University

      Ilya Nemenman, Emory College

      Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

      Dave Thirumalai, University of Texas at Austin

      Martin Weigt, IBPS, Université Pierre et Marie Curie

      Matthieu Wyart, EPFL

      More speakers will be confirmed soon.

       

      Schedule:

      (Please click here for a downloadable version of the schedule.)

      Please note that the schedule for both days is currently tentative and is subject to change.

      May 1, Monday

      TimeSpeakerTopic
      9:00-10:00amSean EddyTBA
      10:00-11:00amMike LaubTBA
      11:00am-12:00pmIlya NemenmanTBA
      May 2, Tuesday
      TimeSpeakerTopic
      9:00-10:00amOrr AshenbergTBA
      10:00-11:00amDebora MarksTBA
      11:00am-12:00pmMartin WeigtTBA
      4:30pm-5:30pmSimona CoccoCMSA Colloquia

       

      May 3, Wednesday
      TimeSpeakerTopic
      9:00-10:00amAndrew MurrayTBA
      10:00-11:00amMatthieu WyartTBA
      11:00am-12:00pmRémi MonassonTBA

       

      May 4, Thursday
      TimeSpeakerTopic
      9:00-10:00amDavid ThirumalaiTBA
      10:00-11:00amChris SanderTBA
      11:00am-12:00pmJohn BartonTBA

       

      Organizers:

      Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      03-07-2016 Mathematical Physics Seminar
      3:41 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-26-2018 Mathematical Physics Seminar
      3:42 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-11-2016 Random Matrix & Probability Theory
      3:42 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-08-2016 Geometric Analysis Seminar
      3:44 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
      3:44 pm
      12/01/2024-05/04/2017

      In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

      To register for this event, please click here.

      Confirmed speakers:

      The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

      For a list of lodging options convenient to the Center, please see our recommended lodgings page.

      Schedule:

      The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

      June 5, Monday (Full day)

      TimeSpeakerTopic
      8:30am – 9:0amBreakfast
      9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
      10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

      Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

      Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

      Video

      3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

      Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

      4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
      Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

      June 6, Tuesday (Full day)

      TimeSpeakerTopic
      8:30am – 9:00amBreakfast
      9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

      Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

      Video

      10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

      Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

      Video

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

      Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

      Video

      3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

      Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

      Video


    • Seminars
      Seminars Colloquia & Seminar
      03-21-2016 Mathematical Physics Seminar
      3:46 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-24-2016 Evolution Equations Seminar
      3:47 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: 2017 Big Data Conference
      3:47 pm
      12/01/2024-08/19/2017
      1 Oxford Street, Cambridge MA 02138

      The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

      The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

      Confirmed Speakers:

       

      Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

      • Jörn Boehnke, Harvard University
      • Nikhil Naik, Harvard University
      • Bradly Stadie, Open AI, University of California, Berkeley

       

      Conference Schedule

      A PDF version of the schedule below can also be downloaded here.

      August 18, Friday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amMohammad Akbarpour

      Video

      Title: Information aggregation in overlapping generations and the emergence of experts

      Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

      9:40 am – 10:20 amLucas Janson

      Video

      Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

      Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

      Slides

      10:20 am – 10:50 amBreak
      10:50 pm – 11:30 pmNoureddine El Karoui

      Video

      Title: Random matrices and high-dimensional statistics: beyond covariance matrices

      Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

      11:30 am – 12:10 pmNikhil Naik

      Video

      Title: Understanding Urban Change with Computer Vision and Street-level Imagery

      Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

      (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

      12:10 pm – 12:25 pmVideo #1

      Video #2

      Data Science Lightning Talks
      12:25 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmTracy Ke

      Video

      Title: A new SVD approach to optimal topic estimation

      Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

      We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

      For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

      2:10 pm – 2:50 pmAlbert-László Barabási

      Video

      Title: Taming Complexity: From Network Science to Controlling Networks

      Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

       

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmMarena Lin

      Video

      Title: Optimizing climate variables for human impact studies

      Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

      4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

      Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

      4:40 pm – 5:20 pmTze Leung Lai

      Video

      Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

      Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

      August 19, Saturday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amNatesh Pillai

      Video

      Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

      Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

      9:40 am – 10:20 amRavi Jagadeesan

      Video

      Title: Designs for estimating the treatment effect in networks with interference

      Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

      10:20 am – 10:50 amBreak
      10:50 am – 11:30 amAnnie Liang

      Video

      Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

      Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

      11:30 am – 12:10 pmZak Stone

      Video

      Title: TensorFlow: Machine Learning for Everyone

      Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

      12:10 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmJann Spiess

      Video

      Title: (Machine) Learning to Control in Experiments

      Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

      2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

      Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
      We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmHau-Tieng Wu

      Video

      Title: When Medical Challenges Meet Modern Data Science

      Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

      4:00 pm – 4:40 pmSifan Zhou

      Video

      Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

      Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

       

      To view photos and video interviews from the conference, please visit the CMSA blog.

       

    • Seminars
      Seminars Colloquia & Seminar
      12-07-2015 Mathematical Physics Seminar
      3:49 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-22-2016 Geometric Analysis Seminar
      3:51 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: CMSA/Math Fall Gathering
      4:00 pm-6:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA
      Friday, Sep 22, 2022
      4:00 pm
      All CMSA and Math affiliates are invited.
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Quantum cohomology as a deformation of symplectic cohomology
      4:00 pm-5:00 pm
      12/01/2024
      20211124_Nick-Sheridan_RESCHEDULED_poster

      Abstract: Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Mina Aganagic
      4:00 pm
      12/01/2024-04/10/2019
      1 Oxford Street, Cambridge MA 02138

      On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

      The lectures took place in Science Center, Hall C

      “Two math lessons from string theory”

      Lecture 1:

       

       

       

       

       

      April 9, 2019

      Title: “Lesson on Integrability”

       

      Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

      Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

      Lecture 2:

       

       

       

       

       

      April 10, 2019

      Title: “Lesson on Knot Categorification”

       

      Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

      The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

      This talk is mostly based on joint work with Andrei Okounkov.

       

      Information about last year’s Math Science Bott lecture can be found here. 

      Aganagic

    • Seminars
      4:00 pm-5:00 pm
      12/01/2024

    • Topological Quantum Matter Seminar
      4:00 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Yizhuang You, UC San Diego

      Title: Symmetric Mass Generation
      Abstract: Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Higher rank DT theory from rank 1
      4:00 pm-5:00 pm
      12/01/2024
      20211110_Richard-Thomas_poster

      Abstract: Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

    • Yip Lecture Series
      Yip Lecture Series Event
      Yip Annual Lecture
      4:00 pm-5:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

      The lecture was held from 4:00-5:00pm in Science Center, Hall A.

      Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
    • Math Science Lectures in Honor of Raoul Bott
      4:00 pm-5:30 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      Fibered ribbon knots vs. major 4D conjectures

      Location: Harvard University Science Center Hall A & via Zoom webinar

      Dates: Feb 20 & 22, 2024

      Time: 4:00-5:30 pm

      Directions and Recommended Lodging

      Registration is required.

      Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin and a Clay Research Fellow.

      This will be the fourth annual Math Science Lecture Series held in Honor of Raoul Bott.

      Talk topic:  Fibered ribbon knots vs. major 4D conjectures

      Feb. 20, 2024

      Title: Fibered ribbon knots and the Poincaré conjecture

      Abstract: A knot is “fibered” if its complement in S^3 is the total space of a bundle over the circle, and ribbon if it bounds a smooth disk into B^4 with no local maxima with respect to radial height. A theorem of Casson-Gordon from 1983 implies that if a fibered ribbon knot does not bound any fibered disk in B^4, then the smooth 4D Poincaré conjecture is false. I’ll show that unfortunately (?) many ribbon disks bounded by fibered knots are fibered, giving some criteria for extending fibrations and discuss how one might search for non-fibered examples.

      Feb. 22, 2024

      Title: Fibered knots and the slice-ribbon conjecture

      Abstract: The slice-ribbon conjecture (Fox, 1962) posits that if a knot bounds any smooth disk into B^4, it also bounds a ribbon disk. The previously discussed work of Casson-Gordon yields an obstruction to many fibered knots being ribbon, yielding many interesting potential counterexamples to this conjecture — if any happy to bound a non-ribbon disk. In 2022, Dai-Kong-Mallick-Park-Stoffregen showed that unfortunately( ?) many of these knots don’t bound a smooth disk into B^4 and thus can’t disprove the conjecture. I’ll show a simple alternate proof that a certain interesting knot (the (2,1)-cable of the figure eight) isn’t slice and discuss remaining open questions. This talk is joint with Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.

       

      Talk Chair: Cliff Taubes (Harvard Mathematics)

      Moderator: Freid Tong (Harvard CMSA)


      Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.

    • Probability Seminar
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Wei-Kuo Chen (University of Minnesota)

      Title: A Gaussian convexity for logarithmic moment generating function

      Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy.

       

    • Quantum Matter
      4:00 pm-5:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.18.22-1583x2048-1

      Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045

    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 Colloquium
      4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/12/2020 Colloquium
      4:00 pm-5:00 pm
      12/01/2024
    • Colloquium
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 03.02.2023

      Speaker: Erez Urbach, Weizmann Institute of Science

      Title: The string/black hole transition in anti de Sitter space

      Abstract: String stars, or Horowitz-Polchinski solutions, are string theory saddles with normalizable condensates of thermal-winding strings. In the past, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux), their possible connection to small black holes in AdS, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model, and their relation to the deconfined phase of 3+1 pure Yang-Mills.

    • Colloquium
      4:00 pm
      12/01/2024
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Lagrangians and mirror symmetry in the Higgs bundle moduli space
      4:00 pm-5:00 pm
      12/01/2024

      Abstract: The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed, but  also to open up new features involving finite-dimensional algebras which are deformations of cohomology algebras. Answering some of the questions raised  requires revisiting basic constructions of stable bundles on curves.

    • Probability Seminar
      4:00 pm-5:00 pm
      12/01/2024
      Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

      Probability Seminar

      Speaker: Marius Lemm, University of Tuebingen

      Title: Light cones for open quantum systems
      Abstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely, if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound on the slope of this light cone (i.e., on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang.

       

    • Topological Quantum Matter Seminar
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Roman Geiko, UCLA

      Title: Homotopy classes of loops of Clifford unitaries

      Abstract: We study Clifford locality-preserving unitaries and stabilizer Hamiltonians by means of Hermitian K-theory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two short-range entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu.  https://arxiv.org/abs/2306.09903.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      4:00 pm-5:00 pm
      12/01/2024

      Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class S[A1]. I will describe the resulting geometric structures using a kind of complexified Hitchin system parameterising bundles on curves equipped with pencils of flat connections.

    • Topological Quantum Matter Seminar
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Daniele Guerci, Flatiron Institute

      Title: Chern Mosaic and ideal bands in helical trilayer graphene

      Abstract: In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat bands features the superposition of a Chern -1 and a Chern 2 bands described by the superposition of two lowest Landau level [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [3]. Building on this knowledge, I will discuss the properties of the zero-modes at higher magic angles.

      [1] Y.Mao,D.Guerci,C.Mora, PRB 107, 125423 (2023) [Editors’ Suggestion]

      [2] D.Guerci,Y.Mao,C.Mora, arXiv:2305.03702 (2023)

      [3] D.Guerci,Y.Mao,C.Mora, arXiv:2308.02638 (2023)

    • Colloquium
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.05.22 (1)

      Colloquium

      Please note this colloquium will be held at a special time:  4:00-5:00 pm.

      Speaker: Subir Sachdev (Harvard)

      Title: Quantum statistical mechanics of charged black holes and strange metals
      Abstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.
      Slides: cmsa22
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-28-2016 Mathematical Physics Seminar
      4:08 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-06-2016 Random Matrix & Probability Theory
      4:10 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-30-2016 Random Matrix & Probability Theory Seminar
      4:11 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:12 pm-5:12 pm
      12/01/2024

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Fast Point Transformer
      4:13 pm-5:13 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-06.02.2022-1583x2048-1

      Abstract: The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine the local predictions together. However, this scheme inevitably involves additional stages for pre- and post-processing and may also degrade the final output due to predictions in a local perspective. This talk introduces Fast Point Transformer that consists of a new lightweight self-attention layer. Our approach encodes continuous 3D coordinates, and the voxel hashing-based architecture boosts computational efficiency. The proposed method is demonstrated with 3D semantic segmentation and 3D detection. The accuracy of our approach is competitive to the best voxel-based method, and our network achieves 129 times faster inference time than the state-of-the-art, Point Transformer, with a reasonable accuracy trade-off in 3D semantic segmentation on S3DIS dataset.

      Bio: Jaesik Park is an Assistant Professor at POSTECH. He received his Bachelor’s degree from Hanyang University in 2009, and he received his Master’s degree and Ph.D. degree from KAIST in 2011 and 2015, respectively. Before joining POSTECH, He worked at Intel as a research scientist, where he co-created the Open3D library. His research interests include image synthesis, scene understanding, and 3D reconstruction. He serves as a program committee at prestigious computer vision conferences, such as Area Chair for ICCV, CVPR, and ECCV.

    • Seminars
      Seminars Colloquia & Seminar
      04-14-2016 Evolution Equations Seminar
      4:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-12-2016 Geometric Analysis Seminar
      4:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Special Seminar
      4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Duality String Seminar, Thursdays
      4:15 pm-6:00 pm
      12/01/2024-10/12/2016

      The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

      For details, please visit the website.

      * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

    • Seminars
      Seminars Colloquia & Seminar
      03-31-2016 Evolution Equations Seminar
      4:15 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      4:15 pm-5:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Mathematical Physics Seminar
      4:20 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-05-2016 Geometric Analysis Seminar
      4:21 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-11-2016 Mathematical Physics Seminar
      4:22 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Entanglement and its key role in quantum information
      4:23 pm-5:23 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-06.30.22-1583x2048-1

      Abstract: Entanglement is a type of correlation found in composite quantum systems, connected with various non-classical phenomena. Currently, entanglement plays a key role in quantum information applications such as quantum computing, quantum communication, and quantum sensing. In this talk the concept of entanglement will be introduced along with various methods that have been proposed to detect and quantify it. The fundamental role of entanglement in both quantum theory and quantum technology will also be discussed.

      Bio: Spyros Tserkis is a postdoctoral researcher at Harvard University, working on quantum information theory. Before joining Harvard in Fall 2021, he was a postdoctoral researcher at MIT and the Australian National University. He received his PhD from the University of Queensland.

    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      4:24 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-06-2016 Seminar on General Relativity
      4:25 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-11-2016 Random Matrix & Probability Theory Seminar
      4:28 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-13-2016 General Relativity Seminar
      4:29 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Colloquium

      Speaker: Justin Moore (Cornell University)

      Title: Homology, higher derived limits, and set theory

      Abstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the “shape” of the space and can give counterintuitive information about its dimension. One remedy of this is to develop a homology theory based on approximating spaces by polyhedra, computing their homologies, and then taking a limit. This is the approach taken by Steenrod-Sitnikov homology and Lisica and Mardesic’s strong homology. Even within the class of locally compact second countable spaces though, the properties of these homology theories — and the higher derived limits which underly them — are dependent on axioms of set theory beyond ZFC. Recently it was shown that it is consistent with (and therefore independent of) ZFC that strong homology and Steenrod Sitnikov homology coincide in the class of locally compact second countable spaces — and therefore each of these homology theories enjoys the desirable properties of the other. These results also point to how we might develop variants of these homology theories which enjoy their desirable properties, but which are less sensitive to set theory. This is joint work with Nathaniel Bannister, Jeff Bergfalk, and Stevo Todorcevic.

    • Seminars
      Seminars Colloquia & Seminar
      04-20-2016 General Relativity Seminar
      4:30 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: CMSA/MATH Fall Gathering
      4:30 pm-6:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      CMSA/MATH Fall Gathering

      Friday, Sep 23, 2022
      4:30–6:00 pm
      All CMSA and Math affiliates are invited.
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/13/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Joel D. Hamkins (Notre Dame and Oxford)

      Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers

      Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually, and in the talk I shall begin slowly with some easy elementary observations. By the end, however, we shall engage with sophisticated ideas in descriptive set theory, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses, for example, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.

    • Colloquium
      4:30 pm
      12/01/2024
    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Cenke Xu (UCSB)

      Title: Quantum field theory approach to quantum information

      Abstract: We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement and decoherence. The Euclidean space-time path integral allows us to map this problem to a quantum field theory with (temporal) boundary or defects. We therefore investigate two types of quantum many-body systems with nontrivial boundary physics: quantum critical points, and states with nontrivial topology, such as Chern insulator and symmetry protected topological states. For example, we demonstrate that a Wilson-Fisher quantum critical point can be driven into an “extraordinary-log” phase after weak-measurement. Another example is that, we argue that a system with higher form symmetry may be driven to a self-dual phase transition under weak measurement.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Seth Koren (Notre Dame)

      Title: Non-invertible symmetries, leptons, quarks, and why multiple generations

      Abstract: Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof.  After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this theory works by virtue of the SM having the same numbers of colors and generations.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      2/20/2019 Colloquium
      4:30 pm-5:00 pm
      12/01/2024
    • Topological Quantum Matter Seminar
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Kaifeng Bu (Harvard University)

      Title: Quantum information: the interplay of mathematics and physics

      Abstract: I will provide an introduction to quantum information, which points to a new connection with experiment on the one hand, and a potential new area of mathematical analysis on the other. I will introduce two recent results about the application of this new area in quantum information: (1) a novel Quantum Central Limit Theorem (QCLT), and (2) a physically realizable protocol for testing and measuring quantum advantage. This talk is based on a collaboration with Arthur Jaffe, and Weichen Gu (PNAS120(25)2023, arXiv: 2302.08423, arXiv:2306.09292).

       

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Yu-Shen Lin (Boston University)

      Title: Gravitational Instantons

      Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk, we will discuss the Torelli theorem of gravitational instantons, how the cohomological invariants of a gravitational instanton determine them. As a consequence, this leads to a description of the moduli space of gravitational instantons.

    • Colloquium
      4:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02/21/2020 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/25/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Colloquium 12/4/2019
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      4:30 pm-5:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/17/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Dana Bartosova (University of Florida)

      Title: What do topological dynamics, combinatorics, and model theory have in common?

      Abstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory.  Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front, however, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts, which is an AIMSQuaRE project with Džamonja, Patel, and Scow.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Jeff W. Lichtman (Harvard University)

      Title: The analytical challenges of connectomics

      Abstract: Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2/14/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/30/2019 Colloquium
      4:30 pm
      12/01/2024
    • Topological Quantum Matter Seminar
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar

      Speaker: Liujun Zou (Perimeter Institute)

      Title: Landscape of quantum phases in quantum materials

      Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.

    • CMSA EVENT: CMSA/MATH Bi-Annual Gathering
      4:30 pm-6:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      On Friday, March 24th, 4:30PM – 6PM, the CMSA will host the CMSA/MATH Bi-Annual Gathering for Harvard CMSA and Math affiliates in the Common Room at 20 Garden Street, Cambridge MA 02138.

    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Topological Quantum Matter Seminar
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Bruno Mera, Instituto Superior Tecnico

      Title: Uniqueness of Landau levels and their analogs with higher Chern numbers

      Abstract: Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged par- ticle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this talk, using the Stone-von Neumann the- orem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions.

      Ref: Bruno Mera and Tomoki Ozawa. Uniqueness of Landau levels and their analogs with higher Chern numbers. arXiv:2304.00866, 2023. arXiv:2304.00866.

       

    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Matthew Foreman (UC Irvine)

      Title: Impossibility results in classical dynamical systems

      Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.

       

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Manuel Cortés-Izurdiaga (University of Malaga)

      Title:  Homotopy categories of rings: some properties and consequences in module categories

      Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the first step in studying other (algebraic) homotopy categories, such as those associated to a scheme. To study these categories, one can use results from the category of modules or the category of complexes. In the first part of the talk, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes, for a natural number N greater than or equal to 2, using some techniques from module categories, such us the deconstruction of a class of modules.

      Another approximation is to use other methods for studying homotopy categories, like those coming from triangulated categories. In some cases, the results obtained in homotopy categories imply some consequences in the category of modules. In the second part of the talk, we will see how to prove the existence of Gorenstein-projective precovers for some specific rings using this approach.

    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/28/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Cameron Krulewski (MIT) and Leon Liu (Harvard)

      Title: A Long Exact Sequence in Symmetry Breaking

      Abstract: We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES).

      The mathematical backbone of the SBLES is the Smith homomorphism, which gives a family of maps between twisted bordism groups. Though many examples have been studied, we give the first completely general account of the Smith homomorphism. We lift it to a map of Thom

      spectra and identify the cofiber, producing a long exact sequence of twisted bordism groups; the SBLES is the Anderson dual of that long exact sequence. Our work develops further the theory of higher Berry phase and its bulk-boundary correspondence and serves as a new computational tool for classifying symmetry protected topological phases.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Boaz Barak (Harvard)

      Title: On Provable Copyright Protection for Generative Model

      Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set.

      Roughly speaking, a generative model p is k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content.

      Joint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870

    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Clay Córdova (U Chicago)

      Title: Anomalies of Non-Invertible Symmetries

    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 RM & PT Seminar
      4:30 pm-5:00 pm
      12/01/2024
    • Seminars
      4:30 pm-5:30 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/4/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/2/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Brian Williams (Boston University)

      Title: Koszul duality in QFT

      Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello, Gaiotto, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory.

       

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Sean Cox, Virginia Commonwealth University

      Title: Predicting non-continuous functions

      Abstract: One of the strangest consequences of the Axiom of Choice is the following Hardin-Taylor 2008 result: there is a “predictor” such that for every function $f$ from the reals to the reals—even nowhere continuous $f$—the predictor applied to $f \restriction (-\infty,t)$ correctly predicts $f(t)$ for *almost every* $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$-invariant predictors? Bajpai-Velleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular, do there exist analytic-invariant predictors? We have partially answered that question: assuming the Continuum Hypothesis (CH), the answer is “no”. Regarding other subgroups of Homeo^+(R), we have affirmative answers that rely solely on topological group-theoretic properties of the subgroup. But these properties are very restrictive; e.g., all known positive examples are metabelian. So there remain many open questions. This is joint work with Aldi, Buffkin, Cline, Cody, Elpers, and Lee.

    • Seminars
      Seminars Colloquia & Seminar
      3/11/2020 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Xuwen Zhu (Northeastern)

      Title: Analysis of ALH* gravitational instantons

      Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.

    • Seminars
      Seminars Colloquia & Seminar
      4/15/2020 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      04-18-2016 Social Science Application Forum
      4:31 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:33 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-19-2016 Geometric Analysis Seminar
      4:33 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:34 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-18-2016 Mathematical Physics Seminar
      4:34 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-21-2016 Evolution Equations Seminar
      4:35 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:36 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-20-2016 Random Matrix & Probability Theory Seminar
      4:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-26-2016 Geometric Analysis Seminar
      4:38 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:39 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-25-2016 Mathematical Physics Seminar
      4:39 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:41 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-27-2016 Random Matrix & Probability Theory Seminar
      4:42 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-27-2016 General Relativity Seminar
      4:44 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-28-2016 CMSA Special Seminar
      4:45 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/4/2020 Colloquium
      4:45 pm-5:45 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      04-28-2016 Evolution Equations Seminar
      4:46 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-04-2016 General Relativity Seminar
      4:48 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-29-2016 CMSA Special Seminar
      4:49 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      05-02-2016 Mathematical Physics Seminar
      4:50 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-05-2016 Evolution Equations Seminar
      4:51 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-25-2016 General Relativity Seminar
      4:52 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      4:54 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      4:56 pm-5:56 pm
      12/01/2024

      Abstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learning-based approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, data-hungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.

    • General Relativity Seminar
      4:58 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      4:59 pm-6:59 pm
      12/01/2024

      Abstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible, and after considerable work by many authors, it is generally conjectured by computer scientists that as the size of matrices becomes large, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk, no knowledge of algebraic geometry or representation theory will be needed.

    • CMSA EVENT: 2017 Ding Shum Lecture
      5:00 pm-6:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

      Learning as a Theory of Everything

      Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

       

    • Seminars
      Seminars Colloquia & Seminar
      2018 HMS Focused Lecture Series
      5:00 pm
      12/01/2024

      As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated below.

      DateSpeakerTitle/Abstract
      January 23, 25, 30 and February 1 

      3-5pm

      *Room G10*

      Ivan Losev 

      (Northeastern)

      Title: BGG category O: towards symplectic duality 

      Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

      Approximate (optimistic) plan of the lectures:

      1) Preliminaries and BGG category O.

      2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

      3) Localization theorem continued. Soergel modules.

      4) Koszul algebras and Koszul duality for categories O.

      Time permitting: other instances of Symplectic duality.

      Prerequisites:

      Semi-simple Lie algebras and their finite dimensional representation theory.

      Some  Algebraic geometry. No prior knowledge of category O/ Geometric

      Representation theory is assumed.

      Scanned from a Xerox Multifunction Device

      February 27, 

      and March 1

      3-5pm

      Colin Diemer 

      (IHES)

      Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

      Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

      March 6 and 8 

      4-5pm

      Adam Jacob 

      (UC Davis)

      Title: The deformed Hermitian-Yang-Mills equation 

      Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

      March 6, 8, 13, 15 

      3-4pm

      Dmytro Shklyarov 

      (TU Chemnitz)

      Title: On categories of matrix factorizations and their homological invariants 

      Abstract: The talks will cover the following topics:

      1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

      2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

      3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

      April 10 & 12 

      3-4pm

      Mauricio Romo 

      (IAS)

      Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

      Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

      Lecture notes

      April 17, 19, 26 

      3-5pm

      Andrew  Harder 

      (University of Miami)

      Title: Perverse sheaves of categories on surfaces 

      Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

      I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

       

      May 15, 17 

      1-3pm

      Charles Doran 

      (University of Alberta)

      Lecture One:
      Title: Picard-Fuchs uniformization and Calabi-Yau geometry
      Abstract:
      Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
      Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

       

      Lecture Two:
      Title: Calabi-Yau fibrations: construction and classification
      Abstract:

      Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

      Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      05-11-2016 Random Matrix & Probability Theory Seminar
      5:00 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
      5:00 pm-6:00 pm
      12/01/2024

      Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Network Science: From the Online World to Cancer Genomics

      Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

       

    • Math Science Literature Lecture Series
      5:00 pm-6:30 pm
      12/01/2024
      Lecture_Sahai-pdf

      Amit Sahai  (UCLA)

      Title: Indistinguishability Obfuscation: How to Hide Secrets within Software

      Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way compiler” remained elusive for decades.

      In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running time) be indistinguishable to any efficient adversary. Leveraging the notion of punctured programming, introduced in our work with Waters in 2013, well over a hundred papers have explored the remarkable power of iO.

      We’ll then discuss the intense effort that recently culminated in our 2020 work with Jain and Lin, finally showing how to construct iO in such a way that, for the first time, we can prove the security of our iO scheme based on well-studied computational hardness conjectures in cryptography.

      Talk chair: Sergiy Verstyuk

      Video

    • Colloquium
      5:00 pm
      12/01/2024
    • CMSA EVENT: 2023 Ding Shum Lecture
      5:00 pm-6:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      Cynthia Dwork

      On March 21, 2023, the CMSA will host the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS and Microsoft Research).

      Time: 5:00-6:00 pm ET

      Location: Harvard University Science Center Hall D

      This event will be held in person and via Zoom webinar.

      Registration is required.

      In-person registration (link)

      Zoom Webinar registration (link)

      Title: Measuring Our Chances: Risk Prediction in This World and its Betters

      Abstract: Prediction algorithms score individuals, assigning a number between zero and one that is often interpreted as an individual probability: a 0.7 “chance” that this child is in danger in the home; an 80% “probability” that this woman will succeed if hired; a 1/3 “likelihood” that they will graduate within 4 years of admission. But what do words like “chance,” “probability,” and “likelihood” actually mean for a non-repeatable activity like going to college? This is a deep and unresolved problem in the philosophy of probability. Without a compelling mathematical definition we cannot specify what an (imagined) perfect risk prediction algorithm should produce, nor even how an existing algorithm should be evaluated. Undaunted, AI and machine learned algorithms churn these numbers out in droves, sometimes with life-altering consequences.

      An explosion of recent research deploys insights from the theory of pseudo-random numbers – sequences of 0’s and 1’s that “look random” but in fact have structure – to yield a tantalizing answer to the evaluation problem, together with a supporting algorithmic framework with roots in the theory of algorithmic fairness.

      We can aim even higher. Both (1) our qualifications, health, and skills, which form the inputs to a prediction algorithm, and (2) our chances of future success, which are the desired outputs from the ideal risk prediction algorithm, are products of our interactions with the real world. But the real world is systematically inequitable. How, and when, can we hope to approximate probabilities not in this world, but in a better world, one for which, unfortunately, we have no data at all? Surprisingly, this novel question is inextricably bound with the very existence of nondeterminism.

      Professor Cynthia Dwork is Gordon McKay Professor of Computer Science at the Harvard University John A. Paulson School of Engineering and Applied Sciences, Affiliated Faculty at Harvard Law School, and Distinguished Scientist at Microsoft. She uses theoretical computer science to place societal problems on a firm mathematical foundation.

      Her recent awards and honors include the 2020 ACM SIGACT and IEEE TCMF Knuth Prize, the 2020 IEEE Hamming Medal, and the 2017 Gödel Prize.

      Talk Chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)
      Moderator: Faidra Monachou (Harvard CMSA)

      The 2020-2022 Ding Shum lectures were postponed due to Covid-19.


      Watch the Lecture on Youtube:

      https://youtu.be/wGpZE8QrCKY

    • CMSA EVENT: Noga Alon Public Talk, 9-7-17
      5:00 pm-6:00 pm
      12/01/2024

      Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Graph Coloring: Local and Global

      Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

    • General Relativity Seminar
      5:02 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:02 pm-6:02 pm
      12/01/2024

      Abstract: Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the ““game” of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.

    • New Technologies in Mathematics Seminar
      5:03 pm-6:03 pm
      12/01/2024

      Abstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions, has allowed major progress on other related questions about M theory, and briefly discuss other applications in field theory and beyond.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-01-2016 Random Matrix & Probability Theory Seminar
      5:03 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-08-2016 Random Matrix & Probability Theory Seminar
      5:04 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:04 pm-6:04 pm
      12/01/2024

      Abstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size.

      We demonstrate the effectiveness of the SAT approach by presenting some recent successes, including the solution of the Boolean Pythagorean Triples problem, computing the fifth Schur number, and resolving the remaining case of Keller’s conjecture. Moreover, we constructed and validated a proof for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular, we discuss our progress on applying SAT solving techniques to the chromatic number of the plane (Hadwiger-Nelson problem), optimal schemes for matrix multiplication, an

    • Seminars
      Seminars Colloquia & Seminar
      07-12-2016 Chinese Economy Seminar
      5:06 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:07 pm-6:07 pm
      12/01/2024

      Speaker: Patrick Massot, Laboratoire de Mathématiques d’Orsay and CNRS

      Title: Why explain mathematics to computers?

      Abstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics, and I won’t assume any prior knowledge about formalization.

    • Seminars
      Seminars Colloquia & Seminar
      07-19-2016 Chinese Economy Seminar
      5:07 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-02-2016 China Gazetteer Seminar
      5:08 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-12-2016 Mathematical Physics Seminar
      5:10 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-19-2016 Mathematical Physics Seminar
      5:11 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:12 pm-6:12 pm
      12/01/2024
      CMSA-NTM-Seminar-11.03.21

      Abstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms.  This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers.  This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-21-2016 Random Matrix & Probability Theory Seminar
      5:13 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      5:15 pm-6:15 pm
      12/01/2024

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-23-2018 Math Physics
      5:15 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      5:15 pm-6:15 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      3/27/2019 Colloquium
      5:15 pm-6:15 pm
      12/01/2024
    • Colloquium
      5:15 pm-6:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4-16-2018 Social Science Applications Forum
      5:16 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:17 pm-6:17 pm
      12/01/2024
      CMSA-NTM-Seminar-12.01.21

      Abstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data.

      In terms of their “microscopic” definition, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem, analogous to criticality, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting, we will explain how the interactions induce representation learning.

      This talk is based on a book, The Principles of Deep Learning Theory, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.

    • Seminars
      Seminars Colloquia & Seminar
      4-20-2018 Social Science Applications Forum
      5:18 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:32 pm-6:32 pm
      12/01/2024
      CMSA-NTM-Seminar-12.08.21

      Abstract: Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured images produced by DALL-E. These large language models are impressive but also very inefficient and costly, which limits their applications and accessibility. We postulate that having an explicit hierarchical architecture is the key to Transformers that efficiently handle long sequences. To verify this claim, we first study different ways to upsample and downsample activations in Transformers so as to make them hierarchical. We use the best performing upsampling and downsampling layers to create Hourglass – a hierarchical Transformer language model. Hourglass improves upon the Transformer baseline given the same amount of computation and can yield the same results as Transformers more efficiently. In particular, Hourglass sets new state-of-the-art for Transformer models on the ImageNet32 generation task and improves language modeling efficiency on the widely studied enwik8 benchmark.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-26-16 Mathematical Physics Seminar
      5:32 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Fluid Dynamics Seminar
      5:33 pm
      12/01/2024

      Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. Links to connect can be found in the schedule below once they are created. 

      In the Spring 2019 Semester, the Center of Mathematical Sciences and Applications will be hosting a seminar on Fluid Dynamics. The seminar will take place on Wednesdays from 3:00-4:00pm in CMSA G10.

      Spring 2020:

      DateSpeakerTitle/Abstract
      2/25/2020Keaton Burns, MITTitle: Flexible spectral simulations of low-Mach-number astrophysical fluids

      Abstract: Fluid dynamical processes are key to understanding the formation and evolution of stars and planets. While the astrophysical community has made exceptional progress in simulating highly compressible flows, models of low-Mach-number stellar and planetary flows typically use simplified equations based on numerical techniques for incompressible fluids. In this talk, we will discuss improved numerical models of three low-Mach-number astrophysical phenomena: tidal instabilities in binary neutron stars, waves and convection in massive stars, and ice-ocean interactions in icy moons. We will cover the basic physics of these systems and how ongoing additions to the open-source Dedalus Project are enabling their efficient simulation in spherical domains with spectral accuracy, implicit timestepping, phase-field methods, and complex equations of state.

      3/4/2020

      G02

      3/11/2020
      3/18/2020
      3/25/2020
      4/1/2020
      4/8/2020 G02
      4/15/2020
      4/22/2020
      4/29/2020

      G02

      5/6/2020
      5/13/2020

      Fall 2019:

      DateSpeakerTitle/Abstract
      9/18/2019Jiawei Zhuang (Harvard)Title: Simulation of 2-D turbulent advection at extreme accuracy with machine learning and differentiable programming

       Abstract: The computational cost of fluid simulations grows rapidly with grid resolution. With the recent slow-down of Moore’s Law, it can take many decades for 10x higher resolution grids to become affordable. To break this major barrier in high-performance scientific computing, we used a data-driven approach to learn an optimal numerical solver that can retain high-accuracy at much coarser grids. We applied this method to 2-D turbulent advection and achieved 4x effective resolution than traditional high-order flux-limited advection solvers. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The model can achieve near-peak FLOPs on CPUs and accelerators via convolutional filters.

      9/25/2019Yantao Yang (Peking University)Title: Double diffusive convection and thermohaline staircases 

      Abstract: Double diffusive convection (DDC), i.e. the buoyancy-driven flow with fluid density depending on two scalar components, is omnipresent in many natural and engineering environments. In ocean this is especially true since the seawater density is mainly determined by temperature and salinity. In upper water of both (sub-) tropical and polar oceans, DDC causes the intriguing thermohaline staircases, which consist of alternatively stacked convection layers and sharp interfaces with high gradients of temperature and salinity. In this talk, we will focus on the fingering DDC usually found in (sub-)tropical ocean, where the mean temperature and salinity decrease with depth. We numerically investigate the formation and the transport properties of finger structures and thermohaline staircases. Moreover, we show that multiple states exit for the exactly same global condition, and individual finger layers and finger layers within staircases exhibit very different transport behaviors.

      10/2/2019No talk
      10/9/2019Samuel Rudy (MIT)Title: Data-driven methods for discovery of partial differential equations and forecasting

      Abstract: A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for partial differential equations with or without parametric dependencies and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will also be discussed.​

      10/16/2019No talk
      10/23/2019Kimee Moore (Harvard)Title: Using magnetic fields to investigate Jupiter’s fluid interior

      Abstract: The present-day interior structure of a planet is an important reflection of the formation and subsequent thermal evolution of that planet. However, despite decades of spacecraft missions to a variety of target bodies, the interiors of most planets in our Solar System remain poorly constrained. In this talk, I will discuss how actively generated planetary magnetic fields (dynamos) can provide important insights into the interior properties and evolution of fluid planets. Using Jupiter as a case study, I will present new results from the analysis of in situ spacecraft magnetometer data from the NASA Juno Mission (currently in orbit about Jupiter). The spatial morphology of Jupiter’s magnetic field shows surprising hemispheric asymmetry, which may be linked to the dissolution of Jupiter’s rocky core in liquid metallic hydrogen. I also report the first definitive detection of time-variation (secular variation) in a planetary dynamo beyond Earth. This time-variation can be explained by the advection of Jupiter’s magnetic field by the zonal winds, which places a lower bound on the velocity of Jupiter’s winds at depth. These results provide an important complement to other analysis techniques, as gravitational measurements are currently unable to uniquely distinguish between deep and shallow wind scenarios, and between solid and dilute core scenarios. Future analysis will continue to resolve Jupiter’s interior, providing broader insight into the physics of giant planets, with implications for the formation of our Solar System.

      10/30/2019No Talk
      11/6/2019Federico Toschi (Eindhoven University of Technology)Title: Deep learning and reinforcement learning for turbulence

      Abstract: This talk tells two stories.

      Chapter 1: We investigate the capability of a state-of-the-art deep neural model at learning features of turbulent velocity signals. Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected. We consider turbulent velocity signals, spanning decades in Reynolds numbers, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of the turbulent signals, we focus on the fundamental question of whether a deep neural network (DNN) is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. Can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning?

      Chapter 2: Thermally driven turbulent flows are common in nature and in industrial applications. The presence of a (turbulent) flow can greatly enhance the heat transfer with respect to its conductive value. It is therefore extremely important -in fundamental and applied perspective- to understand if and how it is possible to control the heat transfer in thermally driven flows. In this work, we aim at maintaining a Rayleigh–Bénard convection (RBC) cell in its conductive state beyond the critical Rayleigh number for the onset of convection. We specifically consider controls based on local modifications of the boundary temperature (fluctuations). We take advantage of recent developments in Artificial Intelligence and Reinforcement Learning (RL) to find -automatically- efficient non-linear control strategies. We train RL agents via parallel, GPU-based, 2D lattice Boltzmann simulations. Trained RL agents are capable of increasing the critical Rayleigh number of a factor 3 in comparison with state-of-the-art linear control approaches. Moreover, we observe that control agents are able to significantly reduce the convective flow also when the conductive state is unobtainable. This is achieved by finding and inducing complex flow fields.

      11/13/2019

       

      2:10pm

      G02

      Martin Lellep (Philipps University of Marburg, Germany)Title: Predictions of relaminarisation in turbulent shear flows using deep learning

       

      Abstract: Given the increasing performance of deep learning algorithms in tasks such as classification during the last years and the vast amount of data that can be generated in turbulence research, I present one application of deep learning to fluid dynamics in this talk. We train a deep learning machine learning model to classify if turbulent shear flow becomes laminar a certain amount of time steps ahead in the future. Prior to this, we use a 2D toy example to develop an understanding how the performance of the deep learning algorithm depends on hyper parameters and how to understand the errors. The performance of both algorithms is high and therefore opens up further steps towards the interpretation of the results in future work.

      11/19/2019

      Tuesday

      3-4 pm

      Pierce Hall 209, 29 Oxford Street 

      Detlef Lohse (University of Twente)Title: Rayleigh vs. Marangoni Abstract: In this talk I will show several examples of an interesting and surprising competition between buoyancy and Marangoni forces. First, I will introduce the audience to the jumping oil droplet – and its sudden death – in a density stratified liquid consisting of water in the bottom and ethanol in the top : After sinking for about a minute, before reaching the equilibrium the droplet suddenly jumps up thanks to the Marangoni forces. This phenomenon repeats about 30-50 times, before the droplet falls dead all the sudden. We explain this phenomenon and explore the phase space where it occurs.

      Next, I will focus on the evaporation of multicomponent droplets, for which the richness of phenomena keeps surprising us. I will show and explain several of such phenomena, namely evaporation-triggered segregation thanks to either weak solutal Marangoni flow or thanks to gravitational effects. The dominance of the latter implies that sessile droplets and pending droplets show very different evaporation behavior, even for Bond number << 1. I will also explain the full phase diagram in the Marangoni number vs Rayleigh number phase space, and show where Rayleigh convections rolls prevail, where Marangoni convection rolls prevail, and where they compete.

      The research work shown in this talks combines experiments, numerical simulations, and theory. It has been done by and in collaboration with Yanshen Li, Yaxing Li, and Christian Diddens, and many others.

      11/20/2019Time: 3:00-3:35 pm

      Speaker:  Haoran Liu

      Title: Applications of Phase Field method: drop impact and multiphase turbulence 

      Abstract: Will a mosquito survive raindrop collisions? How the bubbles under a ship reduce the drag force? In nature and industry, flows with drops and bubbles exist everywhere. To understand these flows, one of the powerful tools is the direct numerical simulation (DNS). Among all the DNS methods, we choose the Phase Field (PF) method and develop some models based on it to simulate the complicated flows, such as flows with moving contact lines, fluid-structure interaction, ternary fluids and turbulence. In this talk, I will firstly introduce the advantages and disadvantages of PF method. Then, I will show its applications: drop impact on an object, compound droplet dynamics, water entry of an object and multiphase turbulence.


      Time: 3:35-4:10 pm

      Speaker:  Steven Chong

      Title: Confined Rayleigh-Bénard, rotating Rayleigh-Bénard, double diffusive convection and quasi-static magnetoconvection: A unifying view on their scalar transport enhancement 

      Abstract: For Rayleigh-Bénard under geometrical confinement, under rotation or the double diffusive convection with the second scalar component stabilizing the convective flow, they seem to be the three different canonical models in turbulent flow. However, previous research coincidentally reported the scalar transport enhancement in these systems. The results are counter-intuitive because the higher efficiency of scalar transport is bought about by the slower flow. In this talk, I will show you a fundamental and unified perspective on such the global transport behavior observed in the seemingly different systems. We further show that the same view can be applied to the quasi-static magnetoconvection, and indeed the regime with heat transport enhancement has been found. The beauty of physics is to understand the seemingly unrelated phenomena by a simplified concept. Here we provide a simplified and generic view, and this concept could be potentially extended to other situations where the turbulent flow is subjected to an additional stabilization.

      11/27/2019
      12/4/2019
      12/11/2019

       

      See previous seminar information here.
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2016 Random Matrix & Probability Theory Seminar
      5:35 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:35 pm-6:35 pm
      12/01/2024
      CMSA-NTM-Seminar-12.15.21

      Abstract: A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular, we will consider the gapped ground states and Gibbs states on low dimensional lattices, which are believed to exhibit ‘low complexity’ due to the widely studied area law behaviour. Here, we will see the crucial role of complexity-theoretic methods in progress on the ‘area law conjecture’ and in the development of efficient algorithms to classically simulate quantum many-body systems.

    • Seminars
      5:36 pm
      12/01/2024

      As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      DateSpeakerTitle/Abstract
      8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

      Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

      9/10/2018Dominic Else, MIT

      Video

      Title: Phases and topology in periodically driven (Floquet) systems

      Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

      9/17/2018Adrian Po, MIT

      Video

      Title: A modern solution to the old problem of symmetries in band theory

      Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

      9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

      Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

      10/1/2018Cancelled
      10/9/2018

      Tuesday

      3:00-4:30pm

      Sagar VijayTitle: Fracton Phases of Matter

      Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

      10/15/2018Ethan LakeTitle: A primer on higher symmetries

      Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

      10/22/2018

      Room G02

      Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

      Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

      10/29/2018Dominic Williamson, Yale

      Video

      Title: Symmetry and topological order in tensor networks

      Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

      11/13/2018

      Tuesday

      3:00-4:30pm

      Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
      11/19/2018X. G. Wen, MIT

      Video

      Title: A classification of 3+1D topological orders

      Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

      12/3/2018

      *Room G02*

      Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

      Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

      12/10/2018

      Room G02

      Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

      Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

      1/8/2019Lukasz Fidkowski, Univ. of Washington

      Video

      Title: Non-trivial quantum cellular automata in 3 dimensions

      Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

      3/18/2019Ari Turner, Technion

      Video

      Title:  Trapping Excitations at Phantasmagoric Wave Vectors

      Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

      4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

      Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

      4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

      Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

      4/16/2019

      Lyman 425

      1:30pm

      Xie Chen (Calthech)Title: Foliated Fracton Order

      Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

      4/24/2019

      10:30am

      Michael Freedman (Microsoft Station Q)

      Video

      Title: Quantum cellular automata in higher dimensions

      Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

      4/26/2019

      10:30am

      Maissam Barkeshli (University of Maryland)

      Video

      Title: Relative anomalies in (2+1)D symmetry enriched topological states

      Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

      5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

      Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

      5/9/2019

      10:30am

      Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

      Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

      5/28/2019

      10:30am

      Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

       

      Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

      7/18/2019Eslam Khalaf (Harvard)

      Title: Dynamical correlations in anomalous disordered wires

      Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
      The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
      The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
    • Seminars
      Seminars Colloquia & Seminar
      Spacetime and Quantum Mechanics Seminar
      5:38 pm
      12/01/2024

      As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

      DateSpeakerTitle/Abstract
      9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
      19/18/2019

      2:00pm

      G02

      Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
      9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

      Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

      Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

      These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

      Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

      9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
      10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
      10/10/2019

      3:30pm

      Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
      10/15/2019

      Tuesday

      3:30pm

       

      Sergey Fomin (Univ. of Michigan)

       

      Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
      10/18/2019

      Friday 

      G02

      Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
      10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
      11/1/2019

      SC 232

      1:30pm

      George Lusztig (MIT)Title: Total positivity in Springer fibres
      11/12/2019

      Tuesday

      G02

      3:30pm

       

      Pierpaolo Mastrolia (University of Padova)

      Title: Feynman Integrals and Intersection Theory
      11/14/2019

      G02

      Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
      11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
      11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
      12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

      Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

       12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
      12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

      Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/10/2018 Math-Physics Seminar
      5:41 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-05-2016 Random Matrix & Probability Theory Seminar
      5:41 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      5:42 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/14/2019 Random Matrix and Probability Theory Seminar
      5:45 pm
      12/01/2024
    • Seminars
      5:48 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      5:52 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      5:52 pm-6:52 pm
      12/01/2024

      Abstract:  Online marketplaces are the main engines of legal and illegal e-commerce, yet the aggregate properties of buyer-seller networks behind them are poorly understood. We analyse two datasets containing 245M transactions (16B USD)  between 2010 and 2021 involving online marketplaces: 28 dark web marketplaces (DWM), unregulated markets whose main currency is Bitcoin, and 144 product markets of one regulated e-commerce platform. We show how transactions in online marketplaces exhibit strikingly similar patterns of aggregate behavior despite significant differences in language, products, time, regulation, oversight, and technology. We find remarkable regularities in the distributions of (i) transaction amounts, (ii) number of transactions, (iii) inter-event times, (iv) time between first and last transactions. We then show how buyer behavior is affected by the memory of past interactions, and draw on these observations to propose a model of network formation able to reproduce the main stylised facts of the data. Our findings have important implications for understanding market power on online marketplaces as well as inter-marketplace competition.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/17/2018 Math-Physics Seminar
      5:53 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/24/2018 Math-Physics Seminar
      5:55 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      5:56 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      5:59 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
      6:00 pm-6:01 pm
      12/01/2024-10/06/2017

      The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

      • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
      • Linear patterns in the primes (Green, Tao, Ziegler);
      • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
      • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

      Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

      • Constructions of pseudorandom objects (eg. extractors and expanders);
      • Constructions of extremal objects (eg. BCH codes);
      • Property testing (eg. testing linearity);
      • Algebraic algorithms (eg. matrix multiplication).

      The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

      Monday, October 2

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

      Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

      The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      10:20-11:00amCoffee Break 
      11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

      Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      12:00-1:30pmLunch 
      1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

      Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

      Joint work with Sivakanth Gopi

      2:20-3:00pmCoffee Break 
      3:00-3:50pmFernando Shao

      Large deviations for arithmetic progressions

      Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

      4:00-6:00pmWelcome Reception

      Tuesday, October 3

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amEmanuele ViolaInterleaved group products

      Authors: Timothy Gowers and Emanuele Viola

      Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

      These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

      10:20-11:00amCoffee Break
      11:00-11:50amVsevolod LevOn Isoperimetric Stability

      Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

      As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

      We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

      12:00-1:30pmLunch
      1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

      Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

      Joint work with Venkata Gandikota and Badih Ghazi.

      2:20-3:00pmCoffee Break
      3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

      Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

      Wednesday, October 4

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

      Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

      Joint work with Thomas Bloom.

      10:20-11:00amCoffee Break 
      11:00-11:50amThomas BloomBounds on capsets via properties of spectra

      This is a continuation of the previous talk by Olof Sisask.

      12:00-1:30pmLunch 
      1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

      Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

      2:20-3:00pmCoffee Break
      3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

      Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

      When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

      Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

      Thursday, October 5

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

       Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

      I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

      Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

      10:20-11:00amCoffee Break
      11:00-11:50amJulia WolfStable arithmetic regularity

      The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

      Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

      This is joint work with Caroline Terry.

      12:00-1:30pmLunch 
      1:30-2:20pmWill Sawin

      Constructions of Additive Matchings

      Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

      2:20-3:00pmCoffee Break
      3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

      Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

      Friday, October 6

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

      Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

      Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

      10:20-11:00amCoffee Break
      11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

      Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

      This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

      Joint work with Hamed Hatami and Shachar Lovett

      12:00-1:30pmLunch
      1:30-2:20pmGuy Kindler

      From the Grassmann graph to Two-to-Two games

      Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

      The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

      These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

      This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

    • CMSA EVENT: Current Developments In Mathematics 2018
      6:00 pm-5:00 pm
      12/01/2024-11/17/2018
      CDM2018

      Current Developments in Mathematics 2018 Conference.

      Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

      Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

      Harvard University Science Center, Hall B

      Visit the conference page here 

    • New Technologies in Mathematics Seminar
      6:00 pm-7:00 pm
      12/01/2024
      CMSA-New-Technologies-Seminar-01.26.2022-1553x2048-1

      Abstract: Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the four colour theorem are among the most notable. Up until now there hasn’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk we will discuss the results of our recent Nature paper, where we worked together with top mathematicians to use machine learning to achieve two new results – proving a new connection between the hyperbolic and geometric structure of knots, and conjecturing a resolution to a 50-year problem in representation theory, the combinatorial invariance conjecture. Through these examples we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/01/2018 Math-Physics Seminar
      6:01 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
      6:02 pm
      12/01/2024-03/15/2018
      Fluid turbulence

      The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Speakers: 

    • General Relativity Seminar
      6:03 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/08/2018 Math-Physics Seminar
      6:04 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:05 pm-7:05 pm
      12/01/2024
      CMSA-NTM-Seminar-02.02.2022-2-1583x2048

      Abstract: In this talk, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry, it is possible to provide a principled view on such GNN architectural choices as positional encoding and graph rewiring as well as explain and remedy the phenomena of oversquashing and bottlenecks.

    • CMSA EVENT: Blockchain Conference
      6:05 pm
      12/01/2024-01/25/2018
      Blockchain

      On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

      https://youtu.be/FyKCCutxMYo

      List of registrants

      Photos

      Speakers: 

    • Seminars
      6:05 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      6:06 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
      6:07 pm
      12/01/2024-11/17/2017

      The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

      Click here for a list of registrants.

      Monday, Nov. 13

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Jozsef Solymosi

       

      On the unit distance problem

      Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

       

      Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

      Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Andrew Hoon Suk

      Ramsey numbers: combinatorial and geometric

      Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Josh Zahl

      Cutting curves into segments and incidence geometry

      4:00-6:00pmWelcome Reception

      Tuesday, Nov. 14

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Péter Pál Pach

      Polynomials, rank and cap sets

      AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

      10:30-11:00amCoffee Break
      11:00-12:00pmJordan Ellenberg

      The Degeneration Method

      Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Larry GuthThe polynomial method in Fourier analysis

      Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

       

      2:30-3:00pm

      Coffee Break
      3:00-4:00pmOpen Problem

      Wednesday, Nov. 15

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

       

      Avi Wigderson

      The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

      Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

      In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

      In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

      This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

      I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

      (despite the fact that a random such tensor has rank quadratic in n).

      No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Venkat Guruswami

      Subspace evasion, list decoding, and dimension expanders

       Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

      Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

      This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

      (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

      12:00-1:30pmLunch
      1:30-2:30pm

       

      David Conlon

      Finite reflection groups and graph norms

      Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

       

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Laszlo Miklós Lovasz

      Removal lemmas for triangles and k-cycles.

      Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

      In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

      The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

      Thursday, Nov. 16

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Janos PachLet’s talk about multiple crossings

      Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Misha Rudnev

      Few products, many sums

      Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

      $$

      |A|^{10} \ll |A-A|^4|AA|^4

      $$

      to

      $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

      The other is the bound 

      $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Adam Sheffer

      Geometric Energies: Between Discrete Geometry and Additive Combinatorics

      Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Boris Bukh

      Ranks of matrices with few distinct entries

      Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

      Friday, Nov. 17

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Benny Sudakov

      Submodular minimization and set-systems with restricted intersections

      AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

      We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

      Joint work with M. Nagele and R. Zenklusen

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Robert Kleinberg 

      Explicit sum-of-squares lower bounds via the polynomial method

      AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

      Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

      Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

      This is joint work with Sam Hopkins.

      12:00-1:30pmLunch

       

    • New Technologies in Mathematics Seminar
      6:07 pm-7:07 pm
      12/01/2024
      CMSA-NTM-Seminar-02.09.2022-1553x2048

      Abstract: Over the past several years, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning, leading to advances in natural language processing, computer vision, code synthesis, protein structure prediction, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet, there is at present limited principled understanding of the reasons for its success. In this talk, I’ll explain how attention mechanisms and Transformers work, and then I’ll share the results of a preliminary investigation into why they work so well. In particular, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions, with statistical generalization guarantees akin to sparse regression.

    • New Technologies in Mathematics Seminar
      6:09 pm-7:09 pm
      12/01/2024
      CMSA-NTM-Seminar-02.16.2022-1553x2048

      Abstract: Hyperbolic manifolds are a class of Riemannian manifolds that are important in mathematics and physics, playing a prominent role in topology, number theory, and string theory. Associated with a given hyperbolic metric is a sequence of numbers corresponding to the discrete eigenvalues of the Laplace-Beltrami operator. While these eigenvalues usually cannot be calculated exactly, they can be found numerically and must also satisfy various bounds. In this talk, I will discuss a new approach for finding numerical bounds on the eigenvalues of closed hyperbolic manifolds using general consistency conditions and semidefinite programming, inspired by the approach of the conformal bootstrap from physics. Although these bootstrap bounds follow from seemingly trivial consistency conditions, they are surprisingly strong and are sometimes almost saturated by actual manifolds; for example, one such bound implies that the first nonzero eigenvalue of a closed hyperbolic surface must be less than 3.83890, and this is very close to being saturated by a particular genus-2 surface called the Bolza surface. I will show how to derive this and other bounds and will discuss some possible future directions for this approach.

    • Special Seminar
      6:10 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      6:11 pm-6:12 pm
      12/01/2024-10/25/2016

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/10/2018 RM & PT Seminar
      6:11 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:11 pm-7:11 pm
      12/01/2024
      03.2.2022-1553x2048-1

      Abstract:  Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes, and prospects for RL and other techniques.

    • General Relativity Seminar
      6:12 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:13 pm-7:13 pm
      12/01/2024
      CMSA-NTM-Seminar-03.09.2022

      Abstract: We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time.
      We curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics, Chemical Engineering, Chemistry, Computer Science, Economics, Electrical Engineering, Materials Science, Mathematics, Mechanical Engineering, Nuclear Science, Physics, and Statistics.
      We generate new questions and use them in a Columbia University course, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations, again for the first time.
      Our approach consists of five steps:
      (i) Given course questions, turn them into programming tasks;
      (ii) Automatically generate programs from the programming tasks using a Transformer model, OpenAI Codex, pre-trained on text and fine-tuned on code;
      (iii) Execute the programs to obtain and evaluate the answers;
      (iv) Automatically explain the correct solutions using Codex;
      (v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.
      This work is a significant step forward in applying machine learning for education, automating a considerable part of the work involved in teaching.
      Our approach allows personalization of questions based on difficulty level and student backgrounds, and scales up to a broad range of courses across the schools of engineering and science.

      This is joint work with students and colleagues at MIT, Harvard University, Columbia University, Worcester Polytechnic Institute, and the University of Waterloo.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-03-16 Mathematical Physics Seminar
      6:13 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:14 pm-7:14 pm
      12/01/2024
      CMSA-NTM-Seminar-03.23.2022-1553x2048-1

      Abstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems,  without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark,  automatically solving multiple challenging problems drawn from high school olympiads.

    • Seminars
      Seminars Colloquia & Seminar
      10/15/2018 Topology Seminar
      6:14 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:15 pm-7:15 pm
      12/01/2024
      CMSA-NTM-Seminar-03.30.2022-1583x2048-1

      Abstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this talk, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.

      Video

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/15/2018 Math Physics Seminar
      6:15 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-12-2016 Random Matrix & Probability Theory Seminar
      6:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      6:17 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-24-2016 Random Matrix & Probability Theory Seminar
      6:18 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      6:19 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2018 RM & PT Seminar
      6:19 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/26/2018 Social Science Applications Forum
      6:20 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:22 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/22/2018 Mathematical Physics Seminar
      6:24 pm
      12/01/2024
    • Member Seminar
      6:24 pm
      12/01/2024

      No additional detail for this event.

    • Member Seminar
      6:26 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:27 pm
      12/01/2024

      No additional detail for this event.

    • Member Seminar
      6:29 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:30 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:31 pm-7:31 pm
      12/01/2024

      Title: Naturalness and muon anomalous magnetic moment

      Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:32 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      6:34 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:34 pm-7:34 pm
      12/01/2024

      Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

      Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      6:36 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:37 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:37 pm-7:37 pm
      12/01/2024

      Title: Cornering the universal shape of fluctuations and entanglement

      Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

      Ref: arXiv:2102.06223

    • Quantum Matter
      6:38 pm-7:38 pm
      12/01/2024

      Title: Quantum gravity from quantum matter

      Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      9/23/2021 Interdisciplinary Science Seminar
      6:40 pm-8:40 pm
      12/01/2024

      Title: The number of n-queens configurations

      Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

      Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

    • Member Seminar
      6:40 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-17-16 Mathematical Physics Seminar
      6:41 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      10/7/2021 Interdisciplinary Science Seminar
      6:41 pm
      12/01/2024

      Title: SiRNA Targeting TCRb: A Proposed Therapy for the Treatment of Autoimmunity

      Abstract: As of 2018, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent, treatment options remain relatively poor, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness over time. Given this, new forms of therapy are needed. To this end, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted, novel means of therapy for the treatment of autoimmune disorders.

      This talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      10/14/2021 Interdisciplinary Science Seminar
      6:42 pm-8:42 pm
      12/01/2024

      Title: D3C: Reducing the Price of Anarchy in Multi-Agent Learning

      Abstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.

    • Quantum Matter
      6:44 pm-7:44 pm
      12/01/2024

      Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

      Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
      Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      10/21/2021 Interdisciplinary Science Seminar
      6:44 pm-8:44 pm
      12/01/2024

      Title: Mathematical resolution of the Liouville conformal field theory.

      Abstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David, Kupiainen, Rhodes, Vargas.

      Many works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable », the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras, representations of Virasoro algebras, the theory of conformal blocks). However, for Liouville Theory this was not done at the mathematical level by algebraic methods.

      I’ll explain how to combine probabilistic, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure, which is viewed as the space of fields, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space.

      This is joint work with A. Kupiainen, R. Rhodes and V. Vargas.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      ARCH: Know What Your Machine Doesn’t Know
      6:45 pm-8:45 pm
      12/01/2024

      Speaker: Jie Yang, Delft University of Technology

      Title: ARCH: Know What Your Machine Doesn’t Know

      Abstract: Despite their impressive performance, machine learning systems remain prohibitively unreliable in safety-, trust-, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk, I will present our ongoing work on ARCH, a knowledge-driven, human-centered, and reasoning-based tool, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk, I will present several applications in which ARCH is currently being developed and tested, including health, finance, and smart buildings.

    • Quantum Matter
      6:46 pm-7:46 pm
      12/01/2024

      Title: Three-particle mechanism for pairing and superconductivity

      Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

      [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
      [2] V. Crepel and L. Fu, arXiv:2103.12060
      [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      11/4/21 CMSA Interdisciplinary Science Seminar
      6:46 pm-8:46 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-11.04.21-1583x2048-1

      Title: Exploring Invertibility in Image Processing and Restoration

      Abstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., image-to-video conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:46 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:47 pm-7:47 pm
      12/01/2024

      Title: The Hilbert Space of large N Chern-Simons matter theories

      Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

    • Member Seminar
      6:52 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:53 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:54 pm-7:54 pm
      12/01/2024

      Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

      Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:54 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      6:59 pm
      12/01/2024

      No additional detail for this event.

    • Yip Lecture Series
      Yip Lecture Series Event
      Third Annual Yip Lecture
      7:00 pm-8:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

      Time: 7:00-8:00 pm ET

      Location: Harvard Science Center Hall A

      Registration is required.

      In-person Registration

      Zoom Webinar Registration

      Title: Black Holes: The Most Mysterious Objects in the Universe

      Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.

      Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.

      Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)

      Moderator: Daniel Kapec (Harvard CMSA)

      The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

       

      https://youtu.be/RpQhQ855WUY


      The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      7:00 pm
      12/01/2024

      No additional detail for this event.

    • Yip Lecture Series
      7:00 pm-8:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      Yip2022_poster_web

      Harvard CMSA hosted the second annual Yip Lecture on April 4, 2022.

      The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.
      This year’s speaker was Avi Loeb (Harvard).

       

      Extraterrestrial Life

      Abstract: Are we alone? It would be arrogant to think that we are, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System, such as `Oumuamua.

      Abraham (Avi) Loeb is the Frank B. Baird, Jr., Professor of Science at Harvard University and a bestselling author (in lists of the New York Times, Wall Street Journal, Publishers Weekly, Die Zeit, Der Spiegel, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986), led the first international project supported by the Strategic Defense Initiative (1983–1988), and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books, including most recently, Extraterrestrial (Houghton Mifflin Harcourt, 2021), and nearly a thousand papers (with an h-index of 118) on a wide range of topics, including black holes, the first stars, the search for extraterrestrial life, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences, the American Physical Society, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade.

      Click here for Loeb’s commentaries on innovation and diversity.

      Website: https://www.cfa.harvard.edu/~loeb/

      See the Harvard Gazette article featuring Avi Loeb: “Oh, if I could talk to the aliens” published March 8, 2022.

      Prof. Loeb’s books:
      Extraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)
      Life in the Cosmos: From Biosignatures to Technosignatures (2021)

      Avil Loeb is the head of the Galileo Project at Harvard.


      The previous Yip Lecture featured Peter Galison (Harvard), who spoke on the EHT’s hunt for an objective image of a black hole.

    • Seminars
      7:03 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-31-16 Mathematical Physics Seminar
      7:05 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      7:30 pm-9:00 pm
      12/01/2024
    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
      CMSA-QMMP-02.09.2022-1544x2048-1

      Speaker: Yuji Tachikawa (Kavli IPMU, U Tokyo)

      Title: On the absence of global anomalies of heterotic string theories

      Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.

      In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.

      The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.

    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
      CMSA-QMMP-02.02.2022-1544x2048

      Title: Kramers-Wannier-like duality defects in higher dimensions

      Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/15/2020 Quantum Matter Seminar
      8:30 pm-10:00 pm
      12/01/2024
    • Quantum Matter
      8:30 pm-10:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-04.13.22-1583x2048-1

      Youtube Video

      Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.

      We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.

      We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.

      Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.

    • Quantum Matter
      8:30 pm-10:30 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.18.22-1583x2048-1

      Speaker: Linhao Li (ISSP, U Tokyo)

      Title: Boundary conditions and LSM anomalies of conformal field theories in 1+1 dimensions

      Abstract: In this talk, we will study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state which is invariant under a symmetry, then the CFT can be gapped with a unique ground state by adding the corresponding gapping potential. This means that the symmetry of the CFT is anomaly free. Using this approach, we will systematically deduce the anomaly-free conditions for various types of CFTs with several different symmetries. When the symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis type ingappability of the system. Our results are consistent with, where available, known results in the literature. Moreover, we extend the discussion to other symmetries including spin groups and generalized time-reversal symmetries. As an application, we propose 1d LSM theorem involving magnetic space group symmetries on the lattice. The extended LSM theorems apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and chiral three-spin interactions.

    • Quantum Matter
      8:30 pm-10:00 pm
      12/01/2024

      Speaker: Nima Arkani-Hamed (IAS Princeton)

      Title: UV/IR and Effective Field Theory

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Tropical disk counts
      8:30 pm-9:30 pm
      12/01/2024

      Abstract: (joint with S. Venugopalan)  I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan)  which is an open analog of the twenty-seven lines.  As an application, I will explain why the Floer cohomology of such tropical fibers is well-defined; this is a generalization fo a result of Fukaya-Oh-Ohta-Ono for toric varieties.

    • Quantum Matter
      8:30 pm-9:30 pm
      12/01/2024
      CMSA-QMMP-03.10.2022-1544x2048-1-1

      Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field.

      This work is based on arxiv: 2201.11681

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/10/2018 Mathematical Physics Seminar
      8:42 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/10/2018 Topology Seminar
      8:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/12/2018 Hodge Seminar
      8:43 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      8:45 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      1/16/2019 Hodge Seminar
      8:46 pm
      12/01/2024

      No additional detail for this event.

    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      4/3/2019 Fluid Dynamics Seminar
      8:54 pm
      12/01/2024

      No additional detail for this event.

    • Program
      9:27 pm
      12/01/2024-12/31/2021

      The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications. This program is funded by the Simons Foundation.

      Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model).

      We envision that our goal of proving HMS in full generality can be accomplished by combining three main viewpoints:

      1. categorical algebraic geometry and non-commutative (nc) spaces: in this language, homological mirror symmetry is the statement that the same nc-spaces can arise either from algebraic geometry or from symplectic geometry.
      2. the Strominger-Yau-Zaslow (SYZ) approach, which provides a global geometric prescription for the construction of mirror pairs.
      3. Lagrangian Floer theory and family Floer cohomology, which provide a concrete path from symplectic geometry near a given Lagrangian submanifold to an open domain in a mirror analytic space.

      The Center of Mathematical Sciences and Applications is hosting the following short-term visitors for an HMS focused semester:

      • Jacob Bourjaily (Neils Bohr Institute)  4/1/2018 – 4/14/2018
      • Colin Diemer (IHES)  2/25/2018 – 3/10/2018
      • Charles Doran (University of Alberta) 5/13/2018 – 5/25/2018
      • Baohua Fu (Chinese Academy of Sciences)  4/15/2018 – 4/28/2018
      • Andrew Harder (University of Miami)  4/15/2018 – 4/28/2018
      • Shinobu Hosono (Gakushuin University) 2/25/2018 – 3/10/2018
      • Adam Jacob (UC Davis) 3/5/2018 – 3/16/2018
      • Tsung-Ju Lee (National Taiwan University) 4/18/2018 – 5/13/2018
      • Ivan Loseu (Northeastern University) 1/21/2018 – 2/3/2018
      • Cheuk-Yu Mak (Cambridge University) 4/1/2018 – 4/15/2018
      • Daniel Pomerleano (Imperial College) 3/19/2018 – 3/23/2018
      • Mauricio Romo (Tsinghua University) 4/1/2018 – 4/18/ 2018
      • Emanuel Scheidegger (Albert Ludwigs University of Freiburg) 2/22/2018 – 3/22/2018
      • Dmytro Shklyarov (Technische Universität Chemnitz) 3/4/2018 – 3/17/2018
      • Alan Thompson (University of Cambridge) 4/15/2018 – 4/21/2018
      • Weiwei Wu (University of Georgia) 4/27/2018 – 5/6/2018
      • Matt Young (Chinese University of Hong Kong) 1/15/2018 – 2/9/2018
      • Jeng-Daw Yu (National Taiwan University) 4/2/2018 – 4/6/2018
      • Minxian Zhu (Yau Mathematical Sciences Center, Tsinghua University) 1/ 22/2018 – 2/25/2018

      As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester.  Click here for information.

      The Collaboration will include two workshops hosted by The Center. The workshops will take place January 10-13, 2018  and April 5-7, 2018 at CMSA. Click here for more information.

    • Seminars
      Seminars Colloquia & Seminar
      7/13/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/27/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/8/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/16/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/22/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
      9:30 pm-10:30 pm
      12/01/2024

      Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

    • Seminars
      Seminars Colloquia & Seminar
      7/20/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Program
      9:32 pm
      12/01/2024-12/31/2021

      The methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example, the first topological states of matter discovered were the integer quantum Hall states. The two dimensional integer quantum Hall effect was characterized by an integral number which can be understood as a Chern number of the Berry phase. Chern numbers are topological invariants that play an important role in different areas of mathematics. More recently, new topological states of matter known as topological insulators and topological superconductors have been realized theoretically and experimentally. The characterization of new phases of matter using topological invariants has allowed for a better understanding and even predictions of new phases of matter. The use of topology could lead to the discovery of new electronic, photonic, and ultracold atomic states of matter previously unknown. The concrete problems in the physical phenomena could inspire new developments in the study of topological invariants in mathematics.

      Here is a list of the scholars participating in this program.

    • Program
      9:35 pm
      12/01/2024-12/31/2021

      A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as
      cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs, using tools such as random walk theory and harmonic analysis.

       

      Here is a list of the scholars participating in this program.

    • Program
      9:36 pm
      12/01/2024-12/31/2021

      In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory, general relativity, and quantum many-body theory.

      String theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as dramatic progress in old branches.

      Several examples from the recent past exemplifying this synergy include the prediction from string theory of mirror symmetry, a highly unexpected mathematical equivalence between distinct pairs of Calabi-Yau manifolds. This fueled exciting developments in algebraic, enumerative and symplectic geometry. At the same time the realization of string theory as a phenomenologically viable physical theory depends crucially on detailed mathematical properties of these manifolds. In Einstein’s theory of general relativity the proofs of the positive energy theorem and the stability of flat spacetime were accompanied by fundamental new results in functional analysis, differential geometry and minimal surface theory. In the coming decades we expect many more important discoveries to arise from the interface of mathematics and physics. The Cheng Fund will foster these efforts.

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

      NameTentative Visiting Dates
      Po-Ning Chen2/1/15-4/30/15
      Hong-Jian He3/5/15-5/5/15
      Monica Guica12/1/14-3/15/15
      Amer Iqbal1/8/15-4/8/15
      Suvrat Raju2/25/15-5/25/15
      Mithat Ünsal9/1/15-12/31/15
    • Program
      9:37 pm
      12/01/2024-12/31/2021

      Most physical phenomena, from the gravitating universe to fluid dynamics, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations.

      The subject underwent rapid developments in the last century and foundational results were established. Compared to linear equations, the difficulty of solving nonlinear equations is of a different order of magnitude and the methods employed in solving them are also much more diversified. To this date, it is an active field with recent exciting discoveries and renewed interests, and several long standing problems seem to be within reach. The special year aims to spur activity in this subject, to provide a natural setting for the most cutting edge results to be communicated, and to facilitate interaction among researchers of different backgrounds.

      During the year, there will be two weekly seminar programs.  Each program participants will be asked to give a talk on geometric analysis, or the evolution of equations, hyperbolic equations, and fluid dynamics.   

      Seminar on Geometric Analysis

      Seminar on Evolution Equations

      Seminar on General Relativity

      Concluding Conference on Nonlinear Equations Program

      Mini-School on Nonlinear Equations, Dec. 2016

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

      NameHome InstitutionTentative Visiting Dates
      Stefano BianchiniSISSA04/01/2016 – 05/31/2016
      Lydia BieriUniversity of Michigan02/01/2016 – 04/30/2016
      Albert ChauUniversity of British Columbia02/26/2016 – 05/26/2016
      Binglong ChenSun Yat-sen University09/01/2015 – 11/30/2015
      Qingtao ChenETHZ (Swiss Federal Institute of Technology in Zurich)03/17/2016 – 04/04/2016
      Piotr ChruscielUniversity of Vienna03/01/2016 – 05/30/2016
      Fernando Coda MarquesPrinceton University04/25/2016 – 04/29/2016 05/23/2016 – 05/27/2016
      Mihalis DafermosPrinceton University04/01/2016 – 04/30/2016
      Camillo De LellisUniversity of Zurich02/01/2016 – 4/30/2016
      Michael EichmairUniversity of Vienna03/21/2016 – 04/01/2016
      Felix FinsterUniversitat Regensburg09/20/2015 – 10/20/2015 03/20/2016 – 04/20/2016
      Xianfeng David GuSUNY at Stony Brook04/01/2016 – 04/30/2016
      Zheng-Cheng GuPerimeter Institute for Theoretical Physics08/15/2015 – 09/15/2015
      Pengfei GuanMcGill University10/10/2015 – 10/17/2015
      Xiaoli HanTsinghua University01/20/2016 – 04/19/2016
      Thomas HouCalifornia Institute of Technology11/01/2016 – 11/30/2016
      Feimin HuangChinese Academy of Sciences02/15/2016 – 04/15/2016
      Xiangdi HuangChinese Academy of Sciences09/10/2015 – 12/10/2015
      Tom IlmanenETH Zurich10/19/2015 – 12/18/2015
      Niky KamranMcGill Univeristy04/04/2016 – 04/08/2016
      Nicolai KrylovUniversity of Minnesota11/01/2015 – 11/30/2015
      Junbin LiSun Yat-sen University02/01/2016 – 04/30/2016
      Yong LinRenmin University of China02/01/2016 – 03/31/2016
      Andre NevesImperial College London4/25/2016 – 4/29/2016; 5/23/2016 – 5/27/2016
      Duong H. PhongColumbia University04/08/2016 – 04/10/2016
      Ovidiu SavinColumbia University10/15/2015 – 12/14/2015
      Richard SchoenStanford University03/21/2016 – 03/25/2016
      Mao ShengUniversity of Science and Technology of China01/15/2016 – 01/28/2016
      Valentino TosattiNorthwestern University02/01/2016 – 04/15/2016
      John TothMcGill University04/04/2016 – 04/08/2016
      Chung-Jun TsaiNational Taiwan University05/01/2016 – 05/08/2016
      Tai-Peng TsaiUniversity of British Columbia03/20/2016 – 05/31/2016
      Li-Sheng TsengUC Irvine02/08/2016 – 02/19/2016; 04/27/2016 – 05/11/2016
      Chun Peng WangJilin University02/01/2016 – 04/30/2016
      Xu-Jia WangAustralian National University04/01/2016 – 05/31/2016
      Ben WeinkoveNorthwestern University02/28/2016 – 03/18/2016
      Sijue WuUniversity of Michigan04/01/2016 – 04/30/2016
      Chunjing XieShanghai Jiao Tong University09/08/2015 – 12/07/2015
      Zhou Ping XinThe Chinese University of Hong Kong10/01/2015 – 11/30/2015
      Hongwei XuZhejiang University09/01/2015 – 11/30/2015
      Peng YeUniversity of Illinois at Urbana-Champaign11/15/2015 – 11/22/2015
      Pin YuTshinghua University09/07/2015 – 12/10/2015
      Yi ZhangFudan University01/18/2016 – 05/31/2016
    • Program
      9:39 pm
      12/01/2024-12/18/2014

      arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

      Here is a partial list of the mathematicians who are participating in this program

    • Program
      9:44 pm
      12/01/2024-12/28/2013

      During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

      As part of the Program, the CMSA will be hosting two workshops:

      .

      Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
      NameTentative Visiting Dates

      Jason Alicea

      11/12/2018-11/16/2018
      Maissam Barkeshli4/22/2019 – 4/26/2019
      Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

      Lukasz Fidkowski

      1/7/2019-1/11/2019

      Zhengcheng Gu

      8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

      Yin Chen He

      10/14/2018-10/27/2018
      Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

      Michael Levin

      3/11/2019-3/15/2019
      Yuan-Ming Lu4/29/2019-6/01/2019

      Adam Nahum

      4/2/2019- 4/19/2019

      Masaki Oshikawa

      4/22/2019-5/22/2019
      Chong Wang 10/22/2018-11/16/2018

      Juven Wang

      4/1/2019-4/16/2019
      Cenke Xu 8/26/2018-10/1/2018

      Yi-Zhuang You

      4/1/2019-4/19/2019

      Mike Zaletel

      5/1/2019-5/10/2019
    • Program
      9:45 pm-9:46 pm
      12/01/2024-12/31/2010

      During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

      Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

      In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

      In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

      The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

      A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

      A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    • Program
      9:48 pm
      12/01/2024-12/31/2010

      Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

      Organizers:

      .

      Workshops:

       

      Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

    • Program
      9:49 pm
      12/01/2024-12/23/2010

      The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

      A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


      Directors:


      Shing-Tung Yau (Harvard University)

      Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


      Professor Bong Lian (Brandeis University)

      BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


      Denis Auroux (Harvard University)

      AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
      Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




      Senior Personnel:

      Artan Sheshmani (Harvard CMSA)

      unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

      Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

      An Huang (Brandeis University)

      unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

      An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



      Siu Cheong Lau (Boston University)
      unnamed

      The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

      Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


      Affiliates:

      • Netanel Rubin-Blaier (Cambridge)
      • Kwokwai Chan (Chinese University of Hong Kong)
      • Mandy Cheung (Harvard University, BP)
      • Chuck Doran (University of Alberta)
      • Honsol Hong (Yonsei University)
      • Shinobu Hosono (Gakushuin University, Japan)
      • Conan Leung (Chinese University of Hong Kong)
      • Yu-shen Lin (Boston University)
      • Hossein Movassati (IMPA Brazil)
      • Arnav Tripathhy (Harvard University, BP)

       

      Postdocs:

      • Dennis Borisov
      • Tsung-Ju Lee
      • Dingxin Zhang
      • Jingyu Zhao
      • Yang Zhou

      Jobs:

      Postdoctoral Fellowship in Algebraic Geometry

      Postdoctoral Fellowship in Mathematical Sciences

       

      To learn about previous programming as part of the Simons Collaboration, click here.

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  • Quantum Matter
    12:00 am-1:30 pm
    12/01/2024-03/19/2021
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-9-2018 Math Physics Seminar

    12:00 am
    12/01/2024
  • Program
    All day
    12/01/2024-03/29/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Arithmetic Quantum Field Theory Program

    To receive email updates and program announcements, visit this link to sign up for the CMSA Arithmetic Quantum Field Theory Program mailing list.

    Dates: Feb. 5–Mar. 29, 2024

    Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138

    Directions to CMSA

    Organizers:

    This program will feature a weekly seminar series, workshops, and a conference.

    The object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions.

    On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions.

    The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions. Conversely, we will explore potential geometric and physical consequences of arithmetic ideas, for example, the Langlands correspondence theory of L-functions for 3-manifolds.


    Schedule

    The first week of the program will feature several lecture series aimed at a broad local community of mathematicians and physicists, aiming to introduce the main ideas underlying our program and help establish a common reference point.

    The program will host a weekly seminar series on Fridays.

    The speakers will be selected with the aim of covering a wide panorama of the subjects over the course of the program.

    The program will conclude with a week-long Conference on Arithmetic Quantum Field Theory March 25–29, 2024.


    AQFT Youtube Playlist

    Lecture series

    All lectures take place in Room G10, Harvard CMSA, 20 Garden Street Cambridge.

    Week 1: Feb. 5–9, 2024

    Abstract: In this lecture series we will introduce some of the themes underlying the CMSA program on Arithmetic Quantum Field Theory taking place this winter and the upcoming conference March 25-29, 2024.

    Some of the themes we plan to discuss include:

    Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.

    The setup of arithmetic topology as a bridge between the background of QFT to that of arithmetic (both “global” and “local”), including the “middle realm” of positive characteristic function fields.

    Questions and structures in arithmetic that have been / might be amenable to inspiration from QFT, in particular the theory of L-functions and the Langlands program.

    Schedule

     

    Monday, Feb. 5, 2024  
    11:00 am – 12:00 pm Minhyong KimArithmetic topology and field theory (Slides part 1 pdf)
    1:30 – 2:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
    2:30 – 3:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    Wednesday, Feb. 7, 2024  
    11:00 am – 12:00 pmMinhyong KimArithmetic topology and field theory (Slides part 2 pdf)
    2:30 – 3:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
    Thursday, Feb.8, 2024  
    2:30 – 3:30 pmMinhyong KimArithmetic topology and field theory (Slides part 3 pdf)
    4:00 – 5:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    Friday, Feb. 9, 2024  
    1:00 – 2:00 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
    2:00 – 3:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    3:30 – 4:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
    Monday, Feb. 26, 2024
    1:00 – 2:00 pmOmer Offen (Brandeis)Period integrals of automorphic forms and the residue method
    Tuesday, Feb. 27, 2024
    2:00 – 3:00 pmWei Zhang (MIT)Shtuka special cycles and their generating series
    Friday, March 1, 2024
    11:00 am – 12:00 pmChen Wan (Rutgers Newark)Some examples of the relative Langlands duality
    2:00 – 3:00 pmPeng Shan (Tsinghua)Skein algebras and quantized Coulomb branches
    Thursday, March 7, 2024
    1:30 – 2:30 pmAn Huang (Brandeis)Tate’s thesis and p-adic strings
    3:00 – 4:00 pmJohn Francis (Northwestern)Integrating braided categories over 3-manifolds
    Friday, March 8, 2024
    1:00 – 2:00 pmDihua Jiang (U Minnesota)Shalika Periods: Functoriality and Arithmetic
    Friday, March 15, 2024
    11:45 – 1:00 pmBaiying Liu (Purdue)Recent progress on certain problems related to local Arthur packets of classical groups
    2:15 – 3:30 pmTasho Kaletha (Michigan)Covers of reductive groups and functoriality
    Monday, March 18, 2024
    1:00 – 3:00 pmXinwen Zhu (Stanford)The tame categorical local Langlands correspondence (Slides)
    4:30 – 5:30 pmNatalie Paquette (U  Washington)Koszul duality & twisted holography for asymptotically flat spacetimes (CMSA)
    Wednesday, March 20, 2024
    11:00 – 12:15 pmStephen D. Miller (Rutgers)What 4-graviton scattering amplitudes had to say about the unitary dual
    Friday, March 22, 2024
    1:45 – 3:00 pmJayce Getz (Duke)The Poisson summation conjecture and the fiber bundle method
    3:30 – 4:30 pmTBATBA

     


    Program Visitors

    • Mina Aganagic, University of California, Berkeley
    • Anne-Marie Aubert, Institut de Mathématiques de Jussieu-Paris Rive Gauche, March 15-29
    • Clark Barwick, University of Edinburgh, February 19-March 15
    • Alexander Braverman, Perimeter Institute
    • Alejandra Castro, Cambridge University, March 25-29
    • YoungJu Choie, Pohang University of Science and Technology, February 12-16; March 22-28
    • John Francis, Northwestern University, March 1-14
    • David Gaiotto, Perimeter Institute, March 25-29
    • Jayce Getz, Duke University, March 18-22
    • Ezra Getzler, Northwestern University, March 11-22
    • Sam Gunningham, Montana State University, February 9-12
    • Sarah Harrison, Northeastern University
    • Dihua Jiang, University of Minnesota, February 29-March 9
    • Tasho Kaletha, University of Michigan, March 12-20
    • Minhyong Kim, University of Edinburgh, February 1-29
    • Axel Kleinschmidt, Max Planck Institute for Gravitational Physics, Potsdam, March 18-28
    • Kim Klinger-Logan, Kansas State University, March 25-29
    • Kobi Kremnitzer, Oxford University, March 25-29
    • Baiying Liu, Purdue University, March 13-16
    • Steven Miller, Rutgers University
    • Greg Moore, Rutgers University, February 5-9
    • David Nadler, University of California, Berkeley, March 17-30
    • Bảo Châu Ngô, University of Chicago, March 25-29
    • George Pappas, Michigan State University, March 25-29
    • Daniel Persson, Chalmers Institute of Technology, March 25-29
    • Sam Raskin, Yale University, March 26-29
    • Yiannis Sakellaridis, Johns Hopkins University, March 18-22
    • Peng Shan, Tsinghua University, February 12-April 14
    • Akshay Venkatesh, Institute for Advanced Study
    • Roberto Volpato, University of Padova, February 4-10
    • Chen Wan, Rutgers University, February 29-March 9
    • Fei Yan, Brookhaven National Laboratory, March 18-29
    • Xinwen Zhu, Stanford University

     

  • CMSA EVENT: Big Data Conference 2021
    All day
    12/01/2024

    On August 24, 2021, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The 2021 Big Data Conference took place virtually on Zoom.

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Time (ET; Boston time)SpeakerTitle/Abstract
    9:00AMConference OrganizersIntroduction and Welcome
    9:10AM – 9:55AMAndrew Blumberg, University of Texas at AustinTitle: Robustness and stability for multidimensional persistent homology

    Abstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However, for many data sets, it is very natural to consider multiple filtrations, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.

    10:00AM – 10:45AMKatrina Ligett, The Hebrew University of JerusalemTitle: Privacy as Stability, for Generalization

    Abstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity, via a connection to the notion of differential privacy. In this talk, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open.

    Joint work with: Christopher Jung (UPenn), Seth Neel (Harvard), Aaron Roth (UPenn), Saeed Sharifi-Malvajerdi (UPenn), and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020

    10:50AM – 11:35AMHima Lakkaraju, Harvard UniversityTitle: Towards Reliable and Robust Model Explanations

    Abstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP, and also introduce novel methods to address some of these vulnerabilities. More specifically, I will first demonstrate that these methods are brittle, unstable, and are vulnerable to a variety of adversarial attacks. Then, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.

    11:40AM – 12:25PMMoran Koren, Harvard CMSATitle: A Gatekeeper’s Conundrum

    Abstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e., ignore her private information with some probability).

    12:25PMConference OrganizersClosing Remarks
  • CMSA EVENT: Mathematics in Science: Perspectives and Prospects
    All day
    12/01/2024-10/28/2023
    1 Oxford Street, Cambridge MA 02138

    Mathematics in Science: Perspectives and Prospects

    A showcase of mathematics in interaction with physics, computer science, biology, and beyond.

    October 27–28, 2023

    Location: Harvard University Science Center Hall D & via Zoom.

    Directions and Recommended Lodging

    Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

    Youtube Playlist

     

    Speakers

    Organizers

    • Michael R. Douglas (Harvard CMSA)
    • Dan Freed (Harvard Math & CMSA)
    • Mike Hopkins (Harvard Math)
    • Cumrun Vafa (Harvard Physics)
    • Horng-Tzer Yau (Harvard Math)

    Schedule

    Friday, October 27, 2023

    2:00–3:15 pmGreg Moore (Rutgers)

    Title: Remarks on Physical Mathematics

    Abstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting, I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet, so I don’t know how it will end any more than you do.

    Slides (PDF)

    3:15–3:45 pmBreak
    3:45–5:00 pmBernd Sturmfels (MPI Leipzig)

    Title: Algebraic Varieties in Quantum Chemistry

    Abstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.

    Slides (PDF)

     

    Saturday, October 28, 2023

    9:00 amBreakfast
    9:30–10:45 amMike Freedman (Harvard CMSA)

    Title: ML, QML, and Dynamics: What mathematics can help us understand and advance machine learning?

    Abstract: Vannila deep neural nets DNN repeatedly stretch and fold. They are reminiscent of the logistic map and the Smale horseshoe.  What kind of dynamics is responsible for their expressivity and trainability. Is chaos playing a role? Is the Kolmogorov Arnold representation theorem relevant? Large language models are full of linear maps. Might we look for emergent tensor structures in these highly trained maps in analogy with emergent tensor structures at local minima of certain loss functions in high-energy physics.

    Slides (PDF)

    10:45–11:15 amBreak
    11:15 am–12:30 pm
    via Zoom
    Nima Arkani-Hamed (IAS)

    Title: All-Loop Scattering as A Counting Problem

    Abstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model, the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

    12:30–2:00 pmLunch break
    2:00–3:15 pmConstantinos Daskalakis (MIT)

    Title: How to train deep neural nets to think strategically

    Abstract: Many outstanding challenges in Deep Learning lie at its interface with Game Theory: from playing difficult games like Go to robustifying classifiers against adversarial attacks, training deep generative models, and training DNN-based models to interact with each other and with humans. In these applications, the utilities that the agents aim to optimize are non-concave in the parameters of the underlying DNNs; as a result, Nash equilibria fail to exist, and standard equilibrium analysis is inapplicable. So how can one train DNNs to be strategic? What is even the goal of the training? We shed light on these challenges through a combination of learning-theoretic, complexity-theoretic, game-theoretic and topological techniques, presenting obstacles and opportunities for Deep Learning and Game Theory going forward.

    Slides (PDF)

    3:15–3:45 pmBreak
    3:45–5:00 pmAlison Etheridge (Oxford)

    Title: Modelling hybrid zones

    Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection, spatial structure, and, if time permits, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection.

    Slides (PDF)

     


    Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to mathsci2023@cmsa.fas.harvard.edu no later than October 9, 2023.

    Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV.

     

  • Holiday
    All day
    12/01/2024

    Holiday: Friday after Thanksgiving

    The CMSA will be closed on Friday, November 25, 2022.

  • Seminars

    Seminars Colloquia & Seminar
    1/27/2020 Math Physics Seminar

    12:00 am-1:00 pm
    12/01/2024
  • CMSA EVENT: Quantum Matter Workshop
    All day
    12/01/2024
    Layer-2-600x338

    Please note: this workshop has been postponed to a later date. Details will be posted to this page when they are available.

    Throughout the summer, scheduled speakers for the Quantum Matter Workshop will give talks on Zoom for the Quantum Matter/Condensed Matter seminar.

    The CMSA will be hosting our second workshop on Quantum Matter. Both of these workshops are part of our program on Quantum Matter in Mathematics and Physics. The first workshop took place in December 2019, and was extremely successful, attracting participants worldwide. Learn more about the first workshop here.

     

    Organizers: Du Pei, Ryan Thorngren, Juven Wang, Yifan Wang, and Shing-Tung Yau.

    Speakers:

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-16-2018 Mathematical Physics Seminar

    12:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/7/2018 Hodge Seminar

    1:30 am-3:00 pm
    12/01/2024
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Some remarks on contact Calabi-Yau 7-manifolds

    3:00 am-4:00 am
    12/01/2024

    Abstract: In geometry and physics it has proved useful to relate G2 and Calabi-Yau geometry via circle bundles. Contact Calabi-Yau 7-manifolds are, in the simplest cases, such circle bundles over Calabi-Yau 3-orbifolds. These 7-manifolds provide testing grounds for the study of geometric flows which seek to find torsion-free G2-structures (and thus Ricci flat metrics with exceptional holonomy). They also give useful backgrounds to examine the heterotic G2 system (also known as the G2-Hull-Strominger system), which is a coupled set of PDEs arising from physics that involves the G2-structure and gauge theory on the 7-manifold. I will report on recent progress on both of these directions in the study of contact Calabi-Yau 7-manifolds, which is joint work with H. Sá Earp and J. Saavedra.

  • Colloquium
    5:00 am
    12/01/2024

    No additional detail for this event.

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Arthur Jaffe (Harvard University)

    Title: Is relativity compatible with quantum theory?

    Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.”  Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed.

    Talk chair: Zhengwei Liu

    Video

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Edward Witten (IAS)

    Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions

    Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification.

    Talk chair: Cliff Taubes

    Video

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Nigel Hitchin (University of Oxford)

    Title: Michael Atiyah: Geometry and Physics

    Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists.

    Talk chair: Peter Kronheimer

    Video

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Alain Connes (Collège de France)

    Title: Noncommutative Geometry, the Spectral Aspect

    Abstract: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function.

    Talk chair: Peter Kronheimer

    Video 

  • CMSA EVENT: Workshop on Quantum Information
    8:00 am-6:07 pm
    12/01/2024-04/24/2017
    banner-image-1

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 23-24, 2018. In the days leading up to the conference, the American Mathematical Society will also be hosting a sectional meeting on quantum information on April 21-22. You can find more information here.

    Register for the event here.

    The following speakers are confirmed:

  • Math Science Literature Lecture Series
    8:00 am-9:00 am
    12/01/2024
    Lecture-Series-Don-pdf

    Donald Rubin (Harvard)

    Title: Why do some universities have separate departments of statistics? And are they all anachronisms, destined to follow the path of other dinosaurs?

    Video | Slides

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Yuri Manin (Max Planck Institute for Mathematics)

    Title: Homotopy spectra and Diophantine equations

    Abstract: For a long stretch of time in the history of mathematics, Number Theory and Topology formed vast, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC)  that contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory, named after Diophantus of Alexandria (about 250 BC). Topology was born much later, but arguably, its cousin — modern measure theory, — goes back to Archimedes, author of Psammites (“Sand Reckoner”), who was approximately a contemporary of Diophantus. In modern language, Archimedes measures the volume of observable universe by counting the number of small grains of sand necessary to fill this volume. Of course, many qualitative geometric models and quantitative estimates of the relevant distances precede his calculations. Moreover, since the estimated numbers of grains of sand are quite large (about $10^{64}$), Archimedes had to invent and describe a system of notation for large numbers going far outside the possibilities of any of the standard ancient systems. The construction of the first bridge between number theory and topology was accomplished only about fifty years ago: it is the theory of spectra in stable homotopy theory. In particular, it connects $Z$, the initial object in the theory of commutative rings, with the sphere spectrum $S$. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this talk based upon the authors’ (Yu. Manin and M. Marcolli) joint research project, I suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.

    Talk chair: Michael Hopkins

    Slides | Video

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrations

    8:00 am-9:30 am
    12/01/2024

    Caucher Birkar (University of Cambridge)

    Title: Log Calabi-Yau fibrations

    Abstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry, differential geometry, arithmetic geometry, mathematical physics, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties, their fibrations, as well as their local birational counterparts such as flips and singularities. Such fibrations can be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations, to remind some known results, and to state some open problems.

    Video

     

  • Special Seminar
    8:00 am-9:00 am
    12/01/2024
    Gromov-Witten

    During the Spring 2021 Semester Artan Sheshmani (CMSA/ I.M. A.U.) will be teaching a CMSA special lecture series on Gromov-Witten/Donaldson Thomas theory and Birational/Symplectic invariants for algebraic surfaces.

    In order to attend this series, please fill out this form.

    The lectures will be held Mondays from 8:00 – 9:30 AM ET and Wednesdays from 8:00 – 9:00 AM ET beginning January 25 on Zoom.

    You can watch Prof. Sheshmani describe the series here. 

  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Andrei Okounkov (Columbia University)

    Title: Classical and quantum integrable systems in enumerative geometry

    Abstract: For more than a quarter of a century, thanks to the ideas and questions originating in modern high-energy physics, there has been a very fruitful interplay between enumerative geometry and integrable system, both classical and quantum. While it is impossible to summarize even the most important aspects of this interplay in one talk, I will try to highlight a few logical points with the goal to explain the place and the role of certain more recent developments.

    Talk chair: Cumrun Vafa

    Video

  • Quantum Matter
    8:00 am-9:30 am
    12/01/2024
  • Math Science Literature Lecture Series
    8:00 am-9:30 am
    12/01/2024

    Yujiro Kawamata (University of Tokyo)

    Title: Kunihiko Kodaira and complex manifolds

    Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions.  After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces.  Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts.

    Talk chair: Baohua Fu

    Video 

  • CMSA EVENT: Geometric Analysis Approach to AI Workshop
    8:30 am-5:30 pm
    12/01/2024-01/21/2019
    Geo-Analysis-Poster-final-e1547584167900

    Geo-Analysis-1-e1543848888343

    Due to inclement weather on Sunday, the second half of the workshop has been moved forward one day. Sunday and Monday’s talks will now take place on Monday and Tuesday.

    On January 18-21, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI.

    This workshop will focus on the theoretic foundations of AI, especially various methods in Deep Learning. The topics will cover the relationship between deep learning and optimal transportation theory, DL and information geometry, DL Learning and information bottle neck and renormalization theory, DL and manifold embedding and so on. Furthermore, the recent advancements, novel methods, and real world applications of Deep Learning will also be reported and discussed.

    The workshop will take place from January 18th to January 23rd, 2019. In the first four days, from January 18th to January 21, the speakers will give short courses; On the 22nd and 23rd, the speakers will give conference representations. This workshop is organized by Xianfeng Gu and Shing-Tung Yau.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please register here

    Speakers: 

  • CMSA EVENT: Big Data Conference 2018
    8:30 am-2:50 pm
    12/01/2024-08/24/2018
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2018-1

     

    shutterstock_547250785-e1527881194717

    On August 23-24, 2018 the CMSA will be hosting our fourth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The talks will take place in Science Center Hall B, 1 Oxford Street.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

    Please register here. 

    Confirmed Speakers: 

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
    • Jun Liu, Professor of Statistics, Harvard University
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
  • CMSA EVENT: 2019 Big Data Conference
    8:30 am-4:40 pm
    12/01/2024-08/20/2019
    1 Oxford Street, Cambridge MA 02138
    Big-Data-2019-Poster-5-2

    shutterstock_547250785-e1527881194717

    On August 19-20, 2019 the CMSA will be hosting our fifth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The talks will take place in Science Center Hall D, 1 Oxford Street.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

    Videos can be found in this Youtube playlist or in the schedule below.

  • CMSA EVENT: Workshop on Aspects of General Relativity
    8:30 am-3:30 pm
    12/01/2024-05/26/2017

    The Center of Mathematical Sciences and Applications will be hosting a workshop on General Relativity from May 23 – 24, 2016. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138The workshop will start on Monday, May 23 at 9am and end on Tuesday, May 24 at 4pm.

    Speakers:

    1. Po-Ning Chen, Columbia University
    2. Piotr T. Chruściel, University of Vienna
    3. Justin Corvino, Lafayette College
    4. Greg Galloway, University of Miami
    5. James Guillochon, Harvard University
    6. Lan-Hsuan Huang, University of Connecticut
    7. Dan Kapec, Harvard University
    8. Dan Lee, CUNY
    9. Alex Lupsasca, Harvard University
    10. Pengzi Miao, University of Miami
    11. Prahar Mitra, Harvard University
    12. Lorenzo Sironi, Harvard University
    13. Jared Speck, MIT
    14. Mu-Tao Wang, Columbia University

    Please click Workshop Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Please click here for registration – Registration is capped at 70 participants.

    Schedule:

    May 23 – Day 1
    8:30amBreakfast
    8:55amOpening remarks
    9:00am – 9:45amGreg Galloway, “Some remarks on photon spheres and their uniqueness
    9:45am – 10:30amPrahar Mitra, “BMS supertranslations and Weinberg’s soft graviton theorem
    10:30am – 11:00amBreak
    11:00am – 11:45amDan Kapec, “Area, Entanglement Entropy and Supertranslations at Null Infinity
    11:45am – 12:30pmPiotr T. Chruściel, “The cosmological constant and the energy of gravitational radiation”
    12:30pm – 2:00pmLunch
    2:00pm – 2:45pmJames Guillochon, “Tidal disruptions of stars by supermassive black holes: dynamics, light, and relics”
    2:45pm – 3:30pmMu-Tao Wang, “Quasi local conserved quantities in general relativity
    3:30pm – 4:00pmBreak
    4:00pm – 4:45pmPo-Ning Chen, “Quasi local energy in presence of gravitational radiations
    4:45pm – 5:30pmPengzi Miao, “Total mean curvature, scalar curvature, and a variational analog of Brown York mass
    May 24 – Day 2
    8:45amBreakfast
    9:00am – 9:45amJustin Corvino, “Scalar curvature deformation and the Bartnik mass
    9:45am – 10:30amLan-Hsuan Huang, “Constraint Manifolds with the Dominant Energy Condition
    10:30am – 11:00amBreak
    11:00am – 11:45amDan Lee, “Lower semicontinuity of Huisken’s isoperimetric mass
    11:45am – 12:30pmJared Speck, “Shock Formation in Solutions to the Compressible Euler Equations
    12:30pm – 2:00pmLunch
    2:00pm – 2:45pmLorenzo Sironi, “Electron Heating and Acceleration in the Vicinity of Supermassive Black Holes
    2:45pm – 3:30pmAlex Lupsasca, “Near Horizon Extreme Kerr Magnetospheres
    * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Workshop on Aspects on General Relativity“.
    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    Organizers: Piotr T. Chruściel and Shing-Tung Yau

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Angular momentum in general relativity

    8:30 am-9:30 am
    12/01/2024

    Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

  • CMSA EVENT: F-Theory Conference
    8:30 am-3:00 pm
    12/01/2024-09/30/2018

    The CMSA will be hosting an F-Theory workshop September 29-30, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. 

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Click here for videos of the talks. 

    Organizers:

    Speakers:

  • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
    8:30 am-2:00 pm
    12/01/2024-10/24/2018

    In Fall 2018, the CMSA will host a Program on Mathematical Biology, which aims to describe recent mathematical advances in using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.

    The plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale, the   shapes seen in a garden at the scale of a pollen grain, a seed, a sapling, a root, a flower or leaf are so numerous that “it is enough to drive the sanest man mad,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively?

    In biology, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists, to understand how polymeric assemblies grow and shrink (in the cytoskeleton), and how cells divide, change size and shape, and move to organize tissues, change their topology and geometry, and link multiple scales and connect biochemical to mechanical aspects of these problems, all in a self-regulated setting.

    To understand these questions, we need to describe shape (biomathematics), predict shape (biophysics), and design shape (bioengineering).

    For example, in mathematics there are some beautiful links to Nash’s embedding theorem,  connections to quasi-conformal geometry, Ricci flows and geometric PDE, to Gromov’s h principle, to geometrical singularities and singular geometries, discrete and computational differential geometry, to stochastic geometry and shape characterization (a la Grenander, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor, Adler) to look for similarities and differences across species during development, and across evolution.

    In physics, there are questions of generalizing classical theories to include activity, break the usual Galilean invariance, as well as isotropy, frame indifference, homogeneity, and create both agent (cell)-based and continuum theories for ordered, active machines, linking statistical to continuum mechanics, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals, polar materials, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied.

    The CMSA will be hosting a Workshop on Morphometrics, Morphogenesis and Mathematics from October 22-24 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Videos of the talks

    Confirmed Speakers:

  • CMSA EVENT: Workshop on Foundations of Computational Science
    8:30 am-2:45 pm
    12/01/2024-08/31/2019
    AI-Poster-3

    On August 29-31, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on Foundations of Computational Science. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA This workshop is organized by David Xianfeng Gu.

    Please register here. 

    Speakers:

    Videos of the talks are contained in the Youtube playlist below. They can also be found through links in the schedule.

  • Quantum Matter
    8:30 am-10:00 am
    12/01/2024
  • CMSA EVENT: Morphogenesis: Geometry and Physics
    8:30 am-2:30 pm
    12/01/2024-12/05/2018

    Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book – a literary masterpiece – is a visionary synthesis of the geometric biology of form. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. So, how far are we from realizing the century-old vision that “Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed” ?

    To address this requires an appreciation of the enormous ‘morphospace’ in terms of the potential shapes and sizes that living forms take, using the language of mathematics. In parallel, we need to consider the biological processes that determine form in mathematical terms is based on understanding how instabilities and patterns in physical systems might be harnessed by evolution.

    In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.
    The first workshop will focus on the interface between Morphometrics and Mathematics, while the second will focus on the interface between Morphogenesis and Physics.The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

    As part of the program on Mathematical Biology a workshop on Morphogenesis: Geometry and Physics will take place on December 3-5, 2018.  The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Videos

    Please Register Here

    PDF of the Schedule

    Speakers:

  • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
    8:30 am-5:20 pm
    12/01/2024-08/20/2018
    Mumford-3

    David_Mumford-1

    On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center, Hall B.

     Saturday, August 18th:  A day of talks on Vision, AI and brain sciences
    Monday, August 20th: a day of talks on Math

    Speakers:

    Organizers:

     

    Publication:

    Pure and Applied Mathematics Quarterly

    Special Issue: In Honor of David Mumford

    Guest Editors: Ching-Li Chai, Amnon Neeman

     

  • Member Seminar
    8:45 am-10:15 am
    12/01/2024

    Speaker: Jörn Boehnke

    Title: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning

    Abstract:  In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.

  • CMSA EVENT: 2015 Conference on Big Data
    8:45 am-4:00 pm
    12/01/2024-10/26/2015
    1 Oxford Street, Cambridge MA 02138

    The Center of Mathematical Sciences and Applications will be having a conference on Big Data August 24-26, 2015, in Science Center Hall B at Harvard University.  This conference will feature many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    For more info, please contact Sarah LaBauve at slabauve@math.harvard.edu.

     

    Registration for the conference is now closed.

    Please click here for a downloadable version of this schedule.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found here.

    Monday, August 24

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amSendhil MullainathanPrediction Problems in Social Science: Applications of Machine Learning to Policy and Behavioral Economics
    9:45amMike LucaDesigning Disclosure for the Digital Age
    10:30Break
    10:45Jianqing FanBig Data Big Assumption: Spurious discoveries and endogeneity
    11:30amDaniel GoroffPrivacy and Reproducibility in Data Science
    12:15pmBreak for Lunch
    2:00pmRyan AdamsExact Markov Chain Monte Carlo with Large Data
    2:45pmDavid DunsonScalable Bayes: Simple algorithms with guarantees
    3:30pmBreak
    3:45pmMichael JordanComputational thinking, inferential thinking and Big Data
    4:30pmJoel TroppApplied Random Matrix Theory
    5:15pmDavid WoodruffInput Sparsity and Hardness for Robust Subspace Approximation

    Tuesday, August 25

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amGunnar CarlssonPersistent homology for qualitative analysis and feature generation
    9:45amAndrea MontanariSemidefinite Programming Relaxations for Graph and Matrix Estimation: Algorithms and Phase Transitions
    10:30amBreak
    10:45amSusan AtheyMachine Learning and Causal Inference for Policy Evaluation
    11:30amDenis NekipelovRobust Empirical Evaluation of Large Competitive Markets
    12:15pmBreak for Lunch
    2:00pmLucy ColwellUsing evolutionary sequence variation to make inferences about protein structure and function: Modeling with Random Matrix Theory
    2:45pmSimona CoccoInverse Statistical Physics approaches for the modeling of protein families
    3:30pmBreak
    3:45pmRemi MonassonInference of top components of correlation matrices with prior informations
    4:30pmSayan MukherjeeRandom walks on simplicial complexes and higher order notions of spectral clustering

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    A Banquet from 7:00 – 8:30pm will follow Tuesday’s talks. This event is by invitation only.

     Wednesday, August 26 

    TimeSpeakerTitle
    8:45amMeet and Greet
    9:00amAnkur MoitraBeyond Matrix Completion
    9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
    10:30amBreak
    10:45amPiotr IndykFast Algorithms for Structured Sparsity
    11:30amGuido ImbensExact p-values for network inference
    12:15pmBreak for lunch
    2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
    2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
    3:30pmBreak
    3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
    4:30pmJelani NelsonDimensionality reductions via sparse matrices
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024
    Lecture_Fukaya-pdf

    Kenji Fukaya (Simons Center for Geometry and Physics)

    Title: Homological (homotopical) algebra and moduli spaces in Topological Field theories

    Abstract: Moduli spaces of various gauge theory equations and of various versions of (pseudo) holomorphic curve equations have played important role in geometry in these 40 years. Started with Floer’s work people start to obtain more sophisticated object such as groups, rings, or categories from (system of) moduli spaces. I would like to survey some of those works and the methods to study family of moduli spaces systematically.

    Talk chair: Peter Kronheimer

    Slides | Video

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Don Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics)

    Title: Quantum topology and new types of modularity

    Abstract: The talk concerns two fundamental themes of modern 3-dimensional topology and their unexpected connection with a theme coming from number theory. A deep insight of William Thurston in the mid-1970s is that the vast majority of complements of knots in the 3-sphere, or more generally of 3-manifolds, have a unique metric structure as hyperbolic manifolds of constant curvature -1, so that 3-dimensional topology is in some sense not really a branch of topology at all, but of differential geometry. In a different direction, the work of Vaughan Jones and Ed Witten in the late 1980s gave rise to the field of Quantum Topology, in which new types of invariants of knot complements and 3-manifolds are introduced that have their origins in ideas coming from quantum field theory. These two themes then became linked by Kashaev’s famous Volume Conjecture, now some 25 years old, which says that the Kashaev invariant _N of a hyperbolic knot K (this is a quantum invariant defined for each positive integer N and whose values are algebraic numbers) grows exponentially as N tends to infinity with an exponent proportional to the hyperbolic volume of the knot complement. About 10 years ago, I was led by numerical experiments to the discovery that Kashaev’s invariant could be upgraded to an invariant having rational numbers as its argument (with the original invariant being the value at 1/N) and that the Volume Conjecture then became part of a bigger story saying that the new invariant has some sort of strange transformation property under the action x -> (ax+b)/(cx+d) of the modular group SL(2,Z) on the argument. This turned out to be only the beginning of a fascinating and multi-faceted story relating quantum invariants, q-series, modularity, and many other topics. In the talk, which is intended for a general mathematical audience, I would like to recount some parts of this story, which is joint work with Stavros Garoufalidis (and of course involving contributions from many other authors). The “new types of modularity” in the title refer to a specific byproduct of these investigations, namely that there is a generalization of the classical notion of holomorphic modular form – which plays an absolutely central role in modern number theory – to a new class of holomorphic functions in the upper half-plane that no longer satisfy a transformation law under the action of the modular group, but a weaker extendability property instead. This new class, called “holomorphic quantum modular forms”, turns out to contain many other functions of a more number-theoretical nature as well as the original examples coming from quantum invariants.

    Talk chair: Mark Kisin

    Video

  • Combinatorics Physics and Probability
    9:00 am-10:00 am
    12/01/2024

    Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Liang Kong (Sustech)

    Title: Topological Wick Rotation and Holographic duality

    Abstract: I will explain a new type of holographic dualities between
    n+1D topological orders with a chosen boundary condition and nD
    (potentially gapless) quantum liquids. It is based on the idea of
    topological Wick rotation, a notion which was first used in
    arXiv:1705.01087 and was named, emphasized and generalized later in
    arXiv:1905.04924. Examples of these holographic dualities include the
    duality between 2+1D toric code model and 1+1D Ising chain and its
    finite-group generalizations (independently discovered by many
    others); those between 2+1D topological orders and 1+1D rational
    conformal field theories; and those between n+1D finite gauge theories
    with a gapped boundary and nD gapped quantum liquids. I will also
    briefly discuss some generalizations of this holographic duality and
    its relation to AdS/CFT duality.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: João Caetano (CERN)

    Title: Unorientable Quantum Field Theories: From crosscaps to holography

    Abstract: In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state.

    In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4-manifold. I will show how to do this in the example of N=4 Supersymmetric Yang-Mills, discuss its holographic description and present a new solvable setup of AdS/CFT.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Michele Del Zotto (Uppsala University)

    Title: On the six-dimensional origin of non-invertible symmetries

    Abstract: I will present a review about recent progress in charting non-invertible symmetries for four-dimensional quantum field theories that have a six-dimensional origin. These include in particular N=4 supersymmetric Yang-Mills theories, and also a large class of N=2 supersymmetric theories which are conformal and do not have a conventional Lagrangian description (the so-called theories of “class S”). Among the main results, I will explain criteria for identifying examples of systems with intrinsic and non-intrinsic non-invertible symmetries, as well as explore their higher dimensional origin. This seminar is based on joint works with Vladimir Bashmakov, Azeem Hasan, and Justin Kaidi.

     

    https://www.youtube.com/watch?v=0Tscbn9RhF8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=31

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 11.2.22

    Topological Quantum Matter Seminar

    Speaker: Junyeong Ahn (Harvard)

    Title: Optical axion electrodynamics

    Abstract: Electromagnetic fields in a magneto-electric medium behave in close analogy to photons coupled to the hypothetical elementary particle, the axion. This emergent axion electrodynamics is expected to provide novel ways to detect and control material properties with electromagnetic fields. Despite having been studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Formulating axion electrodynamics at general optical frequencies requires resolving the difficulty of calculating optical magneto-electric coupling in periodic systems and demands a proper generalization of the axion field. In this talk, I will introduce a theory of optical axion electrodynamics that allows for a simple quantitative analysis. Then, I will move on to discuss the issue of the Kerr effect in axion antiferromagnets, refuting the conventional wisdom that the Kerr effect is a measure of the net magnetic moment. Finally, I will apply our theory to a topological antiferromagnet MnBi2Te4.

    References:
    [1] Theory of Optical Axion Electrodynamics, J. Ahn, S.Y. Xu, A.Vishwanath, arXiv:2205.06843

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Ethan Lake (MIT)

    Title: Insulating BECs and other surprises in dipole-conserving systems

    Abstract: I will discuss recent work on bosonic models whose dynamics conserves both total charge and total dipole moment, a situation which can be engineered in strongly tilted optical lattices. Related models have received significant attention recently for their interesting out-of-equilibrium dynamics, but analytic and numeric studies reveal that they also possess rather unusual ground states. I will focus in particular on a dipole-conserving variant of the Bose-Hubbard model, which realizes an unusual phase of matter that possesses a Bose-Einstein condensate, but which is nevertheless insulating, and has zero superfluid weight. Time permitting, I will also describe the physics of a regime in which these models spontaneously fracture into an exotic type of glassy state.

     

    https://www.youtube.com/watch?v=Nad45apS8TE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=29

  • Quantum Matter
    9:00 am-4:00 pm
    12/01/2024
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Daniel A. Spielman

    Dan Spielman (Yale University)

    Title: Discrepancy Theory and Randomized Controlled Trials

    Abstract: Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other.  By “surprisingly similar” we mean much more similar than a random partition. I will begin by surveying fundamental results in discrepancy theory, including Spencer’s famous existence proofs and Bansal’s recent algorithmic realizations of them. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar.  When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we know information about the experimental subjects, called covariates, we can combine the strengths of randomization with the promises of discrepancy theory. This should allow us to obtain more accurate estimates of the effectiveness of treatments, or to conduct trials with fewer experimental subjects. I will introduce the Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, which produces random solutions to discrepancy problems. I will then explain how Chris Harshaw, Fredrik Sävje, Peng Zhang, and I use this algorithm to improve the design of randomized controlled trials. Our Gram-Schmidt Walk Designs have increased accuracy when the experimental outcomes are correlated with linear functions of the covariates, and are comparable to uniform random assignments in the worst case.

    Talk chair: Salil Vadhan

    Video

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 10.26.22

    Topological Quantum Matter Seminar

    Speaker: Bruno Mera, Tohoku University
    Title: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
    Abstract: The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect, certain geometric constraints, associated with the holomorphic character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.
    References:
    [1] Tomoki Ozawa and Bruno Mera. Relations between topology and the quantum metric for Chern insulators. Phys. Rev. B, 104:045103, Jul 2021.
    [2] Bruno Mera and Tomoki Ozawa. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Phys. Rev. B, 104:045104, Jul 2021.
    [3] Bruno Mera and Tomoki Ozawa. Engineering geometrically flat Chern bands with Fubini-Study  Kähler structure. Phys. Rev. B, 104:115160, Sep 2021.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Francisco Machado  (Berkeley/Harvard)

    Title: Kardar-Parisi-Zhang dynamics in integrable quantum magnets

    Abstract: Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.

    In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.

    Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.

    [1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
    B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
    (PRL in press) – arXiv:2205.02853

    [2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
    D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
    Science (2022) — arXiv:2107.00038

     

    https://www.youtube.com/watch?v=65DjgbX30FU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=27

  • Math Science Literature Lecture Series
    9:00 am-12:13 pm
    12/01/2024

    Harry Shum (Tsinghua University)

    Title: From Deep Learning to Deep Understanding

    Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model,  and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike GPT or similar language models learnt from data, it is a multi-turn decision making system which takes user input, updates the belief state, retrieved from the database via symbolic reasoning, and decides how to complete the task with grounded response.

    Talk chair: Shing-Tung Yau

    Video

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    10/12/2021 Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    Title: On counting algebraically defined graphs

    Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

  • Program
    9:00 am-5:00 pm
    12/01/2024-05/13/2022

    Please visit the Swampland Initiative for current events.

    The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.

     


    During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”

    The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology,  which has led to a great deal of activity in the field in the last few years.

    The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.

    This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.

    Seminars

    Swampland Seminar Series & Group Meetings

    Program Visitors

    • Pieter Bomans, Princeton, 10/30/21 – 11/02/21
    • Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
    • Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
    • Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
    • Timo Weigand, 03/21/22 – 03/28/22
    • Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
    • Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
    • Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
    • Sergio Cecotti, 05/08/22 – 05/21/22
    • Tom Rudelius, 05/09/22 – 05/13/22

    https://sites.harvard.edu/swampland-initiative/

  • Math Science Literature Lecture Series
    9:00 am-9:06 am
    12/01/2024

    Claire Voisin (Collège de France)

    Title: Hodge structures and the topology of algebraic varieties

    Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results  we will discuss  rely on Hodge theory, which  has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization,  is missing in the general Kaehler context. We will also discuss some results and problems related to algebraic cycles and motives.

    Talk chair: Joe Harris

    Video | Slides | Article

  • Conference
    9:00 am-5:30 pm
    12/01/2024-03/01/2023
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Poster_GeometryStatistics_8.5x11.final

    On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

    Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

    This conference will be held in person. Directions and Recommended Lodging

    Registration is required.

    Register here to attend in-person.

    Organizing Committee:
    Stephan Huckemann (Georg-August-Universität Göttingen)
    Ezra Miller (Duke University)
    Zhigang Yao (Harvard CMSA and Committee Chair)

    Scientific Advisors:
    Horng-Tzer Yau (Harvard CMSA)
    Shing-Tung Yau (Harvard CMSA)

    Speakers:

    • Tamara Broderick (MIT)
    • David Donoho (Stanford)
    • Ian Dryden (Florida International University in Miami)
    • David Dunson (Duke)
    • Charles Fefferman (Princeton)
    • Stefanie Jegelka (MIT)
    • Sebastian Kurtek (OSU)
    • Lizhen Lin (Notre Dame)
    • Steve Marron (U North Carolina)
    • Ezra Miller (Duke)
    • Hans-Georg Mueller (UC Davis)
    • Nicolai Reshetikhin (UC Berkeley)
    • Wolfgang Polonik (UC Davis)
    • Amit Singer (Princeton)
    • Zhigang Yao (Harvard CMSA)
    • Bin Yu (Berkeley)

    Moderator: Michael Simkin (Harvard CMSA)

     

    SCHEDULE

    Monday, Feb. 27, 2023 (Eastern Time)

    8:30 amBreakfast
    8:45–8:55 amZhigang YaoWelcome Remarks
    8:55–9:00 amShing-Tung Yau*Remarks
    Morning Session Chair: Zhigang Yao
    9:00–10:00 amDavid DonohoTitle: ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise

    Abstract: Truncation of the singular value decomposition is a true scientific workhorse. But where to Truncate?

    For 55 years the answer, for many scientists, has been to eyeball the scree plot, an approach which still generates hundreds of papers per year.

    I will describe ScreeNOT, a mathematically solid alternative deriving from the many advances in Random Matrix Theory over those 55 years. Assuming a model of low-rank signal plus possibly correlated noise, and adopting an asymptotic viewpoint with number of rows proportional to the number of columns, we show that ScreeNOT has a surprising oracle property.

    It typically achieves exactly, in large finite samples, the lowest possible MSE for matrix recovery, on each given problem instance – i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure.

    The talk is based on joint work with Matan Gavish and Elad Romanov, Hebrew University.

    10:00–10:10 amBreak
    10:10–11:10 amSteve MarronTitle: Modes of Variation in Non-Euclidean Spaces

    Abstract: Modes of Variation provide an intuitive means of understanding variation in populations, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts, including shapes as data objects, vectors of directional data, amplitude and phase variation and compositional data.

    11:10–11:20 amBreak
    11:20 am–12:20 pmZhigang YaoTitle: Manifold fitting: an invitation to statistics

    Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference:https://arxiv.org/abs/1909.10228

     12:20–1:50 pm12:20 pm Group Photo

    followed by Lunch

    Afternoon Session Chair: Stephan Huckemann
    1:50–2:50 pmBin Yu*Title: Interpreting Deep Neural Networks towards Trustworthiness

    Abstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.

    2:50–3:00 pmBreak
    3:00-4:00 pmHans-Georg MuellerTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression

    Abstract: Random objects, i.e., random variables that take values in a separable metric space, pose many challenges for statistical analysis, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions, covariance matrices or surfaces, graph Laplacians to represent networks, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics, an emerging collection of statistical tools to characterize, infer and relate samples of random objects. Recent developments include depth profiles, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey, Y. Chen 2022).

    These distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.

    4:00-4:10 pmBreak
    4:10-5:10 pmStefanie JegelkaTitle: Some benefits of machine learning with invariances

    Abstract: In many applications, especially in the sciences, data and tasks have known invariances. Encoding such invariances directly into a machine learning model can improve learning outcomes, while it also poses challenges on efficient model design. In the first part of the talk, we will focus on the invariances relevant to eigenvectors and eigenspaces being inputs to a neural network. Such inputs are important, for instance, for graph representation learning. We will discuss targeted architectures that can universally express functions with the relevant invariances – sign flips and changes of basis – and their theoretical and empirical benefits.

    Second, we will take a broader, theoretical perspective. Empirically, it is known that encoding invariances into the machine learning model can reduce sample complexity. For the simplified setting of kernel ridge regression or random features, we will discuss new bounds that illustrate two ways in which invariances can reduce sample complexity. Our results hold for learning on manifolds and for invariances to (almost) any group action, and use tools from differential geometry.

    This is joint work with Derek Lim, Joshua Robinson, Behrooz Tahmasebi, Lingxiao Zhao, Tess Smidt, Suvrit Sra, and Haggai Maron.

     

     

     

    Tuesday, Feb. 28, 2023 (Eastern Time)

    8:30-9:00 amBreakfast
    Morning Session Chair: Zhigang Yao
    9:00-10:00 amCharles Fefferman*Title: Lipschitz Selection on Metric Spaces

    Abstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.

    10:00-10:10 amBreak
    10:10-11:10 amDavid DunsonTitle: Inferring manifolds from noisy data using Gaussian processes

    Abstract: In analyzing complex datasets, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm, we provide simulated and real data examples to illustrate the performance. Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478

    11:10-11:20 amBreak
    11:20 am-12:20 pmWolfgang PolonikTitle: Inference in topological data analysis

    Abstract: Topological data analysis has seen a huge increase in popularity finding applications in numerous scientific fields. This motivates the importance of developing a deeper understanding of benefits and limitations of such methods. Using this angle, we will present and discuss some recent results on large sample inference in topological data analysis, including bootstrap for Betti numbers and the Euler characteristics process.

    12:20–1:50 pmLunch
    Afternoon Session Chair: Stephan Huckemann
    1:50-2:50 pmEzra MillerTitle: Geometric central limit theorems on non-smooth spaces

    Abstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data, such as angles or phylogenetic trees, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures, correct analogues of Gaussian random variables, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers, starting with a review of the usual linear CLT and its generalization to smooth manifolds, viewed through a lens that casts the singular CLT as a natural outgrowth, and concluding with how this investigation opens gateways to further advances in geometric probability, topology, and statistics. Joint work with Jonathan Mattingly and Do Tran.

    2:50-3:00 pmBreak
    3:00-4:00 pmLizhen LinTitle: Statistical foundations of deep generative models

    Abstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in empirical performance, theoretical understanding of such models is largely lacking. We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates, and ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session

     

     

     

    Wednesday, March 1, 2023 (Eastern Time)

    8:30-9:00 amBreakfast
    Morning Session Chair: Ezra Miller
    9:00-10:00 amAmit Singer*Title: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning

    Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.

    10:00-10:10 amBreak
    10:10-11:10 amIan DrydenTitle: Statistical shape analysis of molecule data

    Abstract: Molecular shape data arise in many applications, for example high dimension low sample size cryo-electron microscopy (cryo-EM) data and large temporal sequences of peptides from molecular dynamics simulations. In both applications it is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D sub-shape spaces and provide some practical fitting algorithms. The methodology is applied to cryo-EM data of a large sliding clamp multi-protein complex and to cluster analysis of peptides, where different states of the molecules can be identified. Further molecular modeling tasks include resolution matching, where coarse resolution models are back-mapped into high resolution (atomistic) structures. This is joint work with Kwang-Rae Kim, Charles Laughton and Huiling Le.

    11:10-11:20 amBreak
    11:20 am-12:20 pmTamara BroderickTitle: An Automatic Finite-Sample Robustness Metric: Can Dropping a Little Data Change Conclusions?

    Abstract: One hopes that data analyses will be used to make beneficial decisions regarding people’s health, finances, and well-being. But the data fed to an analysis may systematically differ from the data where these decisions are ultimately applied. For instance, suppose we analyze data in one country and conclude that microcredit is effective at alleviating poverty; based on this analysis, we decide to distribute microcredit in other locations and in future years. We might then ask: can we trust our conclusion to apply under new conditions? If we found that a very small percentage of the original data was instrumental in determining the original conclusion, we might not be confident in the stability of the conclusion under new conditions. So we propose a method to assess the sensitivity of data analyses to the removal of a very small fraction of the data set. Analyzing all possible data subsets of a certain size is computationally prohibitive, so we provide an approximation. We call our resulting method the Approximate Maximum Influence Perturbation. Our approximation is automatically computable, theoretically supported, and works for common estimators. We show that any non-robustness our method finds is conclusive. Empirics demonstrate that while some applications are robust, in others the sign of a treatment effect can be changed by dropping less than 0.1% of the data — even in simple models and even when standard errors are small.

     12:20-1:50 pmLunch
    Afternoon Session Chair: Ezra Miller
    1:50-2:50 pmNicolai Reshetikhin*Title: Random surfaces in exactly solvable models in statistical mechanics.

    Abstract: In the first part of the talk I will be an overview of a few models in statistical mechanics where a random variable is a geometric object such as a random surface or a random curve. The second part will be focused on the behavior of such random surfaces in the thermodynamic limit and on the formation of the so-called “limit shapes”.

    2:50-3:00 pmBreak
    3:00-4:00 pmSebastian KurtekTitle: Robust Persistent Homology Using Elastic Functional Data Analysis

    Abstract: Persistence landscapes are functional summaries of persistence diagrams designed to enable analysis of the diagrams using tools from functional data analysis. They comprise a collection of scalar functions such that birth and death times of topological features in persistence diagrams map to extrema of functions and intervals where they are non-zero. As a consequence, variation in persistence diagrams is encoded in both amplitude and phase components of persistence landscapes. Through functional data analysis of persistence landscapes, under an elastic Riemannian metric, we show how meaningful statistical summaries of persistence landscapes (e.g., mean, dominant directions of variation) can be obtained by decoupling their amplitude and phase variations. This decoupling is achieved via optimal alignment, with respect to the elastic metric, of the persistence landscapes. The estimated phase functions are tied to the resolution parameter that determines the filtration of simplicial complexes used to construct persistence diagrams. For a dataset obtained under geometric, scale and sampling variabilities, the phase function prescribes an optimal rate of increase of the resolution parameter for enhancing the topological signal in a persistence diagram. The proposed approach adds to the statistical analysis of data objects with rich structure compared to past studies. In particular, we focus on two sets of data that have been analyzed in the past, brain artery trees and images of prostate cancer cells, and show that separation of amplitude and phase of persistence landscapes is beneficial in both settings. This is joint work with Dr. James Matuk (Duke University) and Dr. Karthik Bharath (University of Nottingham).

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session
    5:10-5:20 pmStephan Huckemann, Ezra Miller, Zhigang YaoClosing Remarks

    * Virtual Presentation


     

  • Algebraic Geometry in String Theory Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 02.24.2023

    Algebraic Geometry in String Theory Seminar

    Speaker: Chao-Ming Lin (University of California, Irvine)

    Title: On the convexity of general inverse $\sigma_k$ equations and some applications

    Abstract: In this talk, I will show my recent work on general inverse $\sigma_k$ equations and the deformed Hermitian-Yang-Mills equation (hereinafter the dHYM equation). First, I will show my recent results. This result states that if a level set of a general inverse $\sigma_k$ equation (after translation if needed) is contained in the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the Monge-Ampère equation, the J-equation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special class of univariate polynomials and give a Positivstellensatz type result. These give a numerical criterion to verify whether the level set will be contained in the positive orthant. Last, as an application, I will prove one of the conjectures by Collins-Jacob-Yau when the dimension equals four. This conjecture states that under the supercritical phase assumption, if there exists a C-subsolution to the dHYM equation, then the dHYM equation is solvable.

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Geodesics and minimal surfaces

    9:00 am-10:00 am
    12/01/2024
    20220209_Andre-Neves_poster

    Abstract: There are several properties of closed geodesics which are proven using its Hamiltonian formulation, which has no analogue for minimal surfaces. I will talk about some recent progress in proving some of these properties for minimal surfaces.

  • Colloquium
    9:00 am-10:00 am
    12/01/2024
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Camillo De Lellis (IAS)

    Title: Area-minimizing integral currents and their regularity

    Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will also touch upon several fundamental open problems which still defy our understanding. 

    Talk Chair: William Minicozzi

    Video

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Rational Polypols

    9:00 am-10:00 am
    12/01/2024

    Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics, positive geometries are real semialgebraic sets together with a rational canonical form. We combine these two worlds by providing an explicit formula for the canonical form of a rational polypol in terms of defining equations of the adjoint curve and the facets of the polypol. For the special case of polygons, we show that the adjoint curve is hyperbolic and provide an explicit description of its nested ovals. Finally, we discuss the map that associates the adjoint curve to a given rational polypol, in particular the cases where this map is finite. For instance, using monodromy we find that a general quartic curve is the adjoint of 864 heptagons.

    This talk is based on joint work with R. Piene, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn,  M.-S. Sorea, and S. Telen.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Greedy maximal independent sets via local limits

    9:00 am-10:00 am
    12/01/2024

    Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge.

    In this talk, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs, such as paths and various random graphs, and by providing new results for other models such as random trees.

    If time allows, I will discuss a more delicate (and combinatorial) result, according to which, in expectation, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order.

    The talk is based on joint work with Michael Krivelevich, Tamás Mészáros and Clara Shikhelman.

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Theorems of Torelli type

    9:00 am-10:30 am
    12/01/2024
    Lecture_Looijenga-pdf

    Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University)

    Title: Theorems of Torelli type

    Abstract: Given a closed manifold of even dimension 2n, then Hodge showed around 1950 that a  kählerian complex structure on that manifold determines a decomposition of its complex cohomology. This decomposition, which can potentially vary continuously with the complex structure, extracts from a non-linear given,  linear data. It can contain a lot of information. When there is essentially no loss of data in this process, we say that the Torelli theorem holds.  We review the underlying theory and then survey some cases where this is the case. This will include the classical case n=1, but the emphasis will be on K3 manifolds (n=2) and more generally, on hyperkählerian manifolds. These cases stand out, since one can then also tell which decompositions occur.

    Talk chair: Gerard van der Geer

    Video 

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Yang Qi (Fudan)

    Title: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon

    Abstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon, leading to a significant broadening of the single-particle spectral functions. Quantitatively, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.

    https://www.youtube.com/watch?v=p1q0ots1X5s&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=20

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 10.12.22

    Topological Quantum Matter Seminar

    Speaker: Jennifer Cano (Stony Brook and Flatiron Institute)

    Title: Engineering topological phases with a superlattice potential
    Abstract: We propose an externally imposed superlattice potential as a platform for manipulating topological phases, which has both advantages and disadvantages compared to a moire superlattice. In the first example, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long sought-after goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example, we show that a superlattice potential applied to Bernal-stacked bilayer graphene can generate flat Chern bands, similar to in twisted bilayer graphene, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry, making it a promising alternative to achieve designer flat bands without a moire heterostructure.
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    10/5/2021 Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    Title: Geodesic Geometry on Graphs

    Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

    We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

    Joint work with Nati Linial.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Federico Bonetti (Oxford)

    Title: Non-Invertible Symmetries from Holography and Branes

    Abstract:  The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects, and of their action on extended operators of the 4d QFT.

    https://www.youtube.com/watch?v=opvlpWdTXr4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=21

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Junkai Dong (Harvard University)

    Title: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

    Abstract: Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

     

    https://www.youtube.com/watch?v=RfUKlzKs70o&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=23

  • Workshop
    9:00 am-3:30 pm
    12/01/2024-12/01/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Videos are available on the CMSA Youtube Playlist.

    On November 28 – Dec 1, 2022, the CMSA hosted a Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.

    Organizers: An Huang (Brandeis University) | Siu-Cheong Lau (Boston University) | Tsung-Ju Lee (CMSA, Harvard) | Andrew Linshaw (University of Denver)

    Scientific Advisor: Shing-Tung Yau (Harvard, Tsinghua)

    Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

    Directions and Recommended Lodging

    The conference was held in hybrid format, both in-person and online.

    The workshop was partially supported by Simons and NSF Grant DMS-2227199.

     

    Speakers: 

    • Tomoyuki Arakawa (Kyoto)
    • Thomas Creutzig (Edmonton)
    • Jonathan Mboyo Esole (Northeastern)
    • Fei Han (National University of Singapore)
    • Shinobu Hosono (Gakushuin University)
    • Flor Orosz Hunziker (Colorado)
    • Cuipo Jiang (Shanghai)
    • Shashank Kanade (Denver)
    • Matt Kerr (Washington University in St. Louis)
    • Carl Lian (Humboldt-Universität zu Berlin)
    • Nai-Chung Conan Leung (CUHK)
    • Ivan Loseu (Yale)
    • Robert McRae (Tsinghua University)
    • Anne Moreau (Université Paris-Saclay, Orsay)
    • Tony Pantev (University of Pennsylvania)
    • Mauricio Romo (Tsinghua University)
    • Bailin Song (USTC)
    • Cumrun Vafa (Harvard University)
    • Chin-Lung Wang (National Taiwan University)
    • Weiqiang Wang (Virginia)
    • Yaping Yang (University of Melbourne)
    • Shing-Tung Yau (Tsinghua University)
    • Chenglong Yu (Tsinghua University)
    • Gufang Zhao (University of Melbourne)

     

    Schedule (Eastern Time)

    Schedule (pdf)

    11/28 (Monday)

    08:30am – 08:55amRefreshments
    08:55am – 09:00amOpening remarks by Horng-Tzer Yau
    09:00am – 09:45amShing-Tung Yau*Title: The Hull-Strominger system through conifold transitions

    Abstract: In this talk I discuss the geometry of C-Y manifolds outside of the Kähler regime and especially describe the Hull-Strominger system through the conifold transitions.

    10:00am – 10:45amChenglong Yu*Title: Commensurabilities among Lattices in PU(1,n)

    Abstract: In joint work with Zhiwei Zheng, we study commensurabilities among certain subgroups in PU(1,n). Those groups arise from the monodromy of hypergeometric functions. Their discreteness and arithmeticity are classified by Deligne and Mostow. Thurston also obtained similar results via flat conic metrics. However, the classification of the lattices among them up to conjugation and finite index (commensurability) is not completed. When n=1, it is the commensurabilities of hyperbolic triangles. The cases of n=2 are almost resolved by Deligne-Mostow and Sauter’s commensurability pairs, and commensurability invariants by Kappes-Möller and McMullen. Our approach relies on the study of some higher dimensional Calabi-Yau type varieties instead of complex reflection groups. We obtain some relations and commensurability indices for higher n and also give new proofs for existing pairs in n=2.

    11:00am – 11:45amThomas Creutzig*Title: Shifted equivariant W-algebras

    Abstract: The CDO of a compact Lie group is a family of VOAs whose top level is the space of functions on the Lie group. Similar structures appear at the intersections of boundary conditions in 4-dimensional gauge theories, I will call these new families of VOAs shifted equivariant W-algebras. I will introduce these algebras, construct them and explain how they can be used to quickly prove the GKO-coset realization of principal W-algebras.

    11:45am – 1:30 pmLunch
    01:30pm – 02:15pmCumrun VafaTitle: Reflections on Mirror Symmetry

    Abstract: In this talk I review some of the motivations leading to the search and discovery of mirror symmetry as well as some of the applications it has had.

    02:30pm – 03:15pmJonathan Mboyo EsoleTitle: Algebraic topology and matter representations in F-theory

    Abstract: Recently, it was observed that representations appearing in geometric engineering in F-theory all satisfy a unique property: they correspond to characteristic representations of embedding of Dynkin index one between Lie algebras. However, the reason why that is the case is still being understood. In this talk, I will present new insights, giving a geometric explanation for this fact using K-theory and the topology of Lie groups and their classifying spaces. In physics, this will be interpreted as conditions on the charge of instantons and the classifications of Wess-Zumino-Witten terms.

    03:15pm – 03:45 pmBreak
    03:45pm – 04:30pmWeiqiang WangTitle: A Drinfeld presentation of affine i-quantum groups

    Abstract: A quantum symmetric pair of affine type (U, U^i) consists of a Drinfeld-Jimbo affine quantum group (a quantum deformation of a loop algebra) U and its coideal subalgebra U^i (called i-quantum group). A loop presentation for U was formulated by Drinfeld and proved by Beck. In this talk, we explain how i-quantum groups can be viewed as a generalization of quantum groups, and then we give a Drinfeld type presentation for the affine quasi-split i-quantum group U^i. This is based on joint work with Ming Lu (Sichuan) and Weinan Zhang (Virginia).

    04:45pm – 05:30pmTony PantevTitle: Decomposition, anomalies, and quantum symmetries

    Abstract: Decomposition is a phenomenon in quantum physics which converts quantum field theories with non-effectively acting gauge symmetries into equivalent more tractable theories in which the fields live on a disconnected space. I will explain the mathematical content of decomposition which turns out to be a higher categorical version of Pontryagin duality. I will examine how this duality interacts with quantum anomalies and secondary quantum symmetries and will show how the anomalies can be canceled by homotopy coherent actions of diagrams of groups. I will discuss in detail the case of 2-groupoids which plays a central role in anomaly cancellation, and will describe a new duality operation that yields decomposition in the presence of anomalies. The talk is based on joint works with Robbins, Sharpe, and Vandermeulen.

     

    11/29 (Tuesday)

     

    Refreshments
    09:00am – 09:45amRobert MacRae*Title: Rationality for a large class of affine W-algebras

    Abstract: One of the most important results in vertex operator algebras is Huang’s theorem that the representation category of a “strongly rational” vertex operator algebra is a semisimple modular tensor category. Conversely, it has been conjectured that every (unitary) modular tensor category is the representation category of a strongly rational (unitary) vertex operator algebra. In this talk, I will describe my results on strong rationality for a large class of affine W-algebras at admissible levels. This yields a large family of modular tensor categories which generalize those associated to affine Lie algebras at positive integer levels, as well as those associated to the Virasoro algebra.

    10:00am – 10:45amBailin Song*Title: The global sections of chiral de Rham complexes on compact Calabi-Yau manifolds

    Abstract: Chiral de Rham complex is a sheaf of vertex algebras on a complex manifold. We will describe the space of global sections of the chiral de Rham complexes on compact Calabi-Yau manifolds.

    11:00am – 11:45amCarl Lian*Title: Curve-counting with fixed domain

    Abstract: The fixed-domain curve-counting problem asks for the number of pointed curves of fixed (general) complex structure in a target variety X subject to incidence conditions at the marked points. The question comes in two flavors: one can ask for a virtual count coming from Gromov-Witten theory, in which case the answer can be computed (in principle) from the quantum cohomology of X, or one can ask for the “honest” geometric count, which tends to be more subtle. The answers are conjectured to agree in the presence of sufficient positivity, but do not always. I will give an overview of some recent results and open directions. Some of this work is joint with Alessio Cela, Gavril Farkas, and Rahul Pandharipande.

    11:45am – 01:30pmLunch
    01:30pm – 02:15pmChin-Lung WangTitle: A blowup formula in quantum cohomology

    Abstract: We study analytic continuations of quantum cohomology $QH(Y)$ under a blowup $\phi: Y \to X$ of complex projective manifolds along the extremal ray variable $q^{\ell}$. Under $H(Y) = \phi^* H(X) plus K$ where $K = \ker \phi_*$, we show that (i) the restriction of quantum product along the $\phi^*H(X)$ direction, denoted by $QH(Y)_X$, is meromorphic in $x := 1/q^\ell$, (ii) $K$ deforms uniquely to a quantum ideal $\widetilde K$ in $QH(Y)_X$, (iii) the quotient ring $QH(Y)_X/\widetilde K$ is regular over $x$, and its restriction to $x = 0$ is isomorphic to $QH(X)$. This is a joint work (in progress) with Y.-P. Lee and H.-W. Lin.

    02:30pm – 03:15pmIvan LoseuTitle: Quantizations of nilpotent orbits and their Lagrangian subvarieties

    Abstract: I’ll report on some recent progress on classifying quantizations of the algebras of regular functions of nilpotent orbits (and their covers) in semisimple Lie algebras, as well as the classification of quantizations of certain Lagrangian subvarieties. An ultimate goal here is to understand the classification of unitary representations of real semisimple Lie groups.

    03:15pm – 03:45pmBreak
    03:45pm – 04:30pmMatt Kerr*Title: $K_2$ and quantum curves

    Abstract: The basic objects for this talk are motives consisting of a curve together with a $K_2$ class, and their mixed Hodge-theoretic invariants.

    My main objective will be to explain a connection (recently proved in joint work with C. Doran and S. Sinha Babu) between (i) Hodge-theoretically distinguished points in the moduli of such motives and (ii) eigenvalues of operators on L^2(R) obtained by quantizing the equations of the curves.

    By local mirror symmetry, this gives evidence for a conjecture in topological string theory (due to M. Marino, A. Grassi, and others) relating enumerative invariants of toric CY 3-folds to spectra of quantum curves.

    04:45pm – 05:30pmFlor Orosz HunzikerTitle: Tensor structures associated to the N=1 super Virasoro algebra

    Abstract:  We have recently shown that there is a natural category of representations associated to the N=1 super Virasoro vertex operator algebras that have braided tensor structure. We will describe this category and discuss the problem of establishing its rigidity at particular central charges. This talk is based on joint work in progress with Thomas Creutzig, Robert McRae and Jinwei Yang.

     

     

     

    11/30 (Wednesday)

    08:30am – 09:00amRefreshments
    09:00am – 09:45amTomoyuki ArakawaTitle: 4D/2D duality and representation theory

    Abstract: This talk is about the 4D/2D duality discovered by Beem et al. rather recently in physics. It associates a vertex operator algebra (VOA) to any 4-dimensional superconformal field theory, which is expected to be a complete invariant of thl theory. The VOAs appearing in this manner may be regarded as chiralization of various symplectic singularities and their representations are expected to be closely related with the Coulomb branch of the 4D theory. I will talk about this remarkable 4D/2D duality from a representation theoretic perspective.

    10:00am – 10:45amShashank KanadeTitle: Combinatorics of principal W-algebras of type A

    Abstract: The combinatorics of principal W_r(p,p’) algebras of type A is controlled by cylindric partitions. However, very little seems to be known in general about fermionic expressions for the corresponding characters. Welsh’s work explains the case of Virasoro minimal models W_2(p,p’). Andrews, Schilling and Warnaar invented and used an A_2 version of the usual (A_1) Bailey machinery to give fermionic characters (up to a factor of (q)_\infty) of some, but not all, W_3(3,p’) modules. In a recent joint work with Russell, we have given a complete set of conjectures encompassing all of the remaining modules for W_3(3,p’), and proved our conjectures for small values of p’. In another direction, characters of W_r(p,p’) algebras also arise as appropriate limits of certain sl_r coloured Jones invariants of torus knots T(p,p’), and we expect this to provide further insights on the underlying combinatorics.

    11:00am – 11:45amGufang ZhaoTitle: Quasimaps to quivers with potentials

    Abstract: This talk concerns non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of the potential. The construction borrows ideas from the theory of gauged linear sigma models as well as recent development in shifted symplectic geometry and Donaldson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual counts arising from quivers with potentials are discussed. This is based on work in progress, in collaboration with Yalong Cao.

    11:45am – 01:30pmGroup Photo, Lunch
    01:30pm – 02:15pmYaping YangTitle: Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

    Abstract: Let X be a smooth local toric Calabi-Yau 3-fold. On the cohomology of the moduli spaces of certain sheaves on X, there is an action of the cohomological Hall algebra (COHA) of Kontsevich and Soibelman via “raising operators”. I will discuss the “double” of the COHA that acts on the cohomology of the moduli space by adding the “lowering operators”. We associate a root system to X. The double COHA is expected to be the shifted Yangian of this root system. We also give a prediction for the shift in terms of an intersection pairing. We provide evidence of the aforementioned expectation in various examples. This is based on my joint work with M. Rapcak, Y. Soibelman, and G. Zhao

    02:30pm – 03:15pmFei HanTitle: Graded T-duality with H-flux for 2d sigma models

    Abstract: T-duality in string theory can be realised as a transformation acting on the worldsheet fields in the two-dimensional nonlinear sigma model. Bouwknegt-Evslin-Mathai established the T-duality in a background flux for the first time upon compactifying spacetime in one direction to a principal circle by constructing the T-dual maps transforming the twisted cohomology of the dual spacetimes. In this talk, we will describe our recent work on how to promote the T-duality maps of Bouwknegt-Evslin-Mathai in two aspects. More precisely, we will introduce (1) graded T-duality, concerning the graded T-duality maps of all levels of twistings; (2) the 2-dimensional sigma model picture, concerning the double loop space of spacetimes. This represents our joint work with Mathai.

    03:15pm – 3:45pmBreak
    03:45pm – 04:30pmMauricio RomoTitle: Networks and BPS Counting: A-branes view point

    Abstract: I will review the countings of BPS invariants via exponential/spectral networks and present an interpretation of this counting as a count of certain points in the moduli space of A-branes corresponding to degenerate Lagrangians.

    04:45pm – 05:30pmShinobu HosonoTitle: Mirror symmetry of abelian fibered Calabi-Yau manifolds with ρ = 2

    Abstract: I will describe mirror symmetry of Calabi-Yau manifolds fibered by (1,8)-polarized abelian surfaces, which have Picard number two. Finding a mirror family over a toric variety explicitly, I  observe that mirror symmetry of all related Calabi-Yau manifods arises from the corresponding boundary points, which are not necessarily toric boundary points.  Calculating Gromov-Witten invariants up to genus 2, I find that the generating functions are expressed elliptic (quasi-)modular forms, which reminds us the modular anomaly equation found for elliptic surfaces. This talk is based on a published work with Hiromichi Takaki (arXiv:2103.08150).

    06:00pmBanquet @ Royal East Restaurant, 782 Main St, Cambridge, MA 02139

     

    12/1 (Thursday)

    08:30am – 09:00amRefreshments
    09:00am – 09:45amConan Nai Chung Leung*Title: Quantization of Kahler manifolds

    Abstract: I will explain my recent work on relationships among geometric quantization, deformation quantization, Berezin-Toeplitz quantization and brane quantization.

    10:00am – 10:45amCuipo Jiang*Title: Cohomological varieties associated to vertex operator algebras

    Abstract: We define and examine the cohomological variety of a vertex algebra, a notion cohomologically dual to that of the associated variety, which measures the smoothness of the associated scheme at the vertex point.  We study its basic properties. As examples, we construct a closed subvariety of the cohomological variety for rational affine vertex operator algebras constructed from finite dimensional simple Lie algebras. We also determine the cohomological varieties of the simple Virasoro vertex operator algebras. These examples indicate that, although the associated variety for a rational $C_2$-cofinite vertex operator algebra is always a simple point, the cohomological variety can have as large a dimension as possible. This talk is based on joint work with Antoine Caradot and Zongzhu Lin.

    11:00am – 11:45amAnne Moreau*Title: Action of the automorphism group on the Jacobian of Klein’s quartic curve

    Abstract: In a joint work with Dimitri Markouchevitch, we prove that the quotient variety of the 3-dimensional Jacobian of the plane Klein quartic curve by its full automorphism group of order 336 is isomorphic to the 3-dimensional weighted projective space with weights 1,2,4,7.

    The latter isomorphism is a particular case of the general conjecture of Bernstein and Schwarzman suggesting that a quotient of the n-dimensional complex space by the action of an irreducible complex crystallographic group generated by reflections is a weighted projective space.

    In this talk, I will explain this conjecture and the proof of our result. An important ingredient is the computation of the Hilbert function of the algebra of invariant theta-functions on the Jacobian.

    11:45am – 11:50amClosing remarks
    11:50amFree discussions and departure

    * = Online speaker

    CMSA COVID-19 Policies

     

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 11.23.22

    Topological Quantum Matter Seminar

    Speaker: Jian Kang, School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

    Title: Continuum field theory of graphene bilayer system

    Abstract: The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the magic-angle twisted bilayer graphene (MATBG), and nowadays is a starting point for most theoretical works. In this talk, I will briefly review the BM model and then present a continuum field theory [1] for graphene bilayer system allowing any smooth lattice deformation including the small twist angle. With the gradient expansion to the second order, the continuum theory for MATBG [2] produces the spectrum that almost perfectly matches the spectrum of the microscopic model, suggesting the validity of this theory. In the presence of the lattice deformation, the inclusion of the pseudo-vector potential does not destroy but shift the flat band chiral limit to a smaller twist angle. Furthermore, the continuum theory contains another important interlayer tunneling term that was overlooked in all previous works. This term non-negligibly breaks the particle-hole symmetry of the narrow bands and may be related with the experimentally observed particle-hole asymmetry.

    1. O. Vafek and JK, arXiv: 2208.05933.
    2. JK and O. Vafek, arXiv: 2208.05953.

     

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Sungwoo Hong (U Chicago & KAIST)

    Title: Neutrino Masses from Generalized Symmetry Breaking

    Abstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

     

    https://www.youtube.com/watch?v=4eZa06kiPCs&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=22

  • Program
    9:00 am-5:00 pm
    12/01/2024-05/24/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Mathematical Aspects of Scattering Amplitudes Program

    To receive email updates and program announcements, visit this link to sign up for the CMSA Mathematical Aspects of Scattering Amplitudes Program mailing list.

    Dates: April 15 – May 24, 2024

    Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138

    Organizers:

    Participants:

    This program will feature a weekly seminar series.
    Further Details TBA.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Justin Kulp (Perimeter Institute)

    Title: Holomorphic Twists and Confinement in N=1 SYM

    Abstract: Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

  • Workshop
    9:00 am-5:00 pm
    12/01/2024-05/05/2022
    GR Workshop Poster

    General Relativity Workshop on scalar curvature, minimal surfaces, and initial data sets

    Dates: May 2–5, 2022

    Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138 and via Zoom webinar.
    Advanced registration for in-person components is required.

    Organizers: Dan Lee (CMSA/CUNY), Martin Lesourd (CMSA/BHI), and Lan-Hsuan Huang (University of Connecticut).

    Speakers:

    • Zhongshan An, University of Connecticut
    • Paula Burkhardt-Guim, NYU
    • Hyun Chul Jang, University of Miami
    • Chao Li, NYU
    • Christos Mantoulidis, Rice University
    • Robin Neumayer, Carnegie Mellon University
    • Andre Neves, University of Chicago
    • Tristan Ozuch, MIT
    • Annachiara Piubello, University of Miami
    • Antoine Song, UC Berkeley
    • Tin-Yau Tsang, UC Irvine
    • Ryan Unger, Princeton
    • Zhizhang Xie, Texas A & M
    • Xin Zhou, Cornell University
    • Jonathan Zhu, Princeton University

    Schedule

    Download PDF

    Monday, May 2, 2022

    9:30–10:30 amHyun Chul JangTitle: Mass rigidity for asymptotically locally hyperbolic manifolds with boundary

    Abstract: Asymptotically locally hyperbolic (ALH) manifolds are a class of manifolds whose sectional curvature converges to −1 at infinity. If a given ALH manifold is asymptotic to a static reference manifold, the Wang-Chruściel-Herzlich mass integrals are well-defined, which is a geometric invariant that essentially measure the difference from the reference manifold. In this talk, I will present the result that an ALH manifold which minimize the mass integrals admits a static potential. To show this, we proved the scalar curvature map is locally surjective when it is defined on (1) the space of ALH metrics that coincide exponentially toward the boundary or (2) the space of ALH metrics with arbitrarily prescribed nearby Bartnik boundary data. And then, we establish the rigidity of the known positive mass theorems by studying the static uniqueness. This talk is based on joint work with L.-H. Huang.

    10:40–11:40 amAnnachiara PiubelloTitle: Estimates on the Bartnik mass and their geometric implications.

    Abstract: In this talk, we will discuss some recent estimates on the Bartnik mass for data with non-negative Gauss curvature and positive mean curvature. In particular, if the metric is round the estimate reduces to an estimate found by Miao and if the total mean curvature approaches 0, the estimate tends to 1/2 the area radius, which is the bound found by Mantoulidis and Schoen in the blackhole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.

    LUNCH BREAK
    1:30–2:30 pmRyan UngerTitle: Density and positive mass theorems for black holes and incomplete manifolds

    Abstract: We generalize the density theorems for the Einstein constraint equations of Corvino-Schoen and Eichmair-Huang-Lee-Schoen to allow for marginally outer trapped boundaries (which correspond physically to apparent horizons). As an application, we resolve the spacetime positive mass theorem in the presence of MOTS boundary in the non-spin case. This also has a surprising application to the Riemannian setting, including a non-filling result for manifolds with negative mass. This is joint work with Martin Lesourd and Dan Lee.

    2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications I

    Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

    TEA BREAK
    4:10–5:10 pmAntoine Song (virtual)Title: The spherical Plateau problem

    Abstract: For any closed oriented manifold with fundamental group G, or more generally any group homology class for a group G, I will discuss an infinite codimension Plateau problem in a Hilbert classifying space for G. For instance, for a closed oriented 3-manifold M, the intrinsic geometry of any Plateau solution is given by the hyperbolic part of M.

    Tuesday, May 3, 2022

    9:30–10:30 amChao LiTitle: Stable minimal hypersurfaces in 4-manifolds

    Abstract: There have been a classical theory for complete minimal surfaces in 3-manifolds, including the stable Bernstein conjecture in R^3 and rigidity results in 3-manifolds with positive Ricci curvature. In this talk, I will discuss how one may extend these results in four dimensions. This leads to new comparison theorems for positively curved 4-manifolds.

    10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds I

    Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

    LUNCH BREAK
    1:30–2:30 pmZhongshan AnTitle: Local existence and uniqueness of static vacuum extensions of Bartnik boundary data

    Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data — the induced metric and mean curvature of the boundary — is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang.

    2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications II

    Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

    TEA BREAK
    4:10–5:10 pmTin-Yau TsangTitle: Dihedral rigidity, fill-in and spacetime positive mass theorem

    Abstract: For compact manifolds with boundary, to characterise the relation between scalar curvature and boundary geometry, Gromov proposed dihedral rigidity conjecture and fill-in conjecture. In this talk, we will see the role of spacetime positive mass theorem in answering the corresponding questions for initial data sets.

    Speakers Banquet

    Wednesday, May 4, 2022

    9:30–10:30 amTristan OzuchTitle: Weighted versions of scalar curvature, mass and spin geometry for Ricci flows

    Abstract: With A. Deruelle, we define a Perelman-like functional for ALE metrics which lets us study the (in)stability of Ricci-flat ALE metrics. With J. Baldauf, we extend some classical objects and formulas from the study of scalar curvature, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.

    10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds II

    Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

    LUNCH BREAK
    1:30–2:30 pmChristos MantoulidisTitle: Metrics with lambda_1(-Delta+kR) > 0 and applications to the Riemannian Penrose Inequality

    Abstract: On a closed n-dimensional manifold, consider the space of all Riemannian metrics for which -Delta+kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally, for different values of k, in the study of scalar curvature in dimension n + 1 via minimal surfaces, the Yamabe problem in dimension n, and Perelman’s surgery for Ricci flow in dimension n = 3. We study these spaces in unison and generalize, as appropriate, scalar curvature results that we eventually apply to k = 1/2, where the space above models apparent horizons in time-symmetric initial data sets to the Einstein equations and whose flexibility properties are intimately tied with the instability of the Riemannian Penrose Inequality. This is joint work with Chao Li.

    2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications III

    Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

    TEA BREAK
    4:10–5:10 pmXin Zhou
    (Virtual)
    Title: Min-max minimal hypersurfaces with higher multiplicity

    Abstract: It is well known that minimal hypersurfaces produced by the Almgren-Pitts min-max theory are counted with integer multiplicities. For bumpy metrics (which form a generic set), the multiplicities are one thanks to the resolution of the Marques-Neves Multiplicity One Conjecture. In this talk, we will exhibit a set of non-bumpy metrics on the standard (n+1)-sphere, in which the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere. Such non-bumpy metrics form the first set of examples where the min-max theory must produce higher multiplicity minimal hypersurfaces. The talk is based on a joint work with Zhichao Wang (UBC).

    May 5, 2022

    9:00–10:00 amAndre NevesTitle: Metrics on spheres where all the equators are minimal

    Abstract: I will talk about joint work with Lucas Ambrozio and Fernando Marques where we study the space of metrics where all the equators are minimal.

    10:10–11:10 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds III

    Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

    11:20–12:20 pmPaula Burkhardt-GuimTitle: Lower scalar curvature bounds for C^0 metrics: a Ricci flow approach

    Abstract: We describe some recent work that has been done to generalize the notion of lower scalar curvature bounds to C^0 metrics, including a localized Ricci flow approach. In particular, we show the following: that there is a Ricci flow definition which is stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C^0 initial data.

    LUNCH BREAK
    1:30–2:30 pmJonathan ZhuTitle: Widths, minimal submanifolds and symplectic embeddings

    Abstract: Width or waist inequalities measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels.

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.26.2022-1583x2048-1

    Abstract: In spatial population genetics, it is important to understand the probability of extinction in multi-species interactions such as growing bacterial colonies, cancer tumor evolution and human migration. This is because extinction probabilities are instrumental in determining the probability of coexistence and the genealogies of populations. A key challenge is the complication due to spatial effect and different sources of stochasticity. In this talk, I will discuss about methods to compute the probability of extinction and other long-time behaviors for stochastic reaction-diffusion equations on metric graphs that flexibly parametrizes the underlying space. Based on recent joint work with Adrian Gonzalez-Casanova and Yifan (Johnny) Yang.

  • Colloquium

    Colloquium Colloquia & Seminar
    Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a seminar on Combinatorics, Physics and Probability, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu).

    The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/25/2022
    *note special time 9:00–10:00 AM ET
    Jacob Bourjaily (Penn State University, Eberly College of ScienceTitle: Adventures in Perturbation Theory

    Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

    2/3/2022Ran Tessler
    (Weizmann Institute of Science)
    Title: The Amplituhedron BCFW Triangulation

    Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

    2/8/2022Anna Seigal (Harvard)Title: Invariant theory for maximum likelihood estimation

    Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

    2/15/2022Igor Balla, Hebrew University of JerusalemTitle: Equiangular lines and regular graphs

    Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

    Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
    the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/21/2021Nima Arkani-Hamed
    IAS (Institute for Advanced Study), School of Natural Sciences
    Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes
    9/28/2021Melissa Sherman-Bennett
    University of Michigan, Department of Mathematics
    Title: The hypersimplex and the m=2 amplituhedron

    Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

    10/5/2021Daniel Cizma, Hebrew UniversityTitle: Geodesic Geometry on Graphs

    Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

    We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

    Joint work with Nati Linial.

    10/12/2021Lisa Sauermann, MITTitle: On counting algebraically defined graphs

    Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

    10/19/2021Pavel Galashin
    UCLA, Department of Mathematics
    Title: Ising model, total positivity, and criticality

    Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
    The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
    I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model.

    10/26/2021Candida Bowtell, University of OxfordTitle: The n-queens problem

    Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

    In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

    This is joint work with Peter Keevash.

    11/9/2021Steven Karp
    Universite du Quebec a Montreal, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)
    Title: Gradient flows on totally nonnegative flag varieties

    Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.
    11/16/2021
    *note special time 12:30–1:30 ET*
    Yinon Spinka (University of British Columbia)Title: A tale of two balloons

    Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
    Joint work with Omer Angel and Gourab Ray.

    11/23/2021Lutz Warnke (UC San Diego)Title: Prague dimension of random graphs

    Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

    11/30/2021Karel Devriendt (University of Oxford)Title: Resistance curvature – a new discrete curvature on graphs

    Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
    In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
    Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
    This work was done in collaboration with Renaud Lambiotte.

    12/7/2021Matthew Jenssen (University of Birmingham)Title: The singularity probability of random symmetric matrices

    Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

    12/14/2021Stefan Glock (ETH Zurich)Title: The longest induced path in a sparse random graph

    Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

    12/21/2021
    01/25/2022Jacob Bourjaily
    Penn State University, Department of Physics
  • Program
    9:00 am-5:00 pm
    12/01/2024-06/12/2022
    CMSA-2-600x338

    The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

    Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

    In this course, we will start with an introduction to computer programming, algorithms, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, and differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

    The program hopes to provide several research mentors from various disciplines who will give some of the course lectures. Students will have the opportunity to work with one of the research mentors offered by the program.

    Prerequisites: Basic coding ability in some programming language (C/Python/Matlab or CS50 experience). Some background in calculus and linear algebra is needed too. If you wish to work with a research mentor on differential geometry, more background in geometry such as from Math 132 or 136 will be useful. If you wish to work with a research mentor on computer science, coding experience mentioned above will be very useful. If you wish to work with a medical scientist, some background in life science or basic organic chemistry is recommended.

    The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

    This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard-related perks (such as a place to live if you are in Boston over the summer.)

    However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third-year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

    If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited, so don’t wait too long to apply.

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.19.22-1583x2048-1

    Abstract: Conditional independence (CI) is an important tool instatistical modeling, as, for example, it gives a statistical interpretation to graphical models. In general, given a list of dependencies among random variables, it is difficult to say which constraints are implied by them. Moreover, it is important to know what constraints on the random variables are caused by hidden variables. On the other hand, such constraints are corresponding to some determinantal conditions on the tensor of joint probabilities of the observed random variables. Hence, the inference question in statistics relates to understanding the algebraic and geometric properties of determinantal varieties such as their irreducible decompositions or determining their defining equations. I will explain some recent progress that arises by uncovering the link to point configurations in matroid theory and incidence geometry. This connection, in particular, leads to effective computational approaches for (1) giving a decomposition for each CI variety; (2) identifying each component in the decomposition as a matroid variety; (3) determining whether the variety has a real point or equivalently there is a statistical model satisfying a given collection of dependencies. The talk is based on joint works with Oliver Clarke, Kevin Grace, and Harshit Motwani.

    The papers are available on arxiv: https://arxiv.org/pdf/2011.02450
    and https://arxiv.org/pdf/2103.16550.pdf

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/22/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Conference
    9:00 am-6:00 pm
    12/01/2024
    150 Western Ave, Allston, MA 02134
    SMaSH_2022-2

    SMaSH: Symposium for Mathematical Sciences at Harvard

    On Tuesday, May 17, 2022, from 9:00 am – 5:30 pm, the Harvard John A Paulson School of Engineering and Applied Sciences (SEAS) and the Harvard Center of Mathematical Sciences and Applications (CMSA) held a Symposium for Mathematical Sciences for the mathematical sciences community at Harvard.

    Organizing Committee

    • Michael Brenner, Applied Mathematics (SEAS)
    • Michael Desai, Organismic and Evolutionary Biology (FAS)
    • Sam Gershman, Psychology (FAS)
    • Michael Hopkins, Mathematics (FAS)
    • Gary King, Government (FAS)
    • Peter Koellner, Philosophy (FAS)
    • Scott Kominers, Economics (FAS) & Entrepreneurial Management (HBS)
    • Xihong Lin, Biostatistics (HSPH) & Statistics (FAS)
    • Yue Lu, Electrical Engineering (SEAS)
    • Susan Murphy, Statistics (FAS) & Computer Science (SEAS)
    • Lisa Randall, Physics (SEAS)
    • Eugene Shakhnovich, Chemistry (FAS)
    • Salil Vadhan, Computer Science (SEAS)
    • Horng-Tzer Yau, Mathematics (FAS)

    This event was held in-person at the Science and Engineering Complex (SEC) at 150 Western Ave, Allston, MA 02134, and streamed on Zoom.

    Harvard graduate students and postdocs presented Poster Sessions.


    Venue: Science and Engineering Complex (SEC)


    Speakers

    • Anurag Anshu, Computer Science (SEAS)
    • Morgane Austern, Statistics (FAS)
    • Demba Ba, Electrical Engineering & Bioengineering (SEAS)
    • Michael Brenner, Applied Mathematics (SEAS)
    • Rui Duan, Biostatistics (HSPH)
    • Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)
    • Kosuke Imai, Government & Statistics (FAS)
    • Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)
    • Seth Neel, Technology & Operations Management (HBS)
    • Melanie Matchett Wood, Mathematics (FAS)

    Schedule PDF

    Schedule

    9:00–9:30 amCoffee and Breakfast
    West Atrium (ground floor of the SEC)
    9:30–10:30 amFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumKosuke Imai, Government & Statistics (FAS): Use of Simulation Algorithms for Legislative Redistricting Analysis and EvaluationYannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS): The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization
    10:30–11:00 amCoffee Break
    West Atrium (ground floor of the SEC)
    11:00–12:00 pmFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumSeth Neel, Technology & Operations Management (HBS): “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy LawDemba Ba, Electrical Engineering & Bioengineering (SEAS): Geometry, AI, and the Brain
    12:00–1:00 pmLunch Break
    Engineering Yard Tent
    1:00–2:30 pmFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMelanie Matchett Wood, Mathematics (FAS): Understanding distributions of algebraic structures through their momentsMorgane Austern, Statistics (FAS): Limit theorems for structured random objectsAnurag Anshu, Computer Science (SEAS): Operator-valued polynomial approximations and their use.
    2:30–3:00 pmCoffee Break
    West Atrium (ground floor of the SEC)
    3:00–4:30 pmFaculty Talks
    Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMichael Brenner, Applied Mathematics (SEAS): Towards living synthetic materialsRui Duan, Biostatistics (HSPH): Federated and transfer learning for healthcare data integrationSham M. Kakade, Computer Science (SEAS) & Statistics (FAS): What is the Statistical Complexity of Reinforcement Learning?
    4:30–5:30 pmReception with Jazz musicians
    & Poster Session
    Engineering Yard Tent

    Faculty Talks

    SpeakerTitle / Abstract / Bio
    Anurag Anshu, Computer Science (SEAS)Title: Operator-valued polynomial approximations and their use.

    Abstract: Approximation of complicated functions with low degree polynomials is an indispensable tool in mathematics. This becomes particularly relevant in computer science, where the complexity of interesting functions is often captured by the degree of the approximating polynomials. This talk concerns the approximation of operator-valued functions (such as the exponential of a hermitian matrix, or the intersection of two projectors) with low-degree operator-valued polynomials. We will highlight the challenges that arise in achieving similarly good approximations as real-valued functions, as well as recent methods to overcome them. We will discuss applications to the ground states in physics and quantum complexity theory: correlation lengths, area laws and concentration bounds.

    Bio: Anurag Anshu is an Assistant Professor of computer science at Harvard University. He spends a lot of time exploring the rich structure of quantum many-body systems from the viewpoint of quantum complexity theory, quantum learning theory and quantum information theory. He held postdoctoral positions at University of California, Berkeley and University of Waterloo and received his PhD from National University of Singapore, focusing on quantum communication complexity.

    Morgane Austern, Statistics (FAS)Title: Limit theorems for structured random objects

    Abstract: Statistical inference relies on numerous tools from probability theory to study the properties of estimators. Some of the most central ones are the central limit theorem and the free central limit theorem. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting. We consider distributionally “structured’ and dependent random object i.e random objects whose distribution is invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory.

    Bio: Morgane Austern is an assistant professor in the Statistics Department of Harvard University. Broadly, she is interested in developing probability tools for modern machine learning and in establishing the properties of learning algorithms in structured and dependent data contexts. She graduated with a PhD in statistics from Columbia University in 2019 where she worked in collaboration with Peter Orbanz and Arian Maleki on limit theorems for dependent and structured data. She was a postdoctoral researcher at Microsoft Research New England from 2019 to 2021.

    Demba Ba, Electrical Engineering & Bioengineering (SEAS)Title: Geometry, AI, and the Brain

    Abstract: A large body of experiments suggests that neural computations reflect, in some sense, the geometry of “the world”. How do artificial and neural systems learn representations of “the world” that reflect its geometry? How, for instance, do we, as humans, learn representations of objects, e.g. fruits, that reflect the geometry of object space? Developing artificial systems that can capture/understand the geometry of the data they process may enable them to learn representations useful in many different contexts and tasks. My talk will describe an artificial neural-network architecture that, starting from a simple union-of-manifold model of data comprising objects from different categories, mimics some aspects of how primates learn, organize, and retrieve concepts, in a manner that respects the geometry of object space.

    Bio: Demba Ba serves as an Associate Professor of electrical engineering and bioengineering in Harvard University’s School of Engineering and Applied Sciences, where he directs the CRISP group. Recently, he has taken a keen interest in the connection between artificial neural networks and sparse signal processing. His group leverages this connection to solve data-driven unsupervised learning problems in neuroscience, to understand the principles of hierarchical representations of sensory signals in the brain, and to develop explainable AI. In 2016, he received a Research Fellowship in Neuroscience from the Alfred P. Sloan Foundation. In 2021, Harvard’s Faculty of Arts and Sciences awarded him the Roslyn Abramson award for outstanding undergraduate teaching.

    Michael Brenner, Applied Mathematics (SEAS)Title: Towards living synthetic materials

    Abstract: Biological materials are much more complicated and functional than synthetic ones. Over the past several years we have been trying to figure out why. A sensible hypothesis is that biological materials are programmable. But we are very far from being able to program materials we create with this level of sophistication.  I will discuss our (largely unsuccessful) efforts to bridge this gap, though as of today I’m somewhat optimistic that we are arriving at a set of theoretical models that is rich enough to produce relevant emergent behavior.

    Bio: I’ve been at Harvard for a long time. My favorite part of Harvard is the students.

    Rui Duan, Biostatistics (HSPH)Title: Federated and transfer learning for healthcare data integration

    Abstract: The growth of availability and variety of healthcare data sources has provided unique opportunities for data integration and evidence synthesis, which can potentially accelerate knowledge discovery and improve clinical decision-making. However, many practical and technical challenges, such as data privacy, high dimensionality, and heterogeneity across different datasets, remain to be addressed. In this talk, I will introduce several methods for the effective and efficient integration of multiple healthcare datasets in order to train statistical or machine learning models with improved generalizability and transferability. Specifically, we develop communication-efficient federated learning algorithms for jointly analyzing multiple datasets without the need of sharing patient-level data, as well as transfer learning approaches that leverage shared knowledge learned across multiple datasets to improve the performance of statistical models in target populations of interest. We will discuss both the theoretical properties and examples of implementation of our methods in real-world research networks and data consortia.

    Bio: Rui Duan is an Assistant Professor of Biostatistics at the Harvard T.H. Chan School of Public Health. She received her Ph.D. in Biostatistics in May 2020 from the University of Pennsylvania. Her research interests focus on developing statistical, machine learning, and informatics tools for (1) efficient data integration in biomedical research, (2) understanding and accounting for the heterogeneity of biomedical data, and improving the generalizability and transferability of models across populations (3) advancing precision medicine research on rare diseases and underrepresented populations.

    Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)Title: The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization

    Abstract: We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε > 0, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples.

    Our fully nonparametric approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that are not necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art.

    Joint work with S. Matthew Weinberg

    Bio: Yannai A. Gonczarowski is an Assistant Professor of Economics and of Computer Science at Harvard University—the first faculty member at Harvard to have been appointed to both of these departments. Interested in both economic theory and theoretical computer science, Yannai explores computer-science-inspired economics: he harnesses approaches, aesthetics, and techniques traditionally originating in computer science to derive economically meaningful insights. Yannai received his PhD from the Departments of Math and CS, and the Center for the Study of Rationality, at the Hebrew University of Jerusalem, where he was advised by Sergiu Hart and Noam Nisan. Yannai is also a professionally-trained opera singer, having acquired a bachelor’s degree and a master’s degree in Classical Singing at the Jerusalem Academy of Music and Dance. Yannai’s doctoral dissertation was recognized with several awards, including the 2018 Michael B. Maschler Prize of the Israeli Chapter of the Game Theory Society, and the ACM SIGecom Doctoral Dissertation Award for 2018. For the design and implementation of the National Matching System for Gap-Year Programs in Israel, he was awarded the Best Paper Award at MATCH-UP’19 and the inaugural INFORMS AMD Michael H. Rothkopf Junior Researcher Paper Prize (first place) for 2020. Yannai is also the recipient of the inaugural ACM SIGecom Award for Best Presentation by a Student or Postdoctoral Researcher at EC’18. His first textbook, “Mathematical Logic through Python” (Gonczarowski and Nisan), which introduces a new approach to teaching the material of a basic Logic course to Computer Science students, tailored to the unique intuitions and strengths of this cohort of students, is forthcoming in Cambridge University Press.

    Kosuke Imai, Government & Statistics (FAS)Title: Use of Simulation Algorithms for Legislative Redistricting Analysis and Evaluation

    Abstract: After the 2020 Census, many states have been redrawing the boundaries of Congressional and state legislative districts. To evaluate the partisan and racial bias of redistricting plans, scholars have developed Monte Carlo simulation algorithms. The idea is to generate a representative sample of redistricting plans under a specified set of criteria and conduct a statistical hypothesis test by comparing a proposed plan with these simulated plans. I will give a brief overview of these redistricting simulation algorithms and discuss how they are used in real-world court cases.

    Bio: Kosuke Imai is Professor in the Department of Government and Department of Statistics at Harvard University. Before moving to Harvard in 2018, Imai taught at Princeton University for 15 years where he was the founding director of the Program in Statistics and Machine Learning. Imai specializes in the development of statistical methods and machine learning algorithms and their applications to social science research. His areas of expertise include causal inference, computational social science, program evaluation, and survey methodology.

    Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)Title: What is the Statistical Complexity of Reinforcement Learning?

    Abstract: This talk will highlight much of the recent progress on the following fundamental question in the theory of reinforcement learning: what (representational or structural) conditions govern our ability to generalize and avoid the curse of dimensionality?  With regards to supervised learning, these questions are reasonably well understood, both practically and theoretically: practically, we have overwhelming evidence on the value of representational learning (say through modern deep networks) as a means for sample efficient learning, and, theoretically, there are well-known complexity measures (e.g. the VC dimension and Rademacher complexity) that govern the statistical complexity of learning.  Providing an analogous theory for reinforcement learning is far more challenging, where even characterizing structural conditions which support sample efficient generalization has been far less well understood, until recently.

    This talk will survey recent advances towards characterizing when generalization is possible in RL, focusing on both necessary and sufficient conditions. In particular, we will introduce a new complexity measure, the Decision-Estimation Coefficient, that is proven to be necessary (and, essentially, sufficient) for sample-efficient interactive learning.

    Bio: Sham Kakade is a professor at Harvard University and a co-director of the Kempner Institute for the Study of Artificial and Natural Intelligence.  He works on the mathematical foundations of machine learning and AI. Sham’s thesis helped lay the statistical foundations of reinforcement learning. With his collaborators, his additional contributions include foundational results on: policy gradient methods in reinforcement learning; regret bounds for linear bandit and Gaussian process bandit models; the tensor and spectral methods for latent variable models; and a number of convergence analyses for convex and non-convex algorithms.  He is the recipient of the ICML Test of Time Award, the IBM Pat Goldberg best paper award, and INFORMS Revenue Management and Pricing Prize. He has been program chair for COLT 2011.

    Sham was an undergraduate at Caltech, where he studied physics and worked under the guidance of John Preskill in quantum computing. He completed his Ph.D. with Peter Dayan in computational neuroscience at the Gatsby Computational Neuroscience Unit. He was a postdoc with Michael Kearns at the University of Pennsylvania.

    Seth Neel, Technology & Operations Management (HBS)Title: “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy Law

    Abstract:  Businesses like Facebook and Google depend on training sophisticated models on user data. Increasingly—in part because of regulations like the European Union’s General Data Protection Act and the California Consumer Privacy Act—these organizations are receiving requests to delete the data of particular users. But what should that mean? It is straightforward to delete a customer’s data from a database and stop using it to train future models. But what about models that have already been trained using an individual’s data? These are not necessarily safe; it is known that individual training data can be exfiltrated from models trained in standard ways via model inversion attacks. In a series of papers we help formalize a rigorous notion of data-deletion and propose algorithms to efficiently delete user data from trained models with provable guarantees in both convex and non-convex settings.

    Bio: Seth Neel is a first-year Assistant Professor in the TOM Unit at Harvard Business School, and Co-PI of the SAFR ML Lab in the D3 Institute, which develops methodology to incorporate privacy and fairness guarantees into techniques for machine learning and data analysis, while balancing other critical considerations like accuracy, efficiency, and interpretability. He obtained his Ph.D. from the University of Pennsylvania in 2020 where he was an NSF graduate fellow. His work has focused primarily on differential privacy, notions of fairness in a variety of machine learning settings, and adaptive data analysis.

    Melanie Matchett Wood, Mathematics (FAS)Title: Understanding distributions of algebraic structures through their moments

    Abstract: A classical tool of probability and analysis is to use the moments (mean, variance, etc.) of a distribution to recognize an unknown distribution of real numbers.  In recent work, we are interested in distributions of algebraic structures that can’t be captured in a single number.  We will explain one example, the fundamental group, that captures something about the shapes of possibly complicated or high dimensional spaces.  We are developing a new theory of the moment problem for random algebraic structures which helps to to identify distributions of such, such as fundamental groups of random three dimensional spaces.  This talk is based partly on joint work with Will Sawin.

    Bio: Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study.  Her work spans number theory, algebraic geometry, algebraic topology, additive combinatorics, and probability. Wood has been awarded a CAREER grant, a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, and the AWM-Microsoft Research Prize in Algebra and Number Theory, and she is a Fellow of the American Mathematical Society. In 2021, Wood received the National Science Foundation’s Alan T. Waterman Award, the nation’s highest honor for early-career scientists and engineers.


  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Frances Kirwan (University of Oxford)

    TitleMoment maps and the Yang-Mills functional

    Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led.

    This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

    Talk chair: Peter Kronheimer

    Video

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/29/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Conference in Memory of Professor Masatake Kuranishi
    9:00 am-12:30 pm
    12/01/2024-05/12/2022
    150 Western Ave, Allston, MA 02134
    Kuranishi_Harvard_10x12-2

    On May 9–12, 2022, the CMSA hosted the conference Deformations of structures and moduli in geometry and analysis: A Memorial in honor of Professor Masatake Kuranishi.

    Organizers:  Tristan Collins (MIT) and Shing-Tung Yau (Harvard and Tsinghua)

    Videos are available on the conference playlist.

     

    Speakers:

    Charles Fefferman (Princeton University)

    Teng Fei (Rutgers University)

    Robert Friedman (Columbia University)

    Kenji Fukaya (Simons Center, Stony Brook)

    Akito Futaki (Tsinghua University)

    Victor Guillemin (Massachusetts Institute of Technology)

    Nigel Hitchin (Oxford University)

    Blaine Lawson (Stony Brook University)

    Yu-Shen Lin (Boston University)

    Melissa C.C. Liu (Columbia University)

    Takeo Ohsawa (Nagoya University)

    Duong H. Phong (Columbia University)

    Sebastien Picard (University of British Columbia)

    Paul Seidel (Massachusetts Institute of Technology)

    Gabor Szekelyhidi (University of Notre Dame)

    Claire Voisin (Institut de Mathematiques, Jussieu, France)

    Shing-Tung Yau (Harvard University)

     

    Schedule (download pdf)


    Monday, May 9, 2022

    8:15 amLight breakfast & coffee/tea
    8:45–9:00 amOpening Remarks
    9:00–10:00 amKenji FukayaTitle: Gromov Hausdorff convergence of filtered A infinity category

    Abstract: In mirror symmetry a mirror to a symplectic manifold is actually believed to be a family of complex manifold parametrized by a disk (of radius 0). The coordinate ring of the parameter space is a kind of formal power series ring the Novikov ring. Novikov ring is a coefficient ring of Floer homology. Most of the works on homological Mirror symmetry so far studies A infinity category over Novikov field, which corresponds to the study of generic fiber. The study of A infinity category over Novikov ring is related to several interesting phenomenon of Hamiltonian dynamics. In this talk I will explain a notion which I believe is useful to study mirror symmetry.

    Video

    10:15–11:15 amNigel Hitchin (Zoom)Title: Deformations: A personal perspective

    Abstract: The talk, largely historical, will focus on different deformation complexes I have encountered in my work, starting with instantons on 4-manifolds, but also monopoles, Higgs bundles and generalized complex structures. I will also discuss some speculative ideas related to surfaces of negative curvature.

    Video

    11:30–12:30 pmH. Blaine LawsonTitle: Projective Hulls, Projective Linking, and Boundaries of Varieties

    Abstract: In 1958 John Wermer proved that the polynomial hull of a compact real analytic curve γ ⊂ Cn was a 1-dim’l complex subvariety of Cn − γ. This result engendered much subsequent activity, and was related to Gelfand’s spectrum of a Banach algebra. In the early 2000’s Reese Harvey and I found a projective analogue of these concepts and wondered whether Wermer’s Theorem could be generalized to the projective setting. This question turned out to be more subtle and quite intriguing, with unexpected consequences. We now know a great deal, a highpoint of which s a result with Harvey and Wermer. It led to conjectures (for Cω-curves in P2C) which imply several results. One says, roughly, that a (2p − 1)-cycle Γ in Pn bounds a positive holomorphic p-chain of mass ≤ Λ ⇐⇒ its normalized linking number with all positive (n − p)-cycles in Pn − |Γ| is ≥ −Λ. Another says that a class τ ∈ H2p(Pn,|Γ|;Z) with ∂τ = Γ contains a positive holomorphic p-chain ⇐⇒ τ•[Z]≥0 for all positive holomorphic (n−p)-cycles Z in Pn−|Γ|

    Video

    12:30–2:30 pmLunch Break
    2:30–3:30 pmGabor SzekelyhidiTitle: Singularities along the Lagrangian mean curvature flow.

    Abstract: We study singularity formation along the Lagrangian mean curvature flow of surfaces. On the one hand we show that if a tangent flow at a singularity is the special Lagrangian union of two transverse planes, then the flow undergoes a “neck pinch”, and can be continued past the flow. This can be related to the Thomas-Yau conjecture on stability conditions along the Lagrangian mean curvature flow. In a different direction we show that ancient solutions of the flow, whose blow-down is given by two planes meeting along a line, must be translators. These are joint works with Jason Lotay and Felix Schulze.

    Video

    3:30–4:00 pmCoffee Break 
    4:00–5:00 pmTakeo OhsawaTitle: Glimpses of embeddings and deformations of CR manifolds

    Abstract: Basic results on the embeddings and the deformations of CR manifolds will be reviewed with emphasis on the reminiscences of impressive moments with Kuranishi since his visit to Kyoto in 1975.

    Video

     

     

     

    Tuesday, May 10, 2022

     

    8:15 amLight breakfast & coffee/tea
    9:00–10:00 amCharles Fefferman (Zoom)Title: Interpolation of Data by Smooth Functions

    Abstract: Let X be your favorite Banach space of continuous functions on R^n. Given an (arbitrary) set E in R^n and an arbitrary function f:E->R, we ask: How can we tell whether f extends to a function F \in X? If such an F exists, then how small can we take its norm? What can we say about its derivatives (assuming functions in X have derivatives)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F as above with norm nearly as small as possible? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few data points (x, f(x)) as “outliers”? Which points should we discard?

    The results were obtained jointly with A. Israel, B. Klartag, G.K. Luli and P. Shvartsman over many years.

    Video

    10:15–11:15 amClaire VoisinTitle: Deformations of K-trivial manifolds and applications to hyper-Kähler geometry

    Summary: I will explain the Ran approach via the T^1-lifting principle to the BTT theorem stating that deformations of K-trivial compact Kähler manifolds are unobstructed. I will explain a similar unobstructedness result for Lagrangian submanifolds of hyper-Kähler manifolds and I will describe important consequences on the topology and geometry of hyper-Kähler manifolds.

    Video

    11:30– 2:30 pmVictor GuilleminTitle: Semi-Classical Functions of Isotropic Type

    Abstract: The world of semiclassical analysis is populated by objects of “Lagrangian type.” The topic of this talk however will be objects in semi-classical analysis that live instead on isotropic submanifolds. I will describe in my talk a lot of interesting examples of such objects.

    Video

    12:30–2:30 pmLunch Break
    2:30–3:30 pmTeng FeiTitle: Symplectic deformations and the Type IIA flow

    Abstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong, Picard and Zhang.

    Video

    Speakers Banquet

     

     

     

    Wednesday, May 11, 2022

     

    8:15 amLight breakfast & coffee/tea
    9:00–10:00 amShing-Tung Yau (Zoom)Title: Canonical metrics and stability in mirror symmetry

    Abstract: I will discuss the deformed Hermitian-Yang-Mills equation, its role in mirror symmetry and its connections to notions of stability.  I will review what is known, and pose some questions for the future.

    Video

    10:15–11:15 amDuong H. PhongTitle: $L^\infty$ estimates for the Monge-Ampere and other fully non-linear equations in complex geometry

    Abstract: A priori estimates are essential for the understanding of partial differential equations, and of these, $L^\infty$ estimates are particularly important as they are also needed for other estimates. The key $L^\infty$ estimates were obtained by S.T. Yau in 1976 for the Monge-Ampere equation for the Calabi conjecture, and sharp estimates obtained later in 1998 by Kolodziej using pluripotential theory. It had been a long-standing question whether a PDE proof of these estimates was possible. We provide a positive answer to this question, and derive as a consequence sharp estimates for general classes of fully non-linear equations. This is joint work with B. Guo and F. Tong.

    Video

    11:30–2:30 pmPaul SeidelTitle: The quantum connection: familiar yet puzzling

    Abstract: The small quantum connection on a Fano variety is possibly the most basic piece of enumerative geometry. In spite of being really easy to write down, it is the subject of far-reaching conjectures (Dubrovin, Galkin, Iritani), which challenge our understanding of mirror symmetry. I will give a gentle introduction to the simplest of these questions.

    Video

    12:30–2:30 pmLunch Break
    2:30–3:30 pmMelissa C.C. LiuTitle: Higgs-Coulumb correspondence for abelian gauged linear sigma models

    Abstract: The underlying geometry of a gauged linear sigma model (GLSM) consists of a GIT quotient of a complex vector space by the linear action of a reductive algebraic group G (the gauge group) and a polynomial function (the superpotential) on the GIT quotient. The Higgs-Coulomb correspondence relates (1) GLSM invariants which are virtual counts of curves in the critical locus of the superpotential (Higgs branch), and (2) Mellin-Barnes type integrals on the Lie algebra of G (Coulomb branch). In this talk, I will describe the correspondence when G is an algebraic torus, and explain how to use the correspondence to study dependence of GLSM invariants on the stability condition. This is based on joint work with Konstantin Aleshkin.

    Video

    3:30–4:00 pmCoffee Break 
    4:00–5:00 pmSebastien PicardTitle: Topological Transitions of Calabi-Yau Threefolds

    Abstract: Conifold transitions were proposed in the works of Clemens, Reid and Friedman as a way to travel in the parameter space of Calabi-Yau threefolds with different Hodge numbers. This process may deform a Kahler Calabi-Yau threefold into a non-Kahler complex manifold with trivial canonical bundle. We will discuss the propagation of differential geometric structures such as balanced hermitian metrics, Yang-Mills connections, and special submanifolds through conifold transitions. This is joint work with T. Collins, S. Gukov and S.-T. Yau.

    Video

     

     

     

    Thursday, May 12, 2022

     

    8:15 amLight breakfast & coffee/tea
    9:00 am–10:00 amAkito Futaki (Zoom)Title: Transverse coupled Kähler-Einstein metrics and volume minimization

    Abstract:
    We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kählercone, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.Video
    10:15 am–11:15 amYu-Shen LinTitle: SYZ Mirror Symmetry of Log Calabi-Yau Surfaces

    Abstract: Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admits special Lagrangian fibrations. The conjecture serves as one of the guiding principles in mirror symmetry. In this talk, I will explain the existence of the special Lagrangian fibrations in some log Calabi-Yau surfaces and their dual fibrations in their expected mirrors. The journey leads us to the study of the moduli space of Ricci-flat metrics with certain asymptotics on these geometries and the discovery of new semi-flat metrics. If time permits, I will explain the application to the Torelli theorem of ALH^* gravitational instantons. The talk is based on joint works with T. Collins and A. Jacob.

    Video

    11:30 am – 12:30 pmRobert FriedmanTitle: Deformations of singular Fano and Calabi-Yau varieties

    Abstract: This talk will describe recent joint work with Radu Laza on deformations of generalized Fano and Calabi-Yau varieties, i.e. compact analytic spaces whose dualizing sheaves are either duals of ample line bundles or are trivial. Under the assumption of isolated hypersurface canonical singularities, we extend results of Namikawa and Steenbrink in dimension three and discuss various generalizations to higher dimensions.

    Video

    12:30 pmConcluding Remarks

     

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/6/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Symposium on Foundations of Responsible Computing (FORC)
    9:00 am-5:00 pm
    12/01/2024-06/08/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Screen-Shot-2020-03-05-at-11.54.28-AM-600x338

    On June 6-8, 2022, the CMSA hosted the 3rd annual Symposium on Foundations of Responsible Computing (FORC).

    The Symposium on Foundations of Responsible Computing (FORC) is a forum for mathematical research in computation and society writ large.  The Symposium aims to catalyze the formation of a community supportive of the application of theoretical computer science, statistics, economics and other relevant analytical fields to problems of pressing and anticipated societal concern.

    Organizers: Cynthia Dwork, Harvard SEAS | Omer Reingold, Stanford | Elisa Celis, Yale

    Schedule

    DOWNLOAD PDF

    June 6, 2022

    9:15 am–10:15 amOpening Remarks

    Keynote Speaker: Caroline Nobo, Yale University

    Title: From Theory to Impact: Why Better Data Systems are Necessary for Criminal Legal Reform

    Abstract: This talk will dive into the messy, archaic, and siloed world of local criminal justice data in America. We will start with a 30,000 foot discussion about the current state of criminal legal data systems, then transition to the challenges of this broken paradigm, and conclude with a call to measure new things – and to measure them better! This talk will leave you with an understanding of criminal justice data infrastructure and transparency in the US, and will discuss how expensive case management software and other technology are built on outdated normative values which impede efforts to reform the system. The result is an infuriating paradox: an abundance of tech products built without theoretical grounding, in a space rich with research and evidence.

    10:15 am–10:45 amCoffee Break
    10:45 am–12:15 pmPaper Session 1Session Chair: Ruth Urner
    Georgy Noarov, University of PennsylvaniaTitle: Online Minimax Multiobjective Optimization

    Abstract: We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. The learner’s objective is to minimize the maximum cumulative loss over all coordinates. We give a simple algorithm that lets the learner do almost as well as if she knew the adversary’s actions in advance. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains, ranging from multicalibration to a large set of no-regret algorithms, to a variant of Blackwell’s approachability theorem for polytopes with fast convergence rates. As a new application, we show how to “(multi)calibeat” an arbitrary collection of forecasters — achieving an exponentially improved dependence on the number of models we are competing against, compared to prior work.

    Matthew Eichhorn, Cornell UniversityTitle: Mind your Ps and Qs: Allocation with Priorities and Quotas

    Abstract: In many settings, such as university admissions, the rationing of medical supplies, and the assignment of public housing, decision-makers use normative criteria (ethical, financial, legal, etc.) to justify who gets an allocation. These criteria can often be translated into quotas for the number of units available to particular demographics and priorities over agents who qualify in each demographic. Each agent may qualify in multiple categories at different priority levels, so many allocations may conform to a given set of quotas and priorities. Which of these allocations should be chosen? In this talk, I’ll formalize this reserve allocation problem and motivate Pareto efficiency as a natural desideratum. I’ll present an algorithm to locate efficient allocations that conform to the quota and priority constraints. This algorithm relies on beautiful techniques from integer and linear programming, and it is both faster and more straightforward than existing techniques in this space. Moreover, its clean formulation allows for further refinement, such as the secondary optimization of some heuristics for fairness.

    Haewon Jeong, Harvard UniversityTitle: Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values

    Abstract: We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature, most of them require a complete training set as input. In practice, data can have missing values, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead, we train a tree with missing incorporated as attribute (MIA), which does not require explicit imputation, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset, through several experiments on real-world datasets.

    Emily Diana, University of PennsylvaniaTitle: Multiaccurate Proxies for Downstream Fairness

    Abstract: We study the problem of training a model that must obey demographic fairness conditions when the sensitive features are not available at training time — in other words, how can we train a model to be fair by race when we don’t have data about race? We adopt a fairness pipeline perspective, in which an “upstream” learner that does have access to the sensitive features will learn a proxy model for these features from the other attributes. The goal of the proxy is to allow a general “downstream” learner — with minimal assumptions on their prediction task — to be able to use the proxy to train a model that is fair with respect to the true sensitive features. We show that obeying multiaccuracy constraints with respect to the downstream model class suffices for this purpose, provide sample- and oracle efficient-algorithms and generalization bounds for learning such proxies, and conduct an experimental evaluation. In general, multiaccuracy is much easier to satisfy than classification accuracy, and can be satisfied even when the sensitive features are hard to predict.

    12:15 pm–1:45 pmLunch Break
    1:45–3:15 pmPaper Session 2Session Chair: Guy Rothblum
    Elbert Du, Harvard UniversityTitle: Improved Generalization Guarantees in Restricted Data Models

    Abstract: Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis — even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that, under this assumption, it is possible to “re-use” privacy budget on different portions of the data, significantly improving accuracy without increasing the risk of overfitting.

    Ruth Urner, York UniversityTitle: Robustness Should not be at Odds with Accuracy

    Abstract: The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability and trustworthiness: in many instances an imperceptible perturbation can falsely flip a neural network’s prediction. Applied research in this area has mostly focused on developing novel adversarial attack strategies or building better defenses against such. It has repeatedly been pointed out that adversarial robustness may be in conflict with requirements for high accuracy. In this work, we take a more principled look at modeling the phenomenon of adversarial examples. We argue that deciding whether a model’s label change under a small perturbation is justified, should be done in compliance with the underlying data-generating process. Through a series of formal constructions, systematically analyzing the the relation between standard Bayes classifiers and robust-Bayes classifiers, we make the case for adversarial robustness as a locally adaptive measure. We propose a novel way defining such a locally adaptive robust loss, show that it has a natural empirical counterpart, and develop resulting algorithmic guidance in form of data-informed adaptive robustness radius. We prove that our adaptive robust data-augmentation maintains consistency of 1-nearest neighbor classification under deterministic labels and thereby argue that robustness should not be at odds with accuracy.

    Sushant Agarwal, University of WaterlooTitle: Towards the Unification and Robustness of Perturbation and Gradient Based Explanations

    Abstract: As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method, and a variant of LIME which is a perturbation based method. More specifically, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation, i.e., when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties, such as robustness and linearity, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally, we empirically validate our theory using extensive experimentation on both synthetic and real world datasets.

    Tijana Zrnic, University of California, BerkeleyTitle: Regret Minimization with Performative Feedback

    Abstract: In performative prediction, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time, the learner needs to deploy a model to get feedback about the distribution it induces. We study the problem of finding near-optimal models under performativity while maintaining low regret. On the surface, this problem might seem equivalent to a bandit problem. However, it exhibits a fundamentally richer feedback structure that we refer to as performative feedback: after every deployment, the learner receives samples from the shifted distribution rather than only bandit feedback about the reward. Our main contribution is regret bounds that scale only with the complexity of the distribution shifts and not that of the reward function. The key algorithmic idea is careful exploration of the distribution shifts that informs a novel construction of confidence bounds on the risk of unexplored models. The construction only relies on smoothness of the shifts and does not assume convexity. More broadly, our work establishes a conceptual approach for leveraging tools from the bandits literature for the purpose of regret minimization with performative feedback.

    3:15 pm–3:45 pmCoffee Break
    3:45 pm–5:00 pmPanel DiscussionTitle: What is Responsible Computing?

    Panelists: Jiahao Chen, Cynthia Dwork, Kobbi Nissim, Ruth Urner

    Moderator: Elisa Celis

     

    June 7, 2022

    9:15 am–10:15 amKeynote Speaker: Isaac Kohane, Harvard Medical SchoolTitle: What’s in a label? The case for and against monolithic group/ethnic/race labeling for machine learning

    Abstract: Populations and group labels have been used and abused for thousands of years. The scale at which AI can incorporate such labels into its models and the ways in which such models can be misused are cause for significant concern. I will describe, with examples drawn from experiments in precision medicine, the task dependence of how underserved and oppressed populations can be both harmed and helped by the use of group labels. The source of the labels and the utility models underlying their use will be particularly emphasized.

    10:15 am–10:45 amCoffee Break
    10:45 am–12:15 pmPaper Session 3Session Chair: Ruth Urner
    Rojin Rezvan, University of Texas at AustinTitle: Individually-Fair Auctions for Multi-Slot Sponsored Search

    Abstract: We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from Chawla and Jagadeesan.

    Judy Hanwen Shen, StanfordTitle: Leximax Approximations and Representative Cohort Selection

    Abstract: Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency, exploiting significant utility improvements, and robustness to noise. Among other definitional contributions, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.

    Jiayuan Ye,
    National University of Singapore
    Title: Differentially Private Learning Needs Hidden State (or Much Faster Convergence)

    Abstract: Differential privacy analysis of randomized learning algorithms typically relies on composition theorems, where the implicit assumption is that the internal state of the iterative algorithm is revealed to the adversary. However, by assuming hidden states for DP algorithms (when only the last-iterate is observable), recent works prove a converging privacy bound for noisy gradient descent (on strongly convex smooth loss function) that is significantly smaller than composition bounds after a few epochs. In this talk, we extend this hidden-state analysis to various stochastic minibatch gradient descent schemes (such as under “shuffle and partition” and “sample without replacement”), by deriving novel bounds for the privacy amplification by random post-processing and subsampling. We prove that, in these settings, our privacy bound is much smaller than composition for training with a large number of iterations (which is the case for learning from high-dimensional data). Our converging privacy analysis, thus, shows that differentially private learning, with a tight bound, needs hidden state privacy analysis or a fast convergence. To complement our theoretical results, we present experiments for training classification models on MNIST, FMNIST and CIFAR-10 datasets, and observe a better accuracy given fixed privacy budgets, under the hidden-state analysis.

    Mahbod Majid, University of WaterlooTitle: Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism

    Abstract: We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution from O(d) independent samples (up to logarithmic factors) subject to pure differential privacy.

    Our main technique is a new approach to use the powerful Sum of Squares method (SoS) to design differentially private algorithms. SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics – estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees. We demonstrate a similar proofs to private algorithms phenomenon: instances of the workhorse exponential mechanism which apparently require exponential time but which can be analyzed with low-degree SoS proofs can be automatically turned into polynomial-time differentially private algorithms. We prove a meta-theorem capturing this phenomenon, which we expect to be of broad use in private algorithm design.

    12:15 pm–1:45 pmLunch Break
    1:45–3:15 pmPaper Session 4Session Chair: Kunal Talwar
    Kunal Talwar,
    Apple
    Title: Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

    Abstract: Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation (SMC) protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected.
    In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.

    Giuseppe Vietri, University of MinnesotaTitle: Improved Regret for Differentially Private Exploration in Linear MDP

    Abstract: We study privacy-preserving exploration in sequential decision-making for environments that rely on sensitive data such as medical records. In particular, we focus on solving the problem of reinforcement learning (RL) subject to the constraint of (joint) differential privacy in the linear MDP setting, where both dynamics and rewards are given by linear functions. Prior work on this problem due to Luyo et al. (2021) achieves a regret rate that has a dependence of O(K^{3/5}) on the number of episodes K. We provide a private algorithm with an improved regret rate with an optimal dependence of O(K^{1/2}) on the number of episodes. The key recipe for our stronger regret guarantee is the adaptivity in the policy update schedule, in which an update only occurs when sufficient changes in the data are detected. As a result, our algorithm benefits from low switching cost and only performs O(log(K)) updates, which greatly reduces the amount of privacy noise. Finally, in the most prevalent privacy regimes where the privacy parameter ? is a constant, our algorithm incurs negligible privacy cost — in comparison with the existing non-private regret bounds, the additional regret due to privacy appears in lower-order terms.

    Mingxun Zhou,
    Carnegie Mellon University
    Title: The Power of the Differentially Oblivious Shuffle in Distributed Privacy MechanismsAbstract: The shuffle model has been extensively investigated in the distributed differential privacy (DP) literature. For a class of useful computational tasks, the shuffle model allows us to achieve privacy-utility tradeoff similar to those in the central model, while shifting the trust from a central data curator to a “trusted shuffle” which can be implemented through either trusted hardware or cryptography. Very recently, several works explored cryptographic instantiations of a new type of shuffle with relaxed security, called differentially oblivious (DO) shuffles. These works demonstrate that by relaxing the shuffler’s security from simulation-style secrecy to differential privacy, we can achieve asymptotical efficiency improvements. A natural question arises, can we replace the shuffler in distributed DP mechanisms with a DO-shuffle while retaining a similar privacy-utility tradeoff?
    In this paper, we prove an optimal privacy amplification theorem by composing any locally differentially private (LDP) mechanism with a DO-shuffler, achieving parameters that tightly match the shuffle model. Moreover, we explore multi-message protocols in the DO-shuffle model, and construct mechanisms for the real summation and histograph problems. Our error bounds approximate the best known results in the multi-message shuffle-model up to sub-logarithmic factors. Our results also suggest that just like in the shuffle model, allowing each client to send multiple messages is fundamentally more powerful than restricting to a single message.
    Badih Ghazi,
    Google Research
    Title: Differentially Private Ad Conversion Measurement

    Abstract: In this work, we study conversion measurement, a central functionality in the digital advertising space, where an advertiser seeks to estimate advertiser site conversions attributed to ad impressions that users have interacted with on various publisher sites. We consider differential privacy (DP), a notion that has gained in popularity due to its strong and rigorous guarantees, and suggest a formal framework for DP conversion measurement, uncovering a subtle interplay between attribution and privacy. We define the notion of an operationally valid configuration of the attribution logic, DP adjacency relation, privacy
    budget scope and enforcement point, and provide, for a natural space of configurations, a complete characterization.

    3:15 pm–3:45 pmCoffee Break
    3:45 pm–5:00 pmOpen Poster Session

     

    June 8, 2022

    9:15 am–10:15 amKeynote Speaker: Nuria Oliver, Data-Pop AllianceTitle: Data Science against COVID-19

    Abstract: In my talk, I will describe the work that I have been doing since March 2020, leading a multi-disciplinary team of 20+ volunteer scientists working very closely with the Presidency of the Valencian Government in Spain on 4 large areas: (1) human mobility modeling; (2) computational epidemiological models (both metapopulation, individual and LSTM-based models); (3) predictive models; and (4) citizen surveys via the COVID19impactsurvey with over 600,000 answers worldwide.

    I will describe the results that we have produced in each of these areas, including winning the 500K XPRIZE Pandemic Response Challenge and best paper award at ECML-PKDD 2021. I will share the lessons learned in this very special initiative of collaboration between the civil society at large (through the survey), the scientific community (through the Expert Group) and a public administration (through the Commissioner at the Presidency level). WIRED magazine just published an article describing our story.

    10:15 am–10:45 amCoffee Break
    10:45 am–12:15 pmPaper Session 5Session Chair: Kunal Talwar
    Shengyuan Hu, Carnegie Mellon UniversityTitle: Private Multi-Task Learning: Formulation and Applications to Federated Learning

    Abstract: Many problems in machine learning rely on multi-task learning (MTL), in which the goal is to solve multiple related machine learning tasks simultaneously. MTL is particularly relevant for privacy-sensitive applications in areas such as healthcare, finance, and IoT computing, where sensitive data from multiple, varied sources are shared for the purpose of learning. In this work, we formalize notions of task-level privacy for MTL via joint differential privacy (JDP), a relaxation of differential privacy for mechanism design and distributed optimization. We then propose an algorithm for mean-regularized MTL, an objective commonly used for applications in personalized federated learning, subject to JDP. We analyze our objective and solver, providing certifiable guarantees on both privacy and utility. Empirically, our method allows for improved privacy/utility trade-offs relative to global baselines across common federated learning benchmarks

    Christina Yu,
    Cornell University
    Title: Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve

    Abstract: We consider the problem of dividing limited resources to individuals arriving over T rounds with a goal of achieving fairness across individuals. In general there may be multiple resources and multiple types of individuals with different utilities. A standard definition of `fairness’ requires an allocation to simultaneously satisfy envy-freeness and Pareto efficiency. However, in the online sequential setting, the social planner must decide on a current allocation before the downstream demand is realized, such that no policy can guarantee these desiderata simultaneously with probability 1, requiring a modified metric of measuring fairness for online policies. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to L_T necessarily suffers an efficiency loss of at least 1 / L_T. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. Our result is the first to provide guarantees for fair online resource allocation with high probability for multiple resource and multiple type settings. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.

    Hedyeh Beyhaghi, Carnegie Mellon UniversityTitle: On classification of strategic agents who can both game and improve

    Abstract: In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

    Keegan Harris, Carnegie Mellon UniversityTitle: Bayesian Persuasion for Algorithmic Recourse

    Abstract: When subjected to automated decision-making, decision subjects may strategically modify their observable features in ways they believe will maximize their chances of receiving a favorable decision. In many practical situations, the underlying assessment rule is deliberately kept secret to avoid gaming and maintain competitive advantage. The resulting opacity forces the decision subjects to rely on incomplete information when making strategic feature modifications. We capture such settings as a game of Bayesian persuasion, in which the decision maker offers a form of recourse to the decision subject by providing them with an action recommendation (or signal) to incentivize them to modify their features in desirable ways. We show that when using persuasion, both the decision maker and decision subject are never worse off in expectation, while the decision maker can be significantly better off. While the decision maker’s problem of finding the optimal Bayesian incentive-compatible (BIC) signaling policy takes the form of optimization over infinitely-many variables, we show that this optimization can be cast as a linear program over finitely-many regions of the space of possible assessment rules. While this reformulation simplifies the problem dramatically, solving the linear program requires reasoning about exponentially-many variables, even under relatively simple settings. Motivated by this observation, we provide a polynomial-time approximation scheme that recovers a near-optimal signaling policy. Finally, our numerical simulations on semi-synthetic data empirically illustrate the benefits of using persuasion in the algorithmic recourse setting.

    12:15 pm–1:45 pmLunch Break
    1:45–3:15 pmPaper Session 6Session Chair: Elisa Celis
    Mark Bun, Boston UniversityTitle: Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling

    Abstract: Sampling schemes are fundamental tools in statistics, survey design, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However, in practice, sampling designs are often more complex than the simple, data-independent sampling schemes that are addressed in prior work. In this work, we extend the study of privacy amplification results to more complex, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms, as well as provide some insight into the study of more general sampling designs.

    Samson Zhou, Carnegie Mellon UniversityTitle: Private Data Stream Analysis for Universal Symmetric Norm Estimation

    Abstract: We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular, we focus on releasing the family of symmetric norms, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include L_p norms, k-support norms, top-k norms, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the “heavy” coordinates in important levels and releases approximate level sizes for the “light” coordinates in important levels. Surprisingly, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover, our mechanism permits (1+\alpha)-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.

    Aloni Cohen, University of ChicagoTitle: Attacks on Deidentification’s Defenses

    Abstract: Quasi-identifier-based deidentification techniques (QI-deidentification) are widely used in practice, including k-anonymity, ?-diversity, and t-closeness. We present three new attacks on QI-deidentification: two theoretical attacks and one practical attack on a real dataset. In contrast to prior work, our theoretical attacks work even if every attribute is a quasi-identifier. Hence, they apply to k-anonymity, ?-diversity, t-closeness, and most other QI-deidentification techniques.
    First, we introduce a new class of privacy attacks called downcoding attacks, and prove that every QI-deidentification scheme is vulnerable to downcoding attacks if it is minimal and hierarchical. Second, we convert the downcoding attacks into powerful predicate singling-out (PSO) attacks, which were recently proposed as a way to demonstrate that a privacy mechanism fails to legally anonymize under Europe’s General Data Protection Regulation. Third, we use LinkedIn.com to reidentify 3 students in a k-anonymized dataset published by EdX (and show thousands are potentially vulnerable), undermining EdX’s claimed compliance with the Family Educational Rights and Privacy Act.

    The significance of this work is both scientific and political. Our theoretical attacks demonstrate that QI-deidentification may offer no protection even if every attribute is treated as a quasi-identifier. Our practical attack demonstrates that even deidentification experts acting in accordance with strict privacy regulations fail to prevent real-world reidentification. Together, they rebut a foundational tenet of QI-deidentification and challenge the actual arguments made to justify the continued use of k-anonymity and other QI-deidentification techniques.

    Steven Wu,
    Carnegie Mellon University
    Title: Fully Adaptive Composition in Differential Privacy

    Abstract: Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. The authors introduce two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the tightness of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. We also construct several general families of odometers. These odometers can match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging recent advances in time-uniform martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss, and conjecture that our results are essentially not improvable (even in constants) in general.

    3:15 pm–3:45 pmFORC Reception
    3:45 pm–5:00 pmSocial Hour
  • Workshop
    9:00 am-5:00 pm
    12/01/2024-04/29/2022
    Blockchain,Network,Concept,,,Distributed,Ledger,,Computer,Connection,Technology,,Matrix

    On April 27–29, 2022, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics.

    Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

    In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

    Speakers:

    • Federico Ardila (San Francisco State)
    • Nima Arkani-Hamed (IAS)
    • Madeline Brandt (Brown)
    • Nick Early (Max Planck Institute)
    • Chris Eur (Harvard)
    • Claudia Fevola (Max Planck Institute)
    • Christian Gaetz (Harvard)
    • Yuji Kodama (Ohio State University)
    • Yelena Mandelshtam (Berkeley)
    • Sebastian Mizera (IAS)
    • Matteo Parisi (Harvard CMSA)
    • Emma Previato (Boston University)
    • Anna Seigal (Harvard)
    • Melissa Sherman-Bennett (University of Michigan)
    • Simon Telen (Max Planck Institute)
    • Charles Wang (Harvard)

    Schedule

    Schedule PDF

    Wednesday, April 27, 2022

    9:30 am–10:30 amFederico ArdilaTitle: Nonlinear spaces from linear spaces

    Abstract: Matroid theory provides a combinatorial model for linearity, but it plays useful roles beyond linearity. In the classical setup, a linear subspace V of an n-dimensional vector space gives rise to a matroid M(V) on {1,…,n}. However, the matroid M(V) also knows about some nonlinear geometric spaces related to V. Conversely, those nonlinear spaces teach us things we didn’t know about matroids. My talk will discuss some examples.

    10:30 am–11:00 amCOFFEE BREAK
    11:00 am–11:45 amChris EurTitle: Tautological classes of matroids

    Abstract: Algebraic geometry has furnished fruitful tools for studying matroids, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (K-classes) on permutohedral varieties, which we call “tautological bundles (classes)” of matroids, as a new framework that unifies, recovers, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget, Hunter Spink, and Dennis Tseng.

    11:45 am–2:00 pmLUNCH BREAK
    2:00 pm–2:45 pmNick EarlyTitle: Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes

    Abstract: The associahedron is known to encapsulate physical properties such as the notion of tree-level factorization for one of the simplest Quantum Field Theories, the biadjoint scalar, which has only cubic interactions.  I will discuss novel instances of the associahedron and the biadjoint scalar in a class of generalized amplitudes, discovered by Cachazo, Early, Guevara and Mizera, by taking certain limits thereof. This connection leads to a simple proof of a new realization of the associahedron involving a Minkowski sum of certain positroid polytopes in the second hypersimplex.

    2:45 pm–3:30 pmAnna SeigalTitle: Invariant theory for maximum likelihood estimation

    Abstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

    3:30 pm–4:00 pmCOFFEE BREAK
    4:00 pm–4:45 pmMatteo ParisiTitle: Amplituhedra, Scattering Amplitudes, and Triangulations

    Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – introduced by physicists to encode interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory.
    Triangulations of polygons are encoded in the associahedron, studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes, constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. I will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between Amplituhedra of “m=2” type and a seemingly unrelated object – the Hypersimplex. The latter is a polytope which appears in many contexts, from matroid theory to tropical geometry.
    Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski.

    4:45 pm–5:30 pmMelissa Sherman-BennettTitle: The hypersimplex and the m=2 amplituhedron

    Abstract: In this talk, I’ll continue where Matteo left off. I’ll give some more details about the curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). The hypersimplex decompositions are closely related to matroidal subdivisions. Along the way, we prove a nice description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers, inspired by an analogous triangulation of the hypersimplex into Eulerian-number-many simplices.

     

    Thursday, April 28, 2022

    9:30 am–10:30 amClaudia FevolaTitle: Nonlinear Algebra meets Feynman integrals

    Abstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. They form a finite-dimensional vector space and the elements of a basis are named “master integrals” in the physics literature. The number of master integrals has been interpreted in different ways: it equals the dimension of a twisted de Rham cohomology group, the Euler characteristic of a very affine variety, and the holonomic rank of a D-module. In this talk, we are interested in a more general family of integrals that contains Feynman integrals as a special case. We explore this setting using tools coming from nonlinear algebra. This is an ongoing project with Daniele Agostini, Anna-Laura Sattelberger, and Simon Telen.

    10:30 am–11:00 amCOFFEE BREAK
    11:00 am–11:45 amSimon TelenTitle: Landau discriminants

    Abstract: The Landau discriminant is a projective variety containing kinematic parameters for which a Feynman integral can have singularities. We present a definition and geometric properties. We discuss how to compute Landau discriminants using symbolic and numerical methods. Our methods can be used, for instance, to compute the Landau discriminant of the pentabox diagram, which is a degree 12 hypersurface in 6-space. This is joint work with Sebastian Mizera.

    11:45 am–2:00 pmLUNCH BREAK
    2:00 pm–2:45 pmChristian GaetzTitle: 1-skeleton posets of Bruhat interval polytopes

    Abstract: Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes, despite not being simple, have interesting h-vectors. In a special case, work of Williams shows that Bruhat interval polytopes are isomorphic to bridge polytopes, so that chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs.

    2:45 pm–3:30 pmMadeleine BrandtTitle: Top Weight Cohomology of $A_g$

    Abstract: I will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of $A_g$. Thus, it can be computed combinatorially. This is joint work with Juliette Bruce, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.

    3:30 pm–4:00 pmCOFFEE BREAK
    4:00 pm–5:00 pmEmma PreviatoTitle: Sigma function on curves with non-symmetric semigroup

    Abstract: We start with an overview of the correspondence between spectral curves and commutative rings of differential operators, integrable hierarchies of non-linear PDEs and Jacobian vector fields. The coefficients of the operators can be written explicitly in terms of the Kleinian sigma function: Weierstrass’ sigma function was generalized to genus greater than one by Klein, and is a ubiquitous tool in integrability. The most accessible case is the sigma function of telescopic curves. In joint work with J. Komeda and S. Matsutani, we construct a curve with non-symmetric Weierstrass semigroup (equivalently, Young tableau), consequently non-telescopic, and its sigma function. We conclude with possible applications to commutative rings of differential operators.

    6:00 pmDinner Banquet, Gran Gusto Trattoria

     

    Friday, April 29, 2022

    9:00 am–10:00 amYuji KodamaTitle: KP solitons and algebraic curves

    Abstract: It is well-known that soliton solutions of the KdV hierarchy are obtained by singular limits of hyper-elliptic curves. However, there is no general results for soliton solutions of the KP hierarchy, KP solitons. In this talk, I will show that some of the KP solitons are related to the singular space curves associated with certain class of numerical semigroups.

    10:00 am–10:30 amCOFFEE BREAK
    10:30 am–11:15 amYelena MandelshtamTitle: Curves, degenerations, and Hirota varieties

    Abstract: The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases, Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This talk is based on joint work with Daniele Agostini, Claudia Fevola, and Bernd Sturmfels.

    11:15 am–12:00 pmCharles WangTitle: Differential Algebra of Commuting Operators

    Abstract: In this talk, we will give an overview of the problem of finding the centralizer of a fixed differential operator in a ring of differential operators, along with connections to integrable hierarchies and soliton solutions to e.g. the KdV or KP equations. Given these interesting connections, it is important to be able to compute centralizers of differential operators, and we discuss how to use techniques from differential algebra to approach this question, as well as how having these computational tools can help in understanding the structure of soliton solutions to these equations.

    12:00 pm–2:00 pmLUNCH BREAK
    2:00 pm–3:00 pmSebastian MizeraTitle: Feynman Polytopes

    Abstract: I will give an introduction to a class of polytopes that recently emerged in the study of scattering amplitudes in quantum field theory.

    3:00 pm–3:30 pmCOFFEE BREAK
    3:30 pm–4:30 pmNima Arkani-HamedTitle: Spacetime, Quantum Mechanics and Combinatorial Geometries at Infinity

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Algebraic Statistics with a View towards Physics

    9:00 am-10:00 am
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.

    **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

    All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

    LINK TO FORM

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/13/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.21.22-1583x2048-1

    Abstract:
    Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure, the adoption of MPC in real industry is still very much limited as of today, the biggest obstacle of which boils down to its efficiency.

    My research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal, my research spans both theoretical and applied cryptography. In theory, I develop new techniques for achieving general MPC with the optimal complexity, bringing theory closer to practice. In practice, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice.

    Biography:
    Peihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC, she received her Ph.D. from the University of California, Berkeley in 2019 and had brief stints at Google, Facebook, Microsoft Research, and Visa Research. Her research interests lie broadly in cryptography, theory, and security, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/20/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Workshop
    9:00 am-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series.

    Location: Room G10, 20 Garden Street, Cambridge, MA 02138.

    Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).

    Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory, algebraic geometry, and representation theory.

    At this workshop, we will bring together mathematicians, theoretical physicists, and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.

    Speakers:

    • James Halverson, Northeastern University Dept. of Physics and IAIFI
    • Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI
    • Andrew Sutherland, MIT Department of Mathematics

     

    https://youtu.be/qseSPgHHFtQ

     

     

    https://youtu.be/JN3mVazeP2E

     

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.14.22-1583x2048

    Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.

  • Member Seminar
    9:00 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Farzan Vafa

    Title: Diffusive growth sourced by topological defects

    Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time, and predict that in the presence of a positive defect, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature, we exploit the fact that for axisymmetric surfaces, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry, for polar order and small bending modulus, is a deformed football.
    We apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    5/27/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    6/3/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Dan Freed (The University of Texas at Austin)

    Title: The Atiyah-Singer Index Theorem

    Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator.

    This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

    Talk chair: Cumrun Vafa

    Video

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Interdisciplinary Science Seminar
    Speaker: Jianfeng Lu, Duke UniversityTitle: Surface hopping algorithms for non-adiabatic quantum systems

    Abstract: Surface hopping algorithm is widely used in chemistry for mixed quantum-classical dynamics. In this talk, we will discuss some of our recent works in mathematical understanding and algorithm development for surface hopping methods. These methods are based on stochastic approximations of semiclassical path-integral representation to the solution of multi-level Schrodinger equations; such methodology also extends to other high-dimensional transport systems.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    7/8/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Big Data Conference 2022
    9:00 am-1:00 pm
    12/01/2024
    Big Data 2022_web

    On August 26, 2022 the CMSA hosted our eighth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    The 2022 Big Data Conference took place virtually on Zoom.

    Organizers:

    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Schedule

    9:00 amConference OrganizersIntroduction and Welcome
    9:10 am – 9:55 amXiaohong ChenTitle: On ANN optimal estimation and inference for policy functionals of nonparametric conditional moment restrictions

    Abstract:  Many causal/policy parameters of interest are expectation functionals of unknown infinite-dimensional structural functions identified via conditional moment restrictions. Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional covariates more effectively than linear sieves. In this talk we present ANN optimal estimation and inference on  policy functionals, such as average elasticities or value functions, of unknown structural functions of endogenous covariates. We provide ANN efficient estimation and optimal t based confidence interval for regular policy functionals such as average derivatives in nonparametric instrumental variables regressions. We also present ANN quasi likelihood ratio based inference for possibly irregular policy functionals of general nonparametric conditional moment restrictions (such as quantile instrumental variables models or Bellman equations) for time series data. We conduct intensive Monte Carlo studies to investigate computational issues with ANN based optimal estimation and inference in economic structural models with endogeneity. For economic data sets that do not have very high signal to noise ratios, there are current gaps between theoretical advantage of ANN approximation theory vs inferential performance in finite samples.
    Some of the results are applied to efficient estimation and optimal inference for average price elasticity in consumer demand and BLP type demand.

    The talk is based on two co-authored papers:
    (1) Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators
    (Authors: Jiafeng Chen, Xiaohong Chen and Elie Tamer)
    https://arxiv.org/abs/2110.06763

    (2) Neural network Inference on Nonparametric conditional moment restrictions with weakly dependent data
    (Authors: Xiaohong Chen, Yuan Liao and Weichen Wang).

    View/Download Lecture Slides (pdf)

    10:00 am – 10:45 amJessica JeffersTitle: Labor Reactions to Credit Deterioration: Evidence from LinkedIn Activity

    Abstract: We analyze worker reactions to their firms’ credit deterioration. Using weekly networking activity on LinkedIn, we show workers initiate more connections immediately following a negative credit event, even at firms far from bankruptcy. Our results suggest that workers are driven by concerns about both unemployment and future prospects at their firm. Heightened networking activity is associated with contemporaneous and future departures, especially at financially healthy firms. Other negative events like missed earnings and equity downgrades do not trigger similar reactions. Overall, our results indicate that the build-up of connections triggered by credit deterioration represents a source of fragility for firms.

    10:50 am – 11:35 amMiles CranmerTitle: Interpretable Machine Learning for Physics

    Abstract: Would Kepler have discovered his laws if machine learning had been around in 1609? Or would he have been satisfied with the accuracy of some black box regression model, leaving Newton without the inspiration to discover the law of gravitation? In this talk I will explore the compatibility of industry-oriented machine learning algorithms with discovery in the natural sciences. I will describe recent approaches developed with collaborators for addressing this, based on a strategy of “translating” neural networks into symbolic models via evolutionary algorithms. I will discuss the inner workings of the open-source symbolic regression library PySR (github.com/MilesCranmer/PySR), which forms a central part of this interpretable learning toolkit. Finally, I will present examples of how these methods have been used in the past two years in scientific discovery, and outline some current efforts.

    View/Download Lecture Slides (pdf) 

    11:40 am – 12:25 pmDan RobertsTitle: A Statistical Model of Neural Scaling Laws

    Abstract: Large language models of a huge number of parameters and trained on near internet-sized number of tokens have been empirically shown to obey “neural scaling laws” for which their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model — a joint generative data model and random feature model — that captures this neural scaling phenomenology. By solving this model using tools from random matrix theory, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws (ii) how nonlinear feature maps, i.e the role played by the deep neural network, enable scaling laws when trained on these datasets, and (iii) how such scaling laws can break down, and what their behavior is when they do. A key feature is the manner in which the power laws that occur in the statistics of natural datasets are translated into power law scalings of the test loss, and how the finite extent of such power laws leads to both bottlenecks and breakdowns.

    View/Download Lecture Slides (pdf)

     

    12:30 pmConference OrganizersClosing Remarks

     

    Information about last year’s conference can be found here.

  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 09.28.22

    Topological Quantum Matter Seminar

    Speaker: Ruihua Fan, Harvard University

    Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow
    Abstract: One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance.
  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024
    CMSA QMMP Seminar 09.26.22

    Quantum Matter in Mathematics and Physics

    Speaker: Avner Karasik (University of Cambridge, UK)

    Title: Candidates for Non-Supersymmetric Dualities

    Abstract: In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

     

  • Math Science Literature Lecture Series
    9:00 am-10:30 pm
    12/01/2024

    Maxim Kontsevich  (IHÉS)

    Title: On the History of quantum cohomology and homological mirror symmetry

    Abstract: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry.  First, the usual cup-product on the cohomology of a complex projective variety admits a canonical multi-parameter deformation to so-called quantum product, satisfying a nice system of differential equations (WDVV equations).  The second discovery, even more striking,  is Mirror Symmetry, a duality between families of Calabi-Yau varieties acting as a mirror reflection on the Hodge diamond.

    Later it was realized that the quantum product belongs to the realm of symplectic geometry, and a half of mirror symmetry (called Homological Mirror Symmetry) is a duality between complex algebraic and symplectic varieties. The search of correct definitions and possible generalizations lead to great advances in many domains, giving mathematicians new glasses, through which they can see familiar objects in a completely new way.

    I will review the history of major mathematical advances in the subject of HMS, and the swirl of ideas around it.

    Talk chair: Paul Seidel

    Video

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    4/1/2021 Strongly Correlated Quantum Materials

    9:00 am-10:30 am
    12/01/2024
  • Topological Quantum Matter Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 09.21.22

    Topological Quantum Matter Seminar

    Speaker: Semyon Klevtsov, University of Strasbourg

    Title: Geometric test for topological states of matter

    Abstract: We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the

    degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille).

     

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024-04/27/2021

    In 2021, the CMSA hosted a lecture series on the literature of the mathematical sciences. This series highlights significant accomplishments in the intersection between mathematics and the sciences. Speakers include Edward Witten, Lydia Bieri, Simon Donaldson, Michael Freedman, Dan Freed, and many more.

    Videos of these talks can be found in this Youtube playlist.

    https://youtu.be/vb_JEhUW9t4

    In the Spring 2021 semester, the CMSA hosted a sub-program on this series titled A Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Below is the schedule for talks in that subprogram

    April 6, 2021 | 9:00 – 10:30am ET

    Edward Witten (IAS)

    TitleIsadore Singer’s Work on Analytic Torsion


    April 13, 2021 | 9:00 – 10:30am ET

    Claire Voisin (College de France)

    Title: K-theory and characteristic classes in topology and complex geometry  (a tribute to Atiyah and Hirzebruch)


    April 20, 2021 | 9:00 – 10:30am ET

    Dan Freed (the University of Texas at Austin)

    TitleThe Atiyah-Singer Index Theorem


    April 27, 2021 | 9:00 – 10:30am ET

    Frances Kirwan (University of Oxford)

    TitleMoment maps and the Yang-Mills functional

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Edward Witten (IAS)

    TitleIsadore Singer’s Work on Analytic Torsion

    Abstract:  I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory.

    This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and Singer.

    Talk chair: Cumrun Vafa

    Slides | Video

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Equiangular lines and regular graphs

    9:00 am-10:00 am
    12/01/2024

    Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

    Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
    the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

  • Quantum Matter
    9:00 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA QMMP Seminar

    Quantum Matter in Mathematics and Physics Seminar

    Speaker: Zhengyan Darius Shi (MIT)
    Title: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
    Abstract: Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity \sigma(mega) \sim mega^{-2/z} (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result \sigma(mega) \sim mega^{-2(z-2)/z}  due to Kim et al. is incorrect for inversion-odd order parameters.
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    7/1/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Interdisciplinary Science Seminar

    Speaker: Yue M. Lu, Harvard University

    Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning

    Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
    In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.

    Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007.  He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.

  • CMSA EVENT: Joint BHI/CMSA Conference on Flat Holography
    9:00 am-5:00 pm
    12/01/2024-06/24/2022

    On June 21–24, 2022, the Harvard Black Hole Initiative and the CMSA hosted the Joint BHI/CMSA Conference on Flat Holography (and related topics).

    The recent discovery of infinitely-many soft symmetries for all quantum theories of gravity in asymptotically flat space has provided a promising starting point for a bottom-up construction of a holographic dual for the real world. Recent developments have brought together previously disparate studies of soft theorems, asymptotic symmetries, twistor theory, asymptotically flat black holes and their microscopic duals, self-dual gravity, and celestial scattering amplitudes, and link directly to AdS/CFT.

    The conference was held in room G10 of the CMSA, 20 Garden Street, Cambridge, MA.

    Organizers:

    • Daniel Kapec, CMSA
    • Andrew Strominger, BHI
    • Shing-Tung Yau, Harvard & Tsinghua

    Confirmed Speakers:

    • Nima Arkani-Hamed, IAS
    • Shamik Banerjee, Bhubaneswar, Inst. Phys.
    • Miguel Campiglia, Republica U., Montevido
    • Geoffrey Compere, Brussels
    • Laura Donnay, Vienna
    • Netta Engelhardt, MIT
    • Laurent Freidel, Perimeter
    • Alex Lupsasca, Princeton
    • Juan Maldacena, IAS
    • Lionel Mason, Oxford
    • Natalie Paquette, U. Washington
    • Sabrina Pasterski, Princeton/Perimeter
    • Andrea Puhm, Ecole Polytechnique
    • Ana-Maria Raclariu, Perimeter
    • Marcus Spradlin, Brown
    • Tomasz Taylor, Northeastern
    • Herman Verlinde, Princeton
    • Anastasia Volovich, Brown
    • Bin Zhu, Northeastern

    Short talks by: Gonçalo Araujo-Regado (Cambridge), Adam Ball (Harvard), Eduardo Casali (Harvard), Jordan Cotler (Harvard), Erin Crawley (Harvard), Stéphane Detournay (Brussels), Alfredo Guevara (Harvard), Temple He (UC Davis), Elizabeth Himwich (Harvard), Yangrui Hu (Brown), Daniel Kapec (Harvard), Rifath Khan (Cambridge), Albert Law (Harvard), Luke Lippstreu (Brown), Noah Miller (Harvard), Sruthi Narayanan (Harvard), Lecheng Ren (Brown), Francisco Rojas (UAI), Romain Ruzziconi (Vienna), Andrew Strominger (Harvard), Adam Tropper (Harvard), Tianli Wang (Harvard), Walker Melton (Harvard)

    Schedule

    Monday, June 20, 2022

    Arrival
    7:00–9:00 pmWelcome Reception at Andy’s residence

     

    Tuesday, June 21, 2022

    9:00–9:30 amBreakfastlight breakfast provided
    Morning SessionChair: Dan Kapec
    9:30–10:00 amHerman VerlindeTitle: Comments on Celestial Dynamics
    10:00–10:30 amJuan MaldacenaTitle: What happens when you spend too much time looking at supersymmetric
    black holes?
    10:30–11:00Coffee break
    11:00–11:30 amMiguel CampigliaTitle: Asymptotic symmetries and loop corrections to soft theorems
    11:30–12:00 pmGeoffrey CompereTitle: Metric reconstruction from $Lw_{1+\infty}$ multipoles

    Abstract: The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be exchanged under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely determined by a set of conserved celestial charges, which uniquely label transitions among non-radiative regions caused by radiative processes. The algebra of the conserved celestial charges is derived from the real $Lw_{1+\infty}$ algebra. The celestial charges are expressed in terms of multipole moments, which allows to holographically reconstruct the metric in de Donder, Newman-Unti or Bondi gauge outside of sources.

    12:00–2:00 pmLunch break
    Afternoon SessionChair: Eduardo Casali
    2:00–2:30 pmNatalie PaquetteTitle: New thoughts on old gauge amplitudes
    2:30–3:00 pmLionel MasonTitle: An open sigma model for celestial gravity

    Abstract: A global twistor construction for conformally self-dual split signature metrics on $S2\times S2$  was developed 15 years ago by Claude LeBrun and the speaker.  This encodes the conformal metric into the location of a finite deformation of the real twistor space inside the flat complex twistor space, $\mathbb{CP}3$. This talk adapts the construction to construct global SD Einstein metrics from conformal boundary data and perturbations around the self-dual sector.  The construction entails determining a family of holomorphic discs in $\mathbb{CP}3$ whose boundaries lie on the deformed real slice and the (chiral) sigma model controls these discs in the Einstein case and provides amplitude formulae.

    3:00–3:30 pmCoffee break
    3:30–4:30 pmShort TalksDaniel Kapec: Soft Scalars and the Geometry of the Space of Celestial CFTs

    Albert Law: Soft Scalars and the Geometry of the Space of Celestial CFTs

    Sruthi Narayanan: Soft Scalars and the Geometry of the Space of Celestial CFTs

    Stéphane Detournay: Non-conformal symmetries and near-extremal black holes

    Francisco Rojas: Celestial string amplitudes beyond tree level

    Temple He: An effective description of energy transport from holography

    4:30–5:00 pmNima Arkani-Hamed(Dual) surfacehedra and flow particles know about strings

     

    Wednesday, June 22, 2022

    9:00–9:30 amBreakfastlight breakfast provided
    Morning SessionChair: Alfredo Guevara
    9:30–10:00 amLaurent FreidelTitle: Higher spin symmetry in gravity

    Abstract: In this talk, I will review how the gravitational conservation laws at infinity reveal a tower of symmetry charges in an asymptotically flat spacetime.
    I will show how the conservation laws, at spacelike infinity, give a tower of soft theorems that connect to the ones revealed by celestial holography.
    I’ll present the expression for the symmetry charges in the radiative phase space, which opens the way to reveal the structure of the algebra beyond the positive helicity sector. Then, if time permits I’ll browse through many questions that these results raise:
    such as the nature of the spacetime symmetry these charges represent, the nature of the relationship with multipole moments, and the insights their presence provides for quantum gravity.

    10:00–10:30 amAna-Maria RaclariuTitle: Eikonal approximation in celestial CFT
    10:30–11:00 amCoffee break
    11:00–11:30 amAnastasia VolovichTitle: Effective Field Theories with Celestial Duals
    11:30–12:00 pmMarcus SpradlinTitle: Loop level gluon OPE’s in celestial holography
    12:00–2:00 pmLunch break
    Afternoon SessionChair: Chiara Toldo
    2:00–2:30 pmNetta EngelhardtTitle: Wormholes from entanglement: true or false?
    2:30–3:00 pmShort TalksLuke Lippstreu: Loop corrections to the OPE of celestial gluons

    Yangrui Hu: Light transforms of celestial amplitudes

    Lecheng Ren: All-order OPE expansion of celestial gluon and graviton primaries from MHV amplitudes

    3:00–3:30 pmCoffee break
    3:30–4:30 pmShort TalksNoah Miller: C Metric Thermodynamics

    Erin Crawley: Kleinian black holes

    Rifath Khan: Cauchy Slice Holography: A New AdS/CFT Dictionary

    Gonçalo Araujo-Regado: Cauchy Slice Holography: A New AdS/CFT Dictionary

    Tianli Wang: Soft Theorem in the BFSS Matrix Model

    Adam Tropper: Soft Theorem in the BFSS Matrix Model

    7:00–9:00 pmBanquetMaharaja Restaurant, 57 JFK Street, Cambridge, MA

     

    Thursday, June 23, 2022

    9:00–9:30 amBreakfastlight breakfast provided
    Morning SessionChair: Jordan Cotler
    9:30–10:00 amLaura DonnayTitle: A Carrollian road to flat space holography
    10:00–10:30 amAndrea PuhmTitle: Celestial wave scattering on Kerr-Schild backgrounds
    10:30–11:00 amCoffee break
    11:00–11:30 amSabrina PasterskiTitle: Mining Celestial Symmetries

    Abstract: The aim of this talk is to delve into the common thread that ties together recent work with H. Verlinde, L. Donnay, A. Puhm, and S. Banerjee exploring, explaining, and exploiting the symmetries encoded in the conformally soft sector.

    Come prepared to debate the central charge, loop corrections, contour prescriptions, and orders of limits!

    11:30–12:00 pmShamik BanerjeeTitle: Virasoro and other symmetries in CCFT

    Abstract:  In this talk I will briefly describe my ongoing work with Sabrina Pasterski. In this work we revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton.  In its original formulation, we find that there is an obstruction to reproducing the expected $TT$ OPE in the double soft limit. This obstruction is related to the existence of the $SL_2$ current algebra symmetry of the CCFT. We propose a modification to the definition of the stress tensor which circumvents this obstruction and also discuss its implications for the existence of other current algebra (w_{1+\infty}) symmetries in CCFT.

    12:00–2:00 pmLunch break
    Afternoon SessionChair: Albert Law
    2:00–2:30 pmTomasz TaylorTitle: Celestial Yang-Mills amplitudes and D=4 conformal blocks
    2:30–3:00 pmBin ZhuTitle:  Single-valued correlators and Banerjee-Ghosh equations

    Abstract:  Low-point celestial amplitudes are plagued with singularities resulting from spacetime translation. We consider a marginal deformation of the celestial CFT which is realized by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators.

    3:00–3:30 pmCoffee break
    3:30–4:00 pmAlex LupsascaTitle: Holography of the Photon Ring
    4:00–5:30 pmShort TalksElizabeth Himwich: Celestial OPEs and w(1+infinity) symmetry of massless and massive amplitudes

    Adam Ball: Perturbatively exact $w_{1+\infty}$ asymptotic symmetry of quantum self-dual gravity

    Romain Ruzziconi: A Carrollian Perspective on Celestial Holography

    Jordan Cotler: Soft Gravitons in 3D

    Alfredo Guevara: Comments on w_1+\inf

    Andrew Strominger: Top-down celestial holograms

    Eduardo Casali: Celestial amplitudes as AdS-Witten diagrams

    Walker Melton: Top-down celestial holograms

     

    Friday, June 24, 2022

    9:00–9:30 amBreakfast
    9:30–12:30 pmOpen Discussion
    12:30–2:30 pmLunch provided at the BHI
    Departure

     

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    Interdisciplinary Science Seminar
    Title: Recent Advances on Maximum Flows and Minimum-Cost Flows

    Abstract: We survey recent advances on computing flows in graphs, culminating in an almost linear time algorithm for solving minimum-cost flow and several other problems to high accuracy on directed graphs. Along the way, we will discuss intuitions from linear programming, graph theory, and data structures that influence these works, and the resulting natural open problems.

    Bio: Yang P. Liu is a final-year graduate student at Stanford University. He is broadly interested in the efficient design of algorithms, particularly flows, convex optimization, and online algorithms. For his work, he has been awarded STOC and ITCS best student papers.

  • Workshop
    9:00 am-5:00 pm
    12/01/2024-08/05/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Phase Transitions_Poster

    On August 2–5, the CMSA hosted a workshop on Phase Transitions and Topological Defects in the Early Universe.

    The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA and online via Zoom webinar.

    The next decade will see a wealth of new cosmological data, which can lead to new insights into fundamental physics. Upcoming facilities (such as LISA) will be able to probe signals of fascinating phenomena in the early universe. These include signals from “Phase Transitions and Topological Defects,” which are ubiquitously given rise to in well-motivated UV models. In-depth studies of such signals requires cross-talks between experts from a wide spectrum of fields.

    The workshop aims to provide a platform for efficient exchange of new ideas related to these topics. It will start with an overview of some of the past and future experimental efforts. Next, there will be a substantial number of talks probing different aspects of phenomenology of phase transitions and topological defects in the early universe. It will finally close with discussions on recent formal development in the field.

    Scientific Advisory: Julian B. Muñoz, Lisa Randall, Matthew Reece, Tracy Slatyer, Shing-Tung Yau

    Organizers:
    Harvard: Nick DePorzio, Katie Fraser, Sam Homiller, Rashmish Mishra, & Aditya Parikh
    MIT: Pouya Asadi, Marianne Moore, & Yitian Sun

    Schedule/Format
    There will be 20+ 10 minute talks, ample discussion time, and lightning chalkboard talks.

    Speakers:

    • Nancy Aggarwal (Northwestern)
    • Jae Hyeok Chang (UMD – JHU)
    • Yanou Cui (UC Riverside)
    • David Dunsky (UC Berkeley)
    • Isabel Garcia-Garcia (KITP – UCSB)
    • Oliver Gould (Nottingham)
    • Yann Gouttenoire (Tel Aviv)
    • Eleanor Hall (UC Berkeley)
    • Sungwoo Hong (Chicago)
    • Anson Hook (UMD)
    • Jessica Howard (UC Irvine)
    • Seth Koren (Chicago)
    • Mrunal Korwar (Wisconsin)
    • Soubhik Kumar (UC Berkeley)
    • Vuk Mandic (Minnesota)
    • Yuto Minami (Osaka)
    • Michael Nee (Oxford)
    • Kai Schmitz (CERN)
    • Stephen R. Taylor (Vanderbilt)
    • Ofri Telem (UC Berkeley)
    • Juven Wang (Harvard)
    • Yikun Wang (Caltech)

    Participants:

    • Manuel Buen Abad (UMD)
    • Pouya Asadi (MIT)
    • Sean Benevedes (MIT)
    • Sandipan Bhattacherjee (Birla Institute of Technology Mesra Ranchi India)
    • Xingang Chen (Harvard University)
    • Nicholas DePorzio (Harvard University)
    • Peizhi Du (Stony Brook University)
    • Nicolas Fernandez (University of Illinois Urbana-Champaign)
    • Joshua Foster (MIT)
    • Katherine Fraser (Harvard University)
    • Sarah Geller (MIT)
    • Aurora Ireland (University of Chicago)
    • Marius Kongsore (New York University)
    • Ho Tat Lam (Massachusetts Institute of Technology)
    • Lingfeng Li (Brown University)
    • Yingying Li (Fermilab)
    • Gustavo Marques-Tavares (UMD)
    • Rashmish Mishra (Harvard University)
    • Siddharth Mishra-Sharma (MIT/Harvard University)
    • Toby Opferkuch (UC Berkeley)
    • Tong Ou (University of Chicago)
    • Aditya Parikh (Harvard University)
    • Yitian Sun (MIT)
    • Juan Sebastian Valbuena-Bermudez (Ludwig Maximilian University of Munich and Max Planck Institute for Physics)
    • Isaac Wang (Rutgers)
    • Wei Xue (University of Florida)
    • Winston Yin (UC Berkeley)
    • Quratulain Zahoor (The Islamia University of Bahwalpur Punjab (Pakistan)

    Schedule

    Tuesday, August 2, 2022

    9:00–9:20 amBreakfast
    9:20–9:30 amRashmish MishraOpening Remarks
    9:30–10:00 amVuk MandicTitle: Searching for the Stochastic Gravitational Wave Background with LISA

    Abstract: The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) will open a window into the milliHertz band of the gravitational wave spectrum. Among the many sources in this band is the stochastic gravitational wave background (SGWB), arising as an incoherent superposition of many uncorrelated gravitational wave sources. The SGWB could be of cosmological origin, carrying unique information about the physical processes that took place within the first minute after the big bang, including possible phase transitions and topological defects. LISA therefore has the potential to illuminate particle physics at very high energy scales that may be inaccessible in laboratories. I will discuss how LISA can be used to search for the SGWB, highlighting a new pipeline developed for this purpose as well as several challenges and limitations that such a search will encounter.

    10:00–10:30 amNancy AggarwalTitle: Gravitational waves at frequencies above 10 kHz

    Abstract: Gravitational waves (GWs) at frequencies higher than the LIGO band can bring us completely new information about the universe. Besides being the most-interesting frequency region for looking at cosmological phenomena, they can also convey signatures of ultralight bosons through blackhole superradiance and light primordial blackholes (PBHs). I will introduce a new global initiative to study GW sources and detectors at ultra-high-frequencies (MHz-GHz), as well as a new experiment at Northwestern University to look for GWs in the frequency band of 10 kHz to 300 kHz using levitated optomechanical sensors. I will summarize the design, the current experimental progress, as well as a path forward for future improvements.

    10:30–11:00 amYuto MinamiTitle: New measurements of the cosmic birefringence

    Abstract: Polarised light of the cosmic microwave background, the remnant light of the Big Bang, is sensitive to parity-violating physics, cosmic birefringence. In this presentation I report on a new measurement of cosmic birefringence from polarisation data of the European Space Agency (ESA)’s Planck satellite released in 2018. The statistical significance of the measured signal is 2.4 sigma. Recently, we found a signal with 3.3 sigma statistical significance when we use the latest Planck data and consider an effect of polarised foreground emission. If confirmed with higher statistical significance in future, it would have important implications for the elusive nature of dark matter and dark energy.

    11:00–1:30 pmBreak
    1:30–3:00 pmLighting Talks 1Lingfeng Li
    Winston Yin
    Marius Kongsore
    Nick DePorzio
    3:00–3:30 pmJae Hyeok ChangTitle: Correlating gravitational wave and gamma-ray signals from primordial black holes

    Abstract: Asteroid-mass primordial black holes (PBHs) can explain the observed dark matter abundance while being consistent with the current indirect detection constraints. These PBHs can produce gamma-ray signals from Hawking radiation that are within the sensitivity of future measurements by the AMEGO and e-ASTROGAM experiments. PBHs which give rise to such observable gamma-ray signals have a cosmic origin from large primordial curvature fluctuations. There must then be a companion, stochastic gravitational wave (GW) background produced by the same curvature fluctuations. I will demonstrate that the resulting GW signals will be well within the sensitivity of future detectors such as LISA, DECIGO, BBO, and the Einstein Telescope. The multimessenger signal from the observed gamma-rays and GWs will allow a precise measurement of the primordial curvature perturbation that produces the PBH. I will also argue that the resulting correlation between the two types of observations can provide a smoking-gun signal of PBHs.

    3:30–4:00 pmAnson Hook
    (Virtual via Zoom)
    Title: Early Universe Cosmology from Stochastic Gravitational Waves

    Abstract:  The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure gstar and beta functions as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the 10^-3 level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to O(1) deviations of gstar and the QCD beta function from their Standard Model value at temperatures ~ 10^5 GeV. In this case, many motivated models such as split SUSY and other solutions to the Electroweak Hierarchy problem would be tested. Future detectors, such as DECIGO, would be 100 times more sensitive than LISA to these effects and be capable of testing other motivated scenarios such as WIMPs and axions. The amazing prospect of using precision gravitational wave measurements to test such well motivated theories provides a benchmark to aim for when developing a precise understanding of the gravitational wave spectrum both experimentally and theoretically.

     

    Wednesday, August 3, 2022

    9:00–9:30 amBreakfast
    9:30–10:00 amKai Schmitz
    (Virtual via Zoom)
    Title: Gravitational waves from metastable cosmic strings

    Abstract: Cosmic strings are predicted by many Standard Model extensions involving the cosmological breaking of an Abelian symmetry and represent a potential source of primordial gravitational waves (GWs). In many Grand Unified Theories (GUTs), cosmic strings especially turn out to be metastable, as the nucleation of GUT monopoles along strings after a finite lifetime eventually leads to the collapse of the entire string network. In this talk, I will discuss the theoretical description of such a network and its individual components as well as the consequences for the emitted GW spectrum. Remarkably, the GW signal from metastable strings may well explain the common-spectrum process recently observed in pulsar timing data, while at the same time and in contrast to stable cosmic strings predicting a signal at higher frequencies that is still within the reach of current-generation ground-based interferometers. On their way to design sensitivity, existing GW experiments will thus have a realistic chance to probe particle physics processes at energies close to the GUT scale via the observation of GWs from metastable strings. This talk is based on 2107.04578 in collaboration with Wilfried Buchmüller and Valerie Domcke.

    10:00–10:30 amOliver Gould
    (Virtual via Zoom)
    Title: Effective field theory for cosmological phase transitions

    Abstract: Phase transitions are driven by thermal loop fluctuations, which modify background fields at leading order. This breaks the loop expansion and leads to large theoretical uncertainties in typical calculations, especially for gravitational wave predictions. I will give an overview of our present understanding of these uncertainties, and of the tools that have been developed to overcome them. Effective field theory has been at the forefront of this development, and I will outline how it can be used to solve a number of decades-long-standing theoretical problems.

    10:30–11:00 amIsabel Garcia-GarciaTitle: The Rocket Science of Expanding Bubbles

    11:00–1:30 pmBreak
    1:30–3:00 pmLightning Talks 2Sarah Geller
    Peizhi Du
    Tong Ou
    Isaac Wang
    Katie Fraser
    3:00–3:30 pmDavid Dunsky
    (Virtual via Zoom)
    Title: Gravitational Wave Gastronomy

    Abstract: The symmetry breaking of grand unified gauge groups in the early universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable and can leave behind unique gravitational wave fingerprints. In this talk, I will discuss the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and “eat” the strings, 2) the collapse and decay of a monopole-string network by strings that “eat” the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and “eat” the wall, and 4) the collapse and decay of a string-bounded wall network by walls that “eat” the strings. We call the gravitational wave signals produced from the “eating” of one topological defect by another “gravitational wave gastronomy”. The gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO(10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects.

    3:30–4:00 pmYanou Cui
    (Virtual via Zoom)
    Title: Cosmic Archaeology with gravitational waves from (axion) cosmic strings

    Abstract: In this talk I will discuss important aspects of cosmology and particle physics that can be probed with GW signals from cosmic strings: probing the pre-BBN primordial dark age and axion physics.  Gravitational waves (GWs) originating from the dynamics of a cosmic string network have the ability to probe many otherwise inaccessible properties of the early universe. In particular, I will discuss how the frequency spectrum of a stochastic GW background (SGWB) from a cosmic string network can be used to probe Hubble expansion rate of the early universe prior to Big Bang Nucleosynthesis (BBN), during the “primordial dark age”. Furthermore I will show that in contrast to the standard expectation, cosmic strings formed before inflation could regrow back into the horizon and leave imprints, with GW bursts potentially being the leading signal. In relation to axion physics I will also demonstrate the detection prospect for SGWB from global/axion strings which may provide a new probe for axion-like dark matter models, considering various scenarios of cosmic history.

    4:00–4:30 pmMichael NeeTitle: The Boring Monopole

    Abstract: First order phase transitions play an important role in the cosmology of many theories of BSM physics. In this talk I will discuss how a population of magnetic monopoles present in the early universe can seed first order phase transitions, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, thus requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. Our results show that monopole-catalysed tunnelling can dominate over the homogeneous decay for a wide range of parameters.

     

    Thursday, August 4, 2022

    9:00–9:30 amBreakfast
    9:30–10:00 amYikun WangTitle: A New Approach to Electroweak Symmetry Non-Restoration

    Abstract: Electroweak symmetry non-restoration up to high temperatures well above the electroweak scale has intriguing implications for (electroweak) baryogenesis and early universe thermal histories. In this talk, I will discuss such a possible fate of the electroweak symmetry in the early universe and a new approach to realize it, via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. Examples of benchmark scenarios that allow for electroweak symmetry non-restoration all the way up to hundreds of TeV temperatures, at the same time featuring suppressed sphaleron washout factors down to the electroweak scale, will be presented. Renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures, have been implemented calculating the thermal history. This method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

    10:00–10:30 amSoubhik KumarTitle: Probing primordial fluctuations through stochastic gravitational wave background anisotropies

    Abstract: Stochastic gravitational wave backgrounds are expected to be anisotropic. While such anisotropies can be of astrophysical origin, a cosmological component of such anisotropies can carry rich information about primordial perturbations. Focusing on the case of a cosmological phase transition, I will talk about how such anisotropies can give us a powerful probe of primordial non-Gaussianities, complementary to current and future CMB and LSS searches. In the scenario where astrophysical foregrounds are also present, I will then discuss some strategies using which we can extract the cosmological signal, focusing on the case of LISA, Taiji and BBO, in particular.

    10:30–11:00 amJessica Howard
    (Virtual via Zoom)
    Title: Dark Matter Freeze-out during SU(2)_L Confinement

    Abstract: We explore the possibility that dark matter is a pair of SU(2)_L doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This phase of confinement causes the Standard Model doublets and dark matter to confine into pion-like objects. Before the weak sector deconfines, the dark pions freezeout and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the observed relic density. We determine which regions of this parameter space evade direct detection and collider bounds.

    11:00–11:30 amJuven WangTitle: Quantum Matter Adventure to Beyond the Standard Model Prediction

    Abstract: Ideas developed from the quantum matter and quantum field theory frontier may guide us to explore new physics beyond the 4d Standard Model. I propose a few such ideas. First, new physics for neutrinos: right-handed neutrinos carry a Z_{16} class mixed gauge-gravitational global anomaly index, which could be replaced by 4d or 5d topological quantum field theory, or 4d interacting conformal field theory. These theories provide possible new neutrino mass mechanisms [arXiv:2012.15860]. Second, deconfined quantum criticality between Grand Unified Theories: dictated by a Z_2 class global anomaly, a gapless quantum critical region can happen between Georgi-Glashow and Pati-Salam models as deformation of the Standard Model, where Beyond the Standard Model physics and Dark Gauge sector occur as neighbor phases [arXiv:2106.16248, arXiv:2112.14765, arXiv:2204.08393]. Third, the Strong CP problem can be solved by a new solution involving Symmetric Mass Generation [arXiv:2204.14271].

    11:30–1:30 pmBreak
    1:30–4:00 pmStephen R. TaylorTitle: Pulsar Timing Arrays: The Next Window onto the Low-frequency Gravitational-wave Universe

    Abstract: The nanohertz-frequency band of gravitational waves should be awash with signals from supermassive black-hole binaries, as well as cosmological signatures of phase transitions, cosmic strings, and other relics of the early Universe. Pulsar-timing arrays (PTAs) like the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and the International Pulsar Timing Array are poised to chart this new frontier of gravitational wave discovery within the next several years. I will present exciting new results from recent cutting-edge searches, discuss some milestones on the road to the next decade of PTA discovery, and take workshop attendees through a guided tutorial of how the broader community can use our production-level analysis pipeline to extract new science with ease.

     

    Friday, August 5, 2022

    9:00–9:30 amBreakfast
    9:30–10:00 amOfri TelemTitle: Charge-Monopole Pairwise Phases from Dressed Quantum States

    10:00–10:30 amSungwoo HongTitle: Coupling a Cosmic String to a TQFT

    Abstract: In the last few years, the notion of symmetry has been enlarged to “generalized symmetry” or “higher-form symmetry” and these more generalized symmetries have played a critical role in deepening our understanding of QFT, notably IR phases of QFT. In this talk, I will discuss a various ways of coupling the axion-Maxwell theory to a topological field theory (TQFT). Contrary to a common wisdom, I will show that such topological modifications can lead to direct changes in the local physics with possible observable consequences. This surprise can be realized by a dimensional reduction, namely, a coupling to a TQFT in 4d leads to a non-trivial and local impact on the 2d string world-sheet QFT. There also exists a topological modification of the theory, i.e. gauging a discrete subgroup of 0-form shift symmetry, and this time it results in a alteration of spectrum of cosmic strings. If time permits, I will also discuss generalized symmetries and associated higher-groups of these theories.

    10:30–11:00 amEleanor Hall
    (Virtual via Zoom)
    Title: Non-perturbative methods for false vacuum decay

    Abstract: Gravitational waves from phase transitions in the early universe are one of our most promising signal channels of BSM physics; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present the quasi-stationary effective action, a new non-perturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. This method opens the door to reliable calculation of gravitational wave signals and false vacuum decay rates for strongly-interacting theories. I will also discuss recent developments and ongoing extensions of the QSEA.

    11:00–1:30 pmBreak
    1:30–2:00 pmMrunal KorwarTitle: Electroweak Symmetric Balls

    Abstract: Electroweak symmetric balls are macroscopic objects with electroweak symmetry restored inside. Such an object can arise in models where dark sectors contain monopole or non-topological soliton with a Higgs portal interaction to the Standard Model. It could be produced in the early universe via phase transition or parametric resonance, accounting for all dark matter. In a scenario where the balls are allowed to evaporate, the observed baryon asymmetry in our universe could be explained by a mechanism of “catalyzed baryogenesis.” In this mechanism, the motion of a ball-like catalyst provides the necessary out-of-equilibrium condition, its outer wall has CP-violating interactions with the Standard Model particles, and its interior has baryon number violating interactions via electroweak Sphaleron. Because of electroweak symmetric cores, such objects have a large geometric cross-section off a nucleus, generating a multi-hit signature in large volume detectors. These objects could radiatively capture a nucleus and release GeV-scale energy for each interaction. The IceCube detector can probe dark matter balls with masses up to a gram.

    2:00–2:30 pmSeth KorenTitle: Discrete Gauged Baryon Minus Lepton Number and the Cosmological Lithium Problem

    Abstract: We study the baryon minus lepton number gauge theory broken by a scalar with charge six. The infrared discrete vestige of the gauge symmetry demands the existence of cosmic string solutions, and their production as dynamical objects in the early universe is guaranteed by causality. These topological defects can support interactions which convert three protons into three positrons, and we argue an `electric’-`magnetic’ interplay can lead to an amplified, strong-scale cross-section in an analogue of the Callan-Rubakov effect.
    The cosmological lithium problem—that theory predicts a primordial abundance thrice as high as that observed—has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We suggest cosmic strings have disintegrated O(1) of the primordial lithium nuclei and estimate the rate in a benchmark scenario. To our knowledge this is the first new physics mechanism with microphysical justification for the abundance of lithium uniquely to be modified after Big Bang Nucleosynthesis.

    2:30–3:00 pmYann GouttenoireTitle: Supercool Composite Dark Matter beyond 100 TeV

     

    Phase-Transitions_Poster

  • CMSA EVENT: Advances in Mathematical Physics
    9:00 am-1:45 pm
    12/01/2024-08/01/2022
    1 Oxford Street, Cambridge MA 02138
    Elliott-Lieb-conference-2022_banner-2-1536x734

    A Conference in Honor of Elliott H. Lieb on his 90th Birthday

    On July 30 – Aug 1, 2022 the Harvard Mathematics Department and the CMSA co-hosted a birthday conference in honor of Elliott Lieb.

    This meeting highlights Elliott’s vast contribution to math and physics. Additionally, this meeting features Prof. Lieb’s more recent impact in strong subadditivity of entropy and integrable systems (ice model, Temperley-Lieb algebra etc.).

    Venue:

    July 30–31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
    August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138

    Schedule (pdf)

    Organizers:
    Michael Aizenman, Princeton University
    Joel Lebowitz, Rutgers University
    Ruedi Seiler, Technische Universität Berlin
    Herbert Spohn, Technical University of Munich
    Horng-Tzer Yau, Harvard University
    Shing-Tung Yau, Harvard University
    Jakob Yngvason, University of Vienna

    SPEAKERS:
    Rafael Benguria, Pontificia Universidad Catolica de Chile
    Eric Carlen, Rutgers University
    Philippe Di Francesco, University of Illinois
    Hugo Duminil-Copin, IHES
    László Erdös, Institute of Science and Technology Austria
    Rupert Frank, Ludwig Maximilian University of Munich
    Jürg Fröhlich, ETH Zurich
    Alessandro Giuliani, Università degli Studi Roma Tre
    Bertrand Halperin, Harvard University
    Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
    Sabine Jansen, Ludwig Maximilian University of Munich
    Mathieu Lewin, Université Paris-Dauphine
    Bruno Nachtergaele, The University of California, Davis
    Yoshiko Ogata, University of Tokyo
    Ron Peled, Tel Aviv University
    Benjamin Schlein, University of Zurich
    Robert Seiringer, Institute of Science and Technology Austria
    Jan Philip Solovej, University of Copenhagen
    Hal Tasaki, Gakushuin University
    Simone Warzel, Technical University of Munich
    Jun Yin, The University of California, Los Angeles

     

    Elliott-Lieb-conference

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    CMSA Interdisciplinary Science Seminar

    Speaker: Sumit Sinha, Harvard University

    Title: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data (https://arxiv.org/abs/2202.10595)

    Abstract: Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.

    Bio: I am a postdoctoral fellow in Harvard SEAS (Applied Mathematics) and Dana Farber Cancer Institute (Data Science) beginning Feb 2022. I finished my PhD in Physics (Theoretical Biophysics) from UT Austin (Jan 2022) on “Theoretical and computational studies of growing tissue”.  I pursued my undergraduate degree in Physics from the Indian Institute of Technology, Kanpur in India (2015). Boradly, I am interested in developing theoretical models, inspired from many-body statistical physics, for biological processes at different length and time scales.

     

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024

    Abstract: The establishment of neural circuitry during early infancy is critical for developing visual, auditory, and motor functions. However, how cortical tissue develops postnatally is largely unknown. By combining T1 relaxation time from quantitative MRI and mean diffusivity (MD) from diffusion MRI, we tracked cortical tissue development in infants across three timepoints (newborn, 3 months, and 6 months). Lower T1 and MD indicate higher microstructural tissue density and more developed cortex. Our data reveal three main findings: First, primary sensory-motor areas (V1: visual, A1: auditory, S1: somatosensory, M1: motor) have lower Tand MD at birth than higher-level cortical areas. However, all primary areas show significant reductions in Tand MD in the first six months of life, illustrating profound tissue growth after birth. Second, significant reductions in Tand MD from newborns to 6-month-olds occur in all visual areas of the ventral and dorsal visual streams. Strikingly, this development was heterogenous across the visual hierarchies: Earlier areas are more developed with denser tissue at birth than higher-order areas, but higher-order areas had faster rates of development. Finally, analysis of transcriptomic gene data that compares gene expression in postnatal vs. prenatal tissue samples showed strong postnatal expression of genes associated with myelination, synaptic signaling, and dendritic processes. Our results indicate that these cellular processes may contribute to profound postnatal tissue growth in sensory cortices observed in our in-vivo measurements. We propose a novel principle of postnatal maturation of sensory systems: development of cortical tissue proceeds in a hierarchical manner, enabling the lower-level areas to develop first to provide scaffolding for higher-order areas, which begin to develop more rapidly following birth to perform complex computations for vision and audition.

    This work is published here: https://www.nature.com/articles/s42003-021-02706-w

  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-07.14.22-1583x2048

    Abstract:  Introducing internal degrees of freedom in the description of crystalline insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses. Here, we present a semiclassical approach to transport and accumulation of general spinor degrees of freedom in adiabatically driven, weakly inhomogeneous crystals of dimensions one, two and three under external electromagnetic fields. Our approach shows that spatio-temporal modulations of the system induce a spinor current and density that is related to geometrical and topological objects — the spinor-Chern fluxes and numbers — defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates.

    The results are available here: https://arxiv.org/abs/2203.14902

    Bio: Ioannis Petrides is a postdoctoral fellow at the School of Engineering and Applied Sciences at Harvard University. He received his Ph.D. from the Institute for Theoretical Physics at ETH Zurich. His research focuses on the topological and geometrical aspects of condensed matter systems.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/15/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar
    9:00 am-10:00 am
    12/01/2024
    Interdisciplinary Science Seminar
    Speaker: Fouad El Baidouri, Broad Institute

    Title: The phenotype of the last universal common ancestor and the evolution of complexity

    Abstract: A fundamental concept in evolutionary theory is the last universal common ancestor (LUCA) from which all living organisms originated. While some authors have suggested a relatively complex LUCA it is still widely assumed that LUCA must have been a very simple cell and that life has subsequently increased in complexity through time. However, while current thought does tend towards a general increase in complexity through time in Eukaryotes, there is increasing evidence that bacteria and archaea have undergone considerable genome reduction during their evolution. This raises the surprising possibility that LUCA, as the ancestor of bacteria and archaea may have been a considerably complex cell. While hypotheses regarding the phenotype of LUCA do exist, all are founded on gene presence/absence. Yet, despite recent attempts to link genes and phenotypic traits in prokaryotes, it is still inherently difficult to predict phenotype based on the presence or absence of genes alone. In response to this, we used Bayesian phylogenetic comparative methods to predict ancestral traits. Testing for robustness to horizontal gene transfer (HGT) we inferred the phenotypic traits of LUCA using two robust published phylogenetic trees and a dataset of 3,128 bacterial and archaeal species.

    Our results depict LUCA as a far more complex cell than has previously been proposed, challenging the evolutionary model of increased complexity through time in prokaryotes. Given current estimates for the emergence of LUCA we suggest that early life very rapidly evolved cellular complexity.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    6/24/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Some new algorithms in statistical genomics

    9:00 am-10:00 am
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-06.23.2022-1583x2048-1

    Abstract: The statistical analysis of genomic data has incubated many innovations for computational method development. This talk will discuss some simple algorithms that may be useful in analyzing such data. Examples include algorithms for efficient resampling-based hypothesis testing, minimizing the sum of truncated convex functions, and fitting equality-constrained lasso problems. These algorithms have the potential to be used in other applications beyond statistical genomics.

    Bio: Hui Jiang is an Associate Professor in the Department of Biostatistics at the University of Michigan. He received his Ph.D. in Computational and Mathematical Engineering from Stanford University. Before joining the University of Michigan, he was a postdoc in the Department of Statistics and Stanford Genome Technology Center at Stanford University. He is interested in developing statistical and computational methods for analyzing large-scale biological data generated using modern high-throughput technologies.

  • Math Science Literature Lecture Series
    9:00 am-10:30 am
    12/01/2024

    Peter Shor (MIT)

    TitleQuantum error correcting codes and fault tolerance

    Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field.

    Talk chair: Zhengwei Liu

    Video

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    The number of n-queens configurations

    9:00 am-10:00 am
    12/01/2024

    Speaker: Michael Simkin, Harvard CMSA

    Title: The number of n-queens configurations

    Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

    Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    6/10/2021 Interdisciplinary Science Seminar

    9:00 am-10:00 am
    12/01/2024
  • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
    9:00 am-12:00 pm
    12/01/2024-01/13/2017
    banner-image-1

    The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

     

    Confirmed Participants:

  • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
    9:00 am-5:00 pm
    12/01/2024-05/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Organizers:

    D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

    Speakers:

    1. Netanel Blaier (MIT)
    2. Kwokwai Chan (CUHK)
    3. Bohan Fang (Peking University)
    4. Amanda Francis (BYU)
    5. Hansol Hong (CUHK)
    6. Heather Lee (Purdue University)
    7. Si Li (Tsinghua University)
    8. Yu-Shen Lin (Stanford University)
    9. Alex Perry (Harvard University)
    10. Hiro Tanaka (Harvard University)
    11. Sara Tukachinsky (HUJ)
    12. Michael Viscardi (MIT)
    13. Eric Zaslow (Northwestern University)
    14. Jingyu Zhao (Columbia University)

    Please click here for the conference Main Website.

    Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Schedule:

    May 6 – Day 1
    9:00amBreakfast
    9:35amOpening remarks
    9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
    10:45am – 11:15amBreak
    11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
    May 7 – Day 2
    9:00amBreakfast
    9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
    10:45am – 11:15amBreak
    11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
    4:00pm – 4:15pmBreak
    4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
    May 8 – Day 3
    9:00amBreakfast
    9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
    10:45am – 11:15amBreak
    11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
    12:15pm – 1:45pmLunch
    1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
    2:45pm – 3:00pmBreak
    3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
    * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

    This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Adventures in Perturbation Theory

    9:00 am-10:00 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-01.25.2022-1

    Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The Amplituhedron BCFW Triangulation

    9:00 am-10:00 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-2.3.2022

    Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

  • CMSA EVENT: Workshop on Optimization in Image Processing
    9:00 am-12:30 pm
    12/01/2024-06/30/2016

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Speakers:

    1. Antonin Chambolle, CMAP, Ecole Polytechnique
    2. Raymond Chan, The Chinese University of Hong Kong
    3. Ke Chen, University of Liverpool
    4. Patrick Louis Combettes, Université Pierre et Marie Curie
    5. Mario Figueiredo, Instituto Superior Técnico
    6. Alfred Hero, University of Michigan
    7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
    8. Mila Nikolova, Ecole Normale Superieure Cachan
    9. Shoham Sabach, Israel Institute of Technology
    10. Martin Benning, University of Cambridge
    11. Jin Keun Seo, Yonsei University
    12. Fiorella Sgallari, University of Bologna
    13. Gabriele Steidl, Kaiserslautern University of Technology
    14. Joachim Weickert, Saarland University
    15. Isao Yamada, Tokyo Institute of Technology
    16. Wotao Yin, UCLA

    Please click Workshop Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

    Schedule:

    June 27 – Day 1
    9:00amBreakfast
    9:20amOpening remarks
    9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
    10:20am – 10:50amBreak
    10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
    11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
    12:30pm – 2:00pmLunch
    2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
    June 28 – Day 2
    9:00amBreakfast
    9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
    10:20am – 10:50amBreak
    10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
    11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 4:40pmDiscussions
    June 29 – Day 3
    9:00amBreakfast
    9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
    10:20am – 10:50amBreak
    10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
    11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
    12:30pm – 2:30pmLunch
    2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
    3:20pm – 3:50pmBreak
    3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
    June 30 – Day 4
    9:00amBreakfast
    9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
    10:20am – 10:50amBreak
    10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
    11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
    * This event is sponsored by CMSA Harvard University.

    Organizers: Raymond Chan and Shing-Tung Yau

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA/Tsinghua Math-Science Literature Lecture: Scott Kominers

    9:00 am-10:30 am
    12/01/2024

    CMSA/Tsinghua Math-Science Literature Lecture

    Prof. Scott Kominers will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

    Date: Monday, November 20, 2023

    Time: 9:00 – 10:30 am ET

    Location: Via Zoom Webinar

    Registration is required.

    Title: 60 Years of Matching: From Gale and Shapley to Trading Networks

    Abstract: Gale and Shapley’s 1962 American Mathematical Monthly paper, “College Admissions and the Stability of Marriage,” is by now one of the most cited articles in the journal’s history, having served as the foundation for an entire branch of the field of market design. This success owes in large part to the beautiful, applicable, and surprisingly general theory of matching mechanisms uncovered in Gale and Shapley’s work. This talk traces the history and evolution of matching theory from that paper forward to the present day, along the way touching on real-world applications to everything from medical residency matching to electricity markets.

    Moderator: Sergiy Verstyuk


    Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

     

    CMSA COVID-19 Policies

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    10/19/2021 Combinatorics, Physics and Probability Seminar

    9:00 am-10:00 am
    12/01/2024

    Title: Ising model, total positivity, and criticality

    Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
    The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
    I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model

  • Workshop
    9:00 am-5:00 pm
    12/01/2024-05/19/2023
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    GRAMSIAcover-600x338

    On May 16 – May 19, 2023 the CMSA hosted a four-day workshop on GRAMSIA: Graphical Models, Statistical Inference, and Algorithms. The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop was organized by David Gamarnik (MIT), Kavita Ramanan (Brown), and Prasad Tetali  (Carnegie Mellon).

    The purpose of this workshop is to highlight various mathematical questions and issues associated with graphical models and message-passing algorithms, and to bring together a group of researchers for discussion of the latest progress and challenges ahead. In addition to the substantial impact of graphical models on applied areas, they are also connected to various branches of the mathematical sciences. Rather than focusing on the applications, the primary goal is to highlight and deepen these mathematical connections.

    Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

     

    Speakers:
    • Jake Abernethy (Georgia Tech)
    • Guy Bresler (MIT)
    • Florent Krzakala (Ecole Polytechnique Federale de Lausanne)
    • Lester Mackey (Microsoft Research New England)
    • Theo McKenzie (Harvard)
    • Andrea Montanari (Stanford)
    • Elchanan Mossel (MIT)
    • Yury Polyanskiy (MIT)
    • Patrick Rebeschini (Oxford)
    • Subhabrata Sen (Harvard)
    • Devavrat Shah (MIT)
    • Pragya Sur (Harvard)
    • Alex Wein (UC Davis)
    • Yihong Wu (Yale)
    • Sarath Yasodharan (Brown)
    • Horng-Tzer Yau (Harvard)
    • Christina Lee Yu (Cornell)
    • Ilias Zadik (MIT)
    Schedule:

    Tuesday, May 16, 2023

    9:00 amBreakfast
    9:15 – 9:30 amIntroductory remarks by organizers
    9:30 – 10:20 amSubhabrata Sen (Harvard)

    Title: Mean-field approximations for high-dimensional Bayesian regression

    Abstract: Variational approximations provide an attractive computational alternative to MCMC-based strategies for approximating the posterior distribution in Bayesian inference. The Naive Mean-Field (NMF) approximation is the simplest version of this strategy—this approach approximates the posterior in KL divergence by a product distribution. There has been considerable progress recently in understanding the accuracy of NMF under structural constraints such as sparsity, but not much is known in the absence of such constraints. Moreover, in some high-dimensional settings, the NMF is expected to be grossly inaccurate, and advanced mean-field techniques (e.g. Bethe approximation) are expected to provide accurate approximations. We will present some recent work in understanding this duality in the context of high-dimensional regression. This is based on joint work with Sumit Mukherjee (Columbia) and Jiaze Qiu (Harvard University).

    10:30 – 11:00 amCoffee break 
    11:00 – 11:50 amElchanan Mossel (MIT)

    Title: Some modern perspectives on the Kesten-Stigum bound for reconstruction on trees.

    Abstract: The Kesten-Stigum bound is a fundamental spectral bound for reconstruction on trees. I will discuss some conjectures and recent progress on understanding when it is tight as well as some conjectures and recent progress on what it signifies even in cases where it is not tight.

    12:00 – 2:00 pmLunch
    2:00 – 2:50 pmChristina Lee Yu (Cornell)

    Title: Exploiting Neighborhood Interference with Low Order Interactions under Unit Randomized Design

    Abstract: Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in many real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we utilize knowledge of the network structure to provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. Central to our contribution is a new framework for balancing between model flexibility and statistical complexity as captured by this low order interactions structure.

    3:00 – 3:30 pmCoffee break
    3:30 – 4:20 pmTheo McKenzie (Harvard)

    Title: Spectral statistics for sparse random graphs

    Abstract: Understanding the eigenvectors and eigenvalues of the adjacency matrix of random graphs is fundamental to many algorithmic questions; moreover, it is related to longstanding questions in quantum physics. In this talk we focus on random models of sparse graphs, giving some properties that are unique to these sparse graphs, as well as some specific obstacles. Based on this, we show some new results on spectral statistics of sparse random graphs, as well as some conjectures.

    4:40 – 6:30 pmLightning talk session + welcome reception

     

    Wednesday, May 17, 2023

    9:00 amBreakfast
    9:30 – 10:20Ilias Zadik (MIT)

    Title: Revisiting Jerrum’s Metropolis Process for the Planted Clique Problem

    Abstract: Jerrum in 1992 (co-)introduced the planted clique model by proving the (worst-case initialization) failure of the Metropolis process to recover any o(sqrt(n))-sized clique planted in the Erdos-Renyi graph G(n,1/2). This result is classically cited in the literature of the problem, as the “first evidence” the o(sqrt(n))-sized planted clique recovery task is “algorithmically hard”.
    In this work, we show that the Metropolis process actually fails to work (under worst-case initialization) for any o(n)-sized planted clique, that is the failure applies well beyond the sqrt(n) “conjectured algorithmic threshold”. Moreover we also prove, for a large number of temperature values, that the Metropolis process fails also under “natural initialization”, resolving an open question posed by Jerrum in 1992.

    10:30 – 11:00Coffee break
    11:00 – 11:50Florent Krzakala (Ecole Polytechnique Federale de Lausanne)

    Title: Are Gaussian data all you need for machine learning theory?

    Abstract: Clearly, no! Nevertheless, the Gaussian assumption remains prevalent among theoreticians, particularly in high-dimensional statistics and physics, less so in traditional statistical learning circles. To what extent are Gaussian features merely a convenient choice for certain theoreticians, or genuinely an effective model for learning? In this talk, I will review recent progress on these questions, achieved using rigorous probabilistic approaches in high-dimension and techniques from mathematical statistical physics. I will demonstrate that, despite its apparent limitations, the Gaussian approach is sometimes much closer to reality than one might expect. In particular, I will discuss key findings from a series of recent papers that showcase the Gaussian equivalence of generative models, the universality of Gaussian mixtures, and the conditions under which a single Gaussian can characterize the error in high-dimensional estimation. These results illuminate the strengths and weaknesses of the Gaussian assumption, shedding light on its applicability and limitations in the realm of theoretical statistical learning.

    12:00 – 2:00 pmLunch
    2:00 – 2:50 pmAndrea Montanari (Stanford)

    Title: Dimension free ridge regression

    Abstract: Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we revisit ridge regression. We allow the feature vector to be high-dimensional, or even infinite-dimensional, in which case it belongs to a separable Hilbert space and assume it to satisfy a certain convex concentration property. Within this setting, we establish non-asymptotic bounds that approximate the bias and variance of ridge regression in terms of the bias and variance of an ‘equivalent’ sequence model (a regression model with diagonal design matrix). Previously, such an approximation result was known only in the proportional regime and only up to additive errors: in particular, it did not allow to characterize the behavior of the excess risk when this converges to 0. Our general theory recovers earlier results in the proportional regime (with better error rates). As a new application, we obtain a completely explicit and sharp characterization of ridge regression for Hilbert covariates with regularly varying spectrum. Finally, we analyze the overparametrized near-interpolation setting and obtain sharp ‘benign overfitting’ guarantees.

    [Based on joint work with Chen Cheng]

    3:00 – 3:50 pmYury Polyanskiy (MIT)

    Title: Recent results on broadcasting on trees and stochastic block model

    Abstract: I will survey recent results and open questions regarding the q-ary stochastic block model and its local version (broadcasting on trees, or BOT). For example, establishing uniqueness of non-trivial solution to distribution recursions (BP fixed point) implies a characterization for the limiting mutual information between the graph and community labels. For q=2 uniqueness holds in all regimes. For q>2 uniqueness is currently only proved above a certain threshold that is asymptotically (for large q) is close to Kesten-Stigum (KS) threshold. At the same time between the BOT reconstruction and KS we show that uniqueness does not hold, at least in the presence of (arbitrary small) vertex-level side information. I will also discuss extension of the robust reconstruction result of Janson-Mossel’2004.

    Based on joint works with Qian Yu (Princeton) and Yuzhou Gu (MIT).

    4:00 – 4:30 pmCoffee break
    4:30 – 5:20 pmAlex Wein (UC Davis)

    Title: Is Planted Coloring Easier than Planted Clique?

    Abstract: The task of finding a planted clique in the random graph G(n,1/2) is perhaps the canonical example of a statistical-computational gap: for some clique sizes, the task is statistically possible but believed to be computationally hard. Really, there are multiple well-studied tasks related to the planted clique model: detection, recovery, and refutation. While these are equally difficult in the case of planted clique, this need not be true in general. In the related planted coloring model, I will discuss the computational complexity of these three tasks and the interplay among them. Our computational hardness results are based on the low-degree polynomial model of computation.By taking the complement of the graph, the planted coloring model is analogous to the planted clique model but with many planted cliques. Here our conclusion is that adding more cliques makes the detection problem easier but not the recovery problem.

     

    Thursday, May 18, 2023

    9:00Breakfast
    9:30 – 10:20Guy Bresler (MIT)

    Title: Algorithmic Decorrelation and Planted Clique in Dependent Random Graphs

    Abstract: There is a growing collection of average-case reductions starting from Planted Clique (or Planted Dense Subgraph) and mapping to a variety of statistics problems, sharply characterizing their computational phase transitions. These reductions transform an instance of Planted Clique, a highly structured problem with its simple clique signal and independent noise, to problems with richer structure. In this talk we aim to make progress in the other direction: to what extent can these problems, which often have complicated dependent noise, be transformed back to Planted Clique? Such a bidirectional reduction between Planted Clique and another problem shows a strong computational equivalence between the two problems.  We develop a new general framework for reasoning about the validity of average-case reductions based on low sensitivity to perturbations. As a concrete instance of our general result, we consider the planted clique (or dense subgraph) problem in an ambient graph that has dependent edges induced by randomly adding triangles to the Erdos-Renyi graph G(n,p), and show how to successfully eliminate dependence by carefully removing the triangles while approximately preserving the clique (or dense subgraph). Joint work with Chenghao Guo and Yury Polyanskiy.

    10:30 – 11:00Coffee break 
    11:00 – 11:50Sarath Yasodharan (Brown)

    Title: A Sanov-type theorem for unimodular marked random graphs and its applications

    Abstract: We prove a Sanov-type large deviation principle for the component empirical measures of certain sequences of unimodular random graphs (including Erdos-Renyi and random regular graphs) whose vertices are marked with i.i.d. random variables. Specifically, we show that the rate function can be expressed in a fairly tractable form involving suitable relative entropy functionals. As a corollary, we establish a variational formula for the annealed pressure (or limiting log partition function) for various statistical physics models on sparse random graphs. This is joint work with I-Hsun Chen and Kavita Ramanan.

    12:00 – 12:15 pm

    12:15 – 2:00 pm

    Group Photo

    Lunch

    2:00 – 2:50 pmPatrick Rebeschini (Oxford)

    Title: Implicit regularization via uniform convergence

    Abstract: Uniform convergence is one of the main tools to analyze the complexity of learning algorithms based on explicit regularization, but it has shown limited applicability in the context of implicit regularization. In this talk, we investigate the statistical guarantees on the excess risk achieved by early-stopped mirror descent run on the unregularized empirical risk with the squared loss for linear models and kernel methods. We establish a direct link between the potential-based analysis of mirror descent from optimization theory and uniform learning. This link allows characterizing the statistical performance of the path traced by mirror descent directly in terms of localized Rademacher complexities of function classes depending on the choice of the mirror map, initialization point, step size, and the number of iterations. We will discuss other results along the way.

    3:00 – 3:50 pmPragya Sur (Harvard)

    Title: A New Central Limit Theorem for the Augmented IPW estimator in high dimensions

    Abstract: Estimating the average treatment effect (ATE) is a central problem in causal inference. Modern advances in the field studied estimation and inference for the ATE in high dimensions through a variety of approaches. Doubly robust estimators such as the augmented inverse probability weighting (AIPW) form a popular approach in this context. However, the high-dimensional literature surrounding these estimators relies on sparsity conditions, either on the outcome regression (OR) or the propensity score (PS) model. This talk will introduce a new central limit theorem for the classical AIPW estimator, that applies agnostic to such sparsity-type assumptions. Specifically, we will study properties of the cross-fit version of the estimator under well-specified OR and PS models, and the proportional asymptotics regime where the number of confounders and sample size diverge proportional to each other. Under assumptions on the covariate distribution, our CLT will uncover two crucial phenomena among others: (i) the cross-fit AIPW exhibits a substantial variance inflation that can be quantified in terms of the signal-to-noise ratio and other problem parameters, (ii) the asymptotic covariance between the estimators used while cross-fitting is non-negligible even on the root-n scale. These findings are strikingly different from their classical counterparts, and open a vista of possibilities for studying similar other high-dimensional effects. On the technical front, our work utilizes a novel interplay between three distinct tools—approximate message passing theory, the theory of deterministic equivalents, and the leave-one-out approach.

    4:00 – 4:30 pmCoffee break
    4:30 – 5:20 pmYihong Wu (Yale)

    Title: Random graph matching at Otter’s threshold via counting chandeliers

    Abstract: We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erdős–Rényi graphs G(n,q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nq\to\infty and the edge correlation coefficient ρ satisfies ρ^2>α≈0.338, where α is Otter’s tree-counting constant. Moreover, this almost exact matching can be made exact under an extra condition that is information-theoretically necessary. This is the first polynomial-time graph matching algorithm that succeeds at an explicit constant correlation and applies to both sparse and dense graphs. In comparison, previous methods either require ρ=1−o(1) or are restricted to sparse graphs. The crux of the algorithm is a carefully curated family of rooted trees called chandeliers, which allows effective extraction of the graph correlation from the counts of the same tree while suppressing the undesirable correlation between those of different trees. This is joint work with Cheng Mao, Jiaming Xu, and Sophie Yu, available at https://arxiv.org/abs/2209.12313

     

    Friday, May 19, 2023

    9:00Breakfast
    9:30 – 10:20Jake Abernethy (Georgia Tech)

    Title: Optimization, Learning, and Margin-maximization via Playing Games

    Abstract: A very popular trick for solving certain types of optimization problems is this: write your objective as the solution of a two-player zero-sum game, endow both players with an appropriate learning algorithm, watch how the opponents compete, and extract an (approximate) solution from the actions/decisions taken by the players throughout the process. This approach is very generic and provides a natural template to produce new and interesting algorithms. I will describe this framework and show how it applies in several scenarios, including optimization, learning, and margin-maximiation problems. Along the way we will encounter a number of novel tools and rediscover some classical ones as well.

    10:30 – 11:00Coffee break 
    11:00 – 11:50Devavrat Shah (MIT)

    Title: On counterfactual inference with unobserved confounding via exponential family

    Abstract: We are interested in the problem of unit-level counterfactual inference with unobserved confounders owing to the increasing importance of personalized decision-making in many domains: consider a recommender system interacting with a user over time where each user is provided recommendations based on observed demographics, prior engagement levels as well as certain unobserved factors. The system adapts its recommendations sequentially and differently for each user. Ideally, at each point in time, the system wants to infer each user’s unknown engagement if it were exposed to a different sequence of recommendations while everything else remained unchanged. This task is challenging since: (a) the unobserved factors could give rise to spurious associations, (b) the users could be heterogeneous, and (c) only a single trajectory per user is available.

    We model the underlying joint distribution through an exponential family. This reduces the task of unit-level counterfactual inference to simultaneously learning a collection of distributions of a given exponential family with different unknown parameters with single observation per distribution. We discuss a computationally efficient method for learning all of these parameters with estimation error scaling linearly with the metric entropy of the space of unknown parameters – if the parameters are an s-sparse linear combination of k known vectors in p dimension, the error scales as O(s log k/p).  En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality.

    Based on a joint work with Raaz Dwivedi, Abhin Shah and Greg Wornell (all at MIT) with manuscript available here: https://arxiv.org/abs/2211.08209

    12:00 – 2:00 pmLunch 
    2:00 – 2:50 pmLester Mackey  (Microsoft Research New England)

    Title: Advances in Distribution Compression

    Abstract: This talk will introduce two new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning:
    1. Given an initial n-point summary (for example, from independent sampling or a Markov chain), kernel thinning finds a subset of only square-root n-points with comparable worst-case integration error across a reproducing kernel Hilbert space.
    2. If the initial summary suffers from biases due to off-target sampling, tempering, or burn-in, Stein thinning simultaneously compresses the summary and improves the accuracy by correcting for these biases.
    These tools are especially well-suited for tasks that incur substantial downstream computation costs per summary point like organ and tissue modeling in which each simulation consumes 1000s of CPU hours.
    Based on joint work with Raaz Dwivedi, Marina Riabiz, Wilson Ye Chen, Jon Cockayne, Pawel Swietach, Steven A. Niederer, Chris. J. Oates, Abhishek Shetty, and Carles Domingo-Enrich.

    3:00 – 3:30 pmCoffee break
    3:30 – 4:20 pmHorng-Tzer Yau (Harvard)

    Title: On the spectral gap of mean-field spin glass models.

    Abstract: We will discuss recent progress regarding spectral gaps for the Glauber dynamics of spin glasses at high temperature. In addition, we will also report on estimating the operator norm  of the covariance matrix for the SK model.

     

    Moderators: Benjamin McKenna, Harvard CMSA & Changji Xu, Harvard CMSA


     

    CMSA COVID-19 Policies

     

  • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
    9:00 am-5:00 pm
    12/01/2024-12/04/2016

    The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

    The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

    Please click here to register for this event.

    Speakers:

    1. Cliff Taubes (Harvard University)
    2. Valentino Tosatti (Northwestern University)
    3. Pengfei Guan (McGill University)
    4. Jared Speck (MIT)

    Schedule:

    December 3rd – Day 1
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
    December 4th – Day 2
    9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
    10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
    12:15pm – 1:45pmLUNCH
    1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
    3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

    Please click Mini-School Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • CMSA EVENT: Mirror symmetry, gauged linear sigma models, matrix factorizations, and related topics
    9:00 am-4:30 pm
    12/01/2024-03/06/2020
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Mirror-Symmetry-poster-1

    On March 4-6, 2020 the CMSA will be hosting a three-day workshop on Mirror symmetry, Gauged linear sigma models, Matrix factorizations, and related topics as part of the Simons Collaboration on Homological Mirror Symmetry. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    Speakers: 

    Schedule

    Videos from the workshop are available in the Youtube playlist.

  • CMSA EVENT: Quantum Matter Workshop
    9:00 am-5:00 pm
    12/01/2024-12/04/2019
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Quantum Matter Workshop

    On December 2-4, 2019 the CMSA will be hosting a workshop on Quantum Matter as part of our program on Quantum Matter in Mathematics and Physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Pictures can be found here.

    Organizers: Juven Wang (CMSA), Xiao-Gang Wen (MIT), and Shing-Tung Yau (Harvard)

    Confirmed Speakers: 

     

  • CMSA EVENT: Workshop on Coding and Information Theory
    9:00 am-3:30 pm
    12/01/2024-04/13/2018

    The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

    Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    Click here for a list of registrants. 

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

  • Workshop
    9:00 am-6:00 pm
    12/01/2024-05/12/2023
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    The CMSA will be hosting a Workshop on Global Categorical Symmetries from May 7 – 12, 2023

    Participation in the workshop is by invitation.

    Public Lectures

    There will be three lectures on Thursday, May 11, 2023, which are open to the public.
    Location:  Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
    Note: The public lectures will be held in-person only.

    2:00 – 2:50 pm
    Speaker: Kantaro Ohmori (U Tokyo )
    Title: Fusion Surface Models: 2+1d Lattice Models from Higher Categories
    Abstract: Generalized symmetry in general dimensions is expected to be described by higher categories. Conversely, one might expect that, given a higher category with appropriate structures, there exist models that admit the category as its symmetry. In this talk I will explain a construction of such 2+1d lattice models for fusion 2-categories defined by Douglas and Reutter, generalizing the work of Aasen, Fendley and Mong on anyon chains. The construction is by decorating a boundary of a topological Freed-Teleman-Moore sandwich into a non-topological boundary. In particular we can construct a family of candidate lattice systems for chiral topological orders.

     

    3:00 – 3:50 pm
    Speaker: David Jordan (Edinburgh)
    Title: Langlands duality for 3-manifolds
    Abstract: Originating in number theory, and permeating representation theory, algebraic geometry, and quantum field theory, Langlands duality is a pattern of predictions relating pairs of mathematical objects which have no clear a priori mathematical relation. In this talk I’ll explain a new conjectural appearance of Langlands duality in the setting of 3-manifold topology, I’ll give some evidence in the form of special cases, and I’ll survey how the conjecture relates to both the arithmetic and geometric Langlands duality conjectures.

    3:50 – 4:30 pm
    Tea/Snack Break

    4:30 – 5:30 pm
    Speaker: Ken Intriligator (UCSD)
    Colloquium
    Title: QFT Aspects of Symmetry
    Abstract: Everything in the Universe, including the photons that we see and the quarks and electrons in our bodies, are actually ripples of quantum fields. Quantum field theory (QFT) is the underlying mathematical framework of Nature, and in the case of electrons and photons it is the most precisely tested theory in science. Strongly coupled aspects, e.g. the confinement of quarks and gluons at long distances, remain challenging. QFT also describes condensed matter systems, connects to string theory and quantum gravity, and describes cosmology. Symmetry has deep and powerful realizations and implications throughout physics, and this is especially so for the study of QFT. Symmetries play a helpful role in characterizing the phases of theories and their behavior under renormalization group flows (zooming out). Quantum field theory has also been an idea generating machine for mathematics, and there has been increasingly fruitful synergy in both directions. We are currently exploring the symmetry-based interconnections between QFT and mathematics in our Simons Collaboration on Global Categorical Symmetry, which is meeting here this week. I will try to provide an accessible, colloquium-level introduction to aspects of symmetries and QFT, both old and new.


  • CMSA EVENT: Big Data Conference 2023
    9:00 am-5:00 pm
    12/01/2024-09/01/2023
    1 Oxford Street, Cambridge MA 02138

    On August 31-Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    Location: Harvard University Science Center Hall D & via Zoom.

    Directions and Recommended Lodging

    Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

    Registration is required.

    Note: In-person registration is at capacity. Please sign up for the Zoom Webinar (registration link).

     

    Speakers:

     

    Organizers:

    • Michael Douglas, CMSA, Harvard University
    • Yannai Gonczarowski, Economics and Computer Science, Harvard University
    • Lucas Janson, Statistics and Computer Science, Harvard University
    • Tracy Ke, Statistics, Harvard University
    • Horng-Tzer Yau, Mathematics and CMSA, Harvard University
    • Yue Lu, Electrical Engineering and Applied Mathematics, Harvard University

    Schedule

    (PDF download)

    Thursday, August 31, 2023

    9:00 AMBreakfast
    9:30 AMIntroductions
    9:45–10:45 AMAlbert-László Barabási (Northeastern, Harvard)

    Title: From Network Medicine to the Foodome: The Dark Matter of Nutrition

    Abstract: A disease is rarely a consequence of an abnormality in a single gene but reflects perturbations to the complex intracellular network. Network medicine offer a platform to explore systematically not only the molecular complexity of a particular disease, leading to the identification of disease modules and pathways, but also the molecular relationships between apparently distinct (patho) phenotypes. As an application, I will explore how we use network medicine to uncover the role individual food molecules in our health. Indeed, our current understanding of how diet affects our health is limited to the role of 150 key nutritional components systematically tracked by the USDA and other national databases in all foods. Yet, these nutritional components represent only a tiny fraction of the over 135,000 distinct, definable biochemicals present in our food. While many of these biochemicals have documented effects on health, they remain unquantified in any systematic fashion across different individual foods. Their invisibility to experimental, clinical, and epidemiological studies defines them as the ‘Dark Matter of Nutrition.’ I will speak about our efforts to develop a high-resolution library of this nutritional dark matter, and efforts to understand the role of these molecules on health, opening novel avenues by which to understand, avoid, and control disease.

    https://youtu.be/UmgzUwi6K3E

    10:45–11:00 AMBreak
    11:00 AM–12:00 PMRachel Cummings (Columbia)

    Title: Differentially Private Algorithms for Statistical Estimation Problems

    Abstract: Differential privacy (DP) is widely regarded as a gold standard for privacy-preserving computation over users’ data.  It is a parameterized notion of database privacy that gives a rigorous worst-case bound on the information that can be learned about any one individual from the result of a data analysis task. Algorithmically it is achieved by injecting carefully calibrated randomness into the analysis to balance privacy protections with accuracy of the results.
    In this talk, we will survey recent developments in the development of DP algorithms for three important statistical problems, namely online learning with bandit feedback, causal interference, and learning from imbalanced data. For the first problem, we will show that Thompson sampling — a standard bandit algorithm developed in the 1930s — already satisfies DP due to the inherent randomness of the algorithm. For the second problem of causal inference and counterfactual estimation, we develop the first DP algorithms for synthetic control, which has been used non-privately for this task for decades. Finally, for the problem of imbalanced learning, where one class is severely underrepresented in the training data, we show that combining existing techniques such as minority oversampling perform very poorly when applied as pre-processing before a DP learning algorithm; instead we propose novel approaches for privately generating synthetic minority points.

    Based on joint works with Marco Avella Medina, Vishal Misra, Yuliia Lut, Tingting Ou, Saeyoung Rho, and Ethan Turok.

    https://youtu.be/0cPE6rb1Roo

    12:00–1:30 PMLunch
    1:30–2:30 PMMorgane Austern (Harvard)

    Title: To split or not to split that is the question: From cross validation to debiased machine learning

    Abstract: Data splitting is a ubiquitous method in statistics with examples ranging from cross-validation to cross-fitting. However, despite its prevalence, theoretical guidance regarding its use is still lacking. In this talk, we will explore two examples and establish an asymptotic theory for it. In the first part of this talk, we study the cross-validation method, a ubiquitous method for risk estimation, and establish its asymptotic properties for a large class of models and with an arbitrary number of folds. Under stability conditions, we establish a central limit theorem and Berry-Esseen bounds for the cross-validated risk, which enable us to compute asymptotically accurate confidence intervals. Using our results, we study the statistical speed-up offered by cross-validation compared to a train-test split procedure. We reveal some surprising behavior of the cross-validated risk and establish the statistically optimal choice for the number of folds. In the second part of this talk, we study the role of cross-fitting in the generalized method of moments with moments that also depend on some auxiliary functions. Recent lines of work show how one can use generic machine learning estimators for these auxiliary problems, while maintaining asymptotic normality and root-n consistency of the target parameter of interest. The literature typically requires that these auxiliary problems are fitted on a separate sample or in a cross-fitting manner. We show that when these auxiliary estimation algorithms satisfy natural leave-one-out stability properties, then sample splitting is not required. This allows for sample reuse, which can be beneficial in moderately sized sample regimes.

    https://youtu.be/L_pHxgoQSgU

    2:30–2:45 PMBreak
    2:45–3:45 PMAnkur Moitra (MIT)

    Title: Learning from Dynamics

    Abstract: Linear dynamical systems are the canonical model for time series data. They have wide-ranging applications and there is a vast literature on learning their parameters from input-output sequences. Moreover they have received renewed interest because of their connections to recurrent neural networks.
    But there are wide gaps in our understanding. Existing works have only asymptotic guarantees or else make restrictive assumptions, e.g. that preclude having any long-range correlations. In this work, we give a new algorithm based on the method of moments that is computationally efficient and works under essentially minimal assumptions. Our work points to several missed connections, whereby tools from theoretical machine learning including tensor methods, can be used in non-stationary settings.

    https://youtu.be/UmgzUwi6K3E

    3:45–4:00 PMBreak
    4:00–5:00 PMMark Sellke (Harvard)

    Title: Algorithmic Thresholds for Spherical Spin Glasses

    Abstract: High-dimensional optimization plays a crucial role in modern statistics and machine learning. I will present recent progress on non-convex optimization problems with random objectives, focusing on the spherical p-spin glass. This model is related to spiked tensor estimation and has been studied in probability and physics for decades. We will see that a natural class of “stable” optimization algorithms gets stuck at an algorithmic threshold related to geometric properties of the landscape. The algorithmic threshold value is efficiently attained via Langevin dynamics or by a second-order ascent method of Subag. Much of this picture extends to other models, such as random constraint satisfaction problems at high clause density.

    https://youtu.be/JoghiwiIbT8

    6:00 – 8:00 PMBanquet for organizers and speakers

     

    Friday, September 1, 2023

    9:00 AMBreakfast
    9:30 AMIntroductions
    9:45–10:45 AMJacob Andreas (MIT)

    Title: What Learning Algorithm is In-Context Learning?

    Abstract: Neural sequence models, especially transformers, exhibit a remarkable capacity for “in-context” learning. They can construct new predictors from sequences of labeled examples (x,f(x)) presented in the input without further parameter updates. I’ll present recent findings suggesting that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context, using in-context linear regression as a model problem. First, I’ll show by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, I’ll show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Finally, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners’ late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. This work is joint with Ekin Akyürek at MIT, and Dale Schuurmans, Tengyu Ma and Denny Zhou at Stanford.

    https://youtu.be/UNVl64G3BzA

    10:45–11:00 AMBreak
    11:00 AM–12:00 PMTommi Jaakkola (MIT)

    Title: Generative modeling and physical processes

    Abstract: Rapidly advancing deep distributional modeling techniques offer a number of opportunities for complex generative tasks, from natural sciences such as molecules and materials to engineering. I will discuss generative approaches inspired from physical processes including diffusion models and more recent electrostatic models (Poisson flow), and how they relate to each other in terms of embedding dimension. From the point of view of applications, I will highlight our recent work on SE(3) invariant distributional modeling over backbone 3D structures with ability to generate designable monomers without relying on pre-trained protein structure prediction methods as well as state of the art image generation capabilities (Poisson flow). Time permitting, I will also discuss recent analysis of efficiency of sample generation in such models.

    https://youtu.be/GLEwQAWQ85E

    12:00–1:30 PMLunch
    1:30–2:30 PMMarinka Zitnik (Harvard Medical School)

    Title: Multimodal Learning on Graphs

    Abstract: Understanding biological and natural systems requires modeling data with underlying geometric relationships across scales and modalities such as biological sequences, chemical constraints, and graphs of 3D spatial or biological interactions. I will discuss unique challenges for learning from multimodal datasets that are due to varying inductive biases across modalities and the potential absence of explicit graphs in the input. I will describe a framework for structure-inducing pretraining that allows for a comprehensive study of how relational structure can be induced in pretrained language models. We use the framework to explore new graph pretraining objectives that impose relational structure in the induced latent spaces—i.e., pretraining objectives that explicitly impose structural constraints on the distance or geometry of pretrained models. Applications in genomic medicine and therapeutic science will be discussed. These include TxGNN, an AI model enabling zero-shot prediction of therapeutic use across over 17,000 diseases, and PINNACLE, a contextual graph AI model dynamically adjusting its outputs to contexts in which it operates. PINNACLE enhances 3D protein structure representations and predicts the effects of drugs at single-cell resolution.

    https://youtu.be/hjt4nsN_8iM

    2:30–2:45 PMBreak
    2:45–3:45 PMJianqing Fan (Princeton)

    Title: UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

    Abstract: Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts. Numerous methods are available for constructing prediction intervals, such as quantile regression and conformal predictions, among others. Nevertheless, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this work, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions.  Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics. (Joint work Jiawei Ge and Debarghya Mukherjee).

    https://youtu.be/WY6dr1oEOrk

    3:45–4:00 PMBreak
    4:00–5:00 PMMelissa Dell (Harvard)

    Title: Efficient OCR for Building a Diverse Digital History

    Abstract: Many users consult digital archives daily, but the information they can access is unrepresentative of the diversity of documentary history. The sequence-to-sequence architecture typically used for optical character recognition (OCR) – which jointly learns a vision and language model – is poorly extensible to low-resource document collections, as learning a language-vision model requires extensive labeled sequences and compute. This study models OCR as a character-level image retrieval problem, using a contrastively trained vision encoder. Because the model only learns characters’ visual features, it is more sample-efficient and extensible than existing architectures, enabling accurate OCR in settings where existing solutions fail. Crucially, it opens new avenues for community engagement in making digital history more representative of documentary history.

    https://youtu.be/u0JY9vURUAs

     


    Information about the 2022 Big Data Conference can be found here.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Invariant theory for maximum likelihood estimation

    9:00 am-10:00 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-2.8.2022

    Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

  • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
    9:00 am-1:30 pm
    12/01/2024-02/09/2018

    The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

    There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

    The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The n-queens problem

    9:00 am-10:00 am
    12/01/2024

    Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

    In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

    This is joint work with Peter Keevash.

  • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
    9:00 am-6:15 pm
    12/01/2024-03/26/2018
    GIC-Poster-2-e1520002551865

    On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

    The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

    Please click here to register for the event.

    Confirmed Speakers:

  • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
    9:00 am-11:55 am
    12/01/2024-03/29/2019
    Machine-Learning-Poster

    The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Speakers:

  • CMSA EVENT: The 2017 Charles River Lectures
    9:15 am-5:30 pm
    12/01/2024

    The 2017 Charles River Lectures

    Charles River with Bench at Sunset

    Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

    The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


    ***************************************************

    UPDATED LOCATION

    Harvard University

    Harvard Science Center (Halls C & E)

    1 Oxford Street, Cambridge, MA 02138 (Map)

    Monday, October 2, 2017

    9:15 AM – 5:30 PM

    **************************************************

    Please note that registration has closed.

    Speakers:

    Agenda:

    In Harvard Science Center Hall C:

    8:45 am – 9:15 amCoffee/light breakfast

    9:15 am – 10:15 am: Ofer Zeitouni

    Title: Noise stability of the spectrum of large matrices

    Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

    The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

    10:20 am – 11:20 am: Andrea Montanari

    Title: Algorithms for estimating low-rank matrices 

    Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

    11:20 am – 11:45 amBreak

    11:45 am – 12:45 pm: Paul Bourgade

    Title: Random matrices, the Riemann zeta function and trees

    Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

    1:00 pm – 2:30 pm: Lunch

    In Harvard Science Center Hall E:

    2:45 pm – 3:45 pm: Roman Vershynin

    Title: Deviations of random matrices and applications

    Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

    3:45 pm – 4:15 pm: Break

    4:15 pm – 5:15 pm: Massimiliano Gubinelli

    Title: Weak universality and Singular SPDEs

    Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

    Poster:

    2017 Charles River Lectures Poster

    Organizers:

     Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

  • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
    9:15 am-3:25 pm
    12/01/2024-09/11/2019
    Topology-Poster

    On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

    New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

    Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

    This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Click here for a list of restaurants in the area. 

    Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

    Partial list of speakers:

    Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

  • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
    9:15 am-10:00 am
    12/01/2024-04/17/2019

    As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

    This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

    In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Videos

    Tentative Speaker List:

    Schedule:

    Monday, April 15

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:15amWelcome and Introduction
    9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

    Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

    10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

    Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

    In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

    I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

    10:45 – 11:15amCoffee Break
    11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

    12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    12:45 – 2:00pmLunch
    2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

    My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

    2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

    Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

    Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

    4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

    Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

    5:30 – 6:30pmReception

     

    Tuesday, April 16

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

    Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

    9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

    Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

    While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

    Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

    11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

    Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

    12:30 – 2:00pmLunch
    2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

    Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

    2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    3:30 – 4:00pmTea Break
    4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

    Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

    4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

    Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


    Wednesday, April 17

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

    Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

    Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

    (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

    (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

    (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

    University of Jerusalem, Jerusalem, 91904, Israel

    9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

    Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

    This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

    10:30 – 11:00amCoffee Break
    11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

    Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

    11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

    Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

    12:30 – 1:30pmLunch
    1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

    Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

    2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

    Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

    3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

    Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

    3:45 – 4:00pmL Mahadevan – summary
  • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
    9:20 am-3:15 pm
    12/01/2024-08/28/2018
    Topological-1

    Screen-Shot-2018-08-13-at-2.28.22-PM

    On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

    This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please register here

    Speakers: 

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Max Wiesner

    Title: Light strings, strong coupling, and the Swampland

    Abstract: In this talk, I will start by reviewing central ideas of the so-called Swampland Program. The Swampland Program aims to identify criteria that distinguish low-energy effective field theories, that can be consistently coupled to quantum gravity, from those theories that become inconsistent in the presence of quantum gravity.

    In my talk I will specialize to four-dimensional effective field theories with N=2 and N=1 supersymmetry. In weakly-coupled regions of the scalar field space of such theories, it has been shown that light strings are crucial to realize certain Swampland criteria. Complementary to that, the focus of this talk will be on the role of such light strings away from these weak-coupling regimes. In this context, I will first discuss a relation between light perturbative strings and strong coupling singularities in the Kähler moduli space of 4d N=1 compactifications of F-theory. More precisely, in regions of moduli space, in which a critical string classically becomes light, I will show that non-perturbative corrections yield to strong coupling singularities for D7-brane gauge theories which obstruct weak-coupling limits. Moreover, I will demonstrate that in the vicinity of this strong coupling singularity, the critical, light string in fact leaves the spectrum of BPS strings thereby providing an explanation for the obstruction of the weak coupling limit.

    I will then move on and discuss the backreaction of perturbative strings in 4d EFTs. Away from the string core, the backreaction of such strings necessarily leads to strong coupling regions where naively the energy stored in the backreaction diverges. I will show how the introduction of additional non-critical strings can regulate this backreaction and how this can be used to study the spectrum of BPS strings and their tensions even beyond weak coupling regions. In this context, I will demonstrate how the requirement, that the total string tension should not exceed the Planck scale, constrains the possible BPS string charges.

  • Special Seminar
    9:30 am-11:00 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Speaker: Bong Lian

    Title: Singular Calabi-Yau mirror symmetry

    Abstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors, including Matsumoto, Sasaki, Yoshida and others, mainly from the viewpoint of their moduli spaces and their comparisons.  I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono, Tsung-Ju Lee, Hiromichi Takagi, Shing-Tung Yau.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Tsung-Ju Lee

    Title: Periods for singular CY families and Riemann–Hilbert correspondence

    Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and mirror symmetry. In this talk, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.

  • Member Seminar
    9:30 am-11:30 am
    12/01/2024

    Member Seminar

    Speaker: Chuck Doran

    Title: The Greene-Plesser Construction Revisited

    Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The threshold for stacked triangulations

    9:30 am-10:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10
    CMSA-Combinatorics-Physics-and-Probability-Seminar-05.03.22

    Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{[n]}3$, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle.
    Suppose that every triangle is initially infected independently with probability p=p(n), what is the threshold probability for percolation — the event that all triangles get infected? How many new triangles do get infected in the subcritical regime?

    This notion of percolation can be viewed as a simplification of simple-connectivity. Namely, a stacked triangulation of a triangle is obtained by repeatedly subdividing an inner face into three faces.
    We ask: for which $p$ does the random simplicial complex Y_2(n,p) contain, for every triple $xyz$, the faces of a stacked triangulation of $xyz$ whose internal vertices are arbitrarily labeled in [n].

    We consider this problem in every dimension d>=2, and our main result identifies a sharp probability threshold for percolation, showing it is asymptotically (c_d*n)^(-1/d), where c_d is the growth rate of the Fuss–Catalan numbers of order d.

    The proof hinges on a second moment argument in the supercritical regime, and on Kalai’s algebraic shifting in the subcritical regime.

    Joint work with Eyal Lubetzky.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-Seminar-09.13.22

    Quantum Matter in Mathematics and Physics

    Speaker: Yichul Cho (SUNY Stony Brook)

    Title: Non-invertible Symmetries in Nature

    Abstract: In this talk, I will discuss non-invertible symmetries in
    familiar 3+1d quantum field theories describing our Nature. In
    massless QED, the classical U(1) axial symmetry is not completely
    broken by the ABJ anomaly. Instead, it turns into a discrete,
    non-invertible symmetry. The non-invertible symmetry operator is
    obtained by dressing the naïve U(1) axial symmetry operator with a
    fractional quantum Hall state. We also find a similar non-invertible
    symmetry in the massless limit of QCD, which provides an alternative
    explanation for the neutral pion decay. In the latter part of the
    talk, I will discuss non-invertible time-reversal symmetries in 3+1d
    gauge theories. In particular, I will show that in free Maxwell
    theory, there exists a non-invertible time-reversal symmetry at every
    rational value of the theta angle.

    Based on https://arxiv.org/abs/2205.05086 and https://arxiv.org/abs/2208.04331.

     

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Mathlit_WOODIN

    CMSA/Tsinghua Math-Science Literature Lecture

    woodin_portait_books

    Prof. Hugh Woodin will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

    Date: Wednesday, November 9, 2022

    Time: 9:30 – 11:00 am ET

    Location: Via Zoom Webinar and Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

    Directions and Recommended Lodging

    Registration is required.

     

    Title: Large cardinals and small sets: The AD+ Duality Program

    Abstract: The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers.  The modern view is that determinacy axioms concern generalizations of the borel sets, and deep connections with large cardinal axioms have emerged.

    The study of determinacy axioms has led to a specific technical refinement of AD, this is the axiom AD+. The further connections with large axioms have in turn implicitly led to a duality program, this is the AD+ Duality Program.

    The main open problems here are intertwined with those of the Inner Model Program, which is the central program in the study of large cardinal axioms.

    This has now all been distilled into a series of specific conjectures.

     

    Talk chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)

    Moderator: Alejandro Poveda Ruzafa (Harvard CMSA)

     

    Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

     

    CMSA COVID-19 Policies

  • Member Seminar
    9:30 am-11:00 am
    12/01/2024

    Member Seminar

    Speaker: Sergiy Verstyuk

    Title: Machine Learning the Gravity Equation for International Trade

    Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 11.10.22

    General Relativity Seminar

    Speaker: Pierre Heidmann (Johns Hopkins)

    Title: Schwarzschild-like Topological Solitons in Gravity

    Abstract: We present large classes of non-extremal solitons in gravity that are asymptotic to four-dimensional Minkowski spacetime plus extra compact dimensions. They correspond to smooth horizonless geometries induced by topology in spacetime and supported by electromagnetic flux, which characterize coherent states of quantum gravity. We discuss a new approach to deal with Einstein-Maxwell equations in more than four dimensions, such that they decompose into a set of Ernst equations. We generate the solitons by applying different techniques associated with the Ernst formalism. We focus on solitons with zero net charge yet supported by flux, and compare them to Schwarzschild black holes. These are also ultra-compact geometries with very high redshift but differ in many aspects. At the end of the talk, we discuss the stability properties of the solitons and their gravitational signatures.

  • Algebraic Geometry in String Theory Seminar
  • CMSA EVENT: Math-Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024
    Math-Science Literature Lecture Series

    Mathematics & Literature Lecture Series

    Beginning in Spring 2020, the CMSA will be hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars. Talks will take place throughout the semester. All talks will take place virtually. You must register to attend. Recordings will be posted to this page.

    Written articles will accompany each lecture in this series and be available as part of the publication “The Literature and History of Mathematical Science

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry, transforming Calabi-Yau 3-folds between A- and B-models. In this talk, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X, detail the change of derived categories from its smoothing to its small resolution.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Pok Man Tam (University of Pennsylvania)

    Title: Topology of the Fermi sea: Ordinary metals as topological materials

    Abstract: It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F  to experimental observables, namely: (i) equal-time density/number correlations [1], and (ii) Andreev state transport along a planar Josephson junction [2]. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.

    [1] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)

    [2] P. M. Tam and C. L. Kane, arXiv:2210.08048

     

    https://www.youtube.com/watch?v=AXHLAo8kMHQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=25

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Title: Asymptotic localization, massive fields, and gravitational singularities

    Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-03.09.2022

    Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Prague dimension of random graphs

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-11.23.21

    Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    General Relativity Seminar

    Speaker: Semyon Dyatlov (MIT)

    Title: Ringdown and geometry of trapping for black holes

    Abstract: Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of a black hole merger when the dynamics is expected to be driven by linear effects. In this talk I give an overview of various results in pure mathematics which relate asymptotic behavior of quasi-normal modes at high frequency to the geometry of the set of trapped null geodesics, such as the photon sphere in Schwarzschild (-de Sitter). These trapped geodesics have two kinds of behavior: the geodesic flow is hyperbolic in directions normal to the trapped set (a feature stable under perturbations) and it is completely integrable on the trapped set. It turns out that normal hyperbolicity gives information about the rate of decay of quasi-normal modes, while complete integrability gives rise to a quantization condition.

  • Colloquium
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Elliptic chiral homology and chiral index

    9:30 am-10:30 am
    12/01/2024
    20220330_Si-LI_poster

    Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture – Karen Uhlenbeck

    9:30 am-2:26 pm
    12/01/2024
    Lecture_Uhlenbeck_12921

    Karen Uhlenbeck (Institute for Advanced Study)

    Title: The Noether Theorems in Geometry: Then and Now

    Abstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature.

    Talk Chair: Laura DeMarco

    VIDEO

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Gabriel Wong (Harvard CMSA)

    Title: 3D gravity and gravitational entanglement entropy

    Abstract: Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime. Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge modes.

     

    https://www.youtube.com/watch?v=xD0hWdS-OAc&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=24

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Changji Xu

    Title: On the solution space of the Ising perceptron model

    Abstract:  Consider the discrete cube $\{-1,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk, we will talk about its sharp threshold phenomenon, the frozen structure of the solution space, and the Gardner formula.

  • Joint Harvard-CUHK-YMSC Differential Geometry
    9:30 am-10:30 am
    12/01/2024
    Jim-Bryan_poster_3Nov2021

    Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g,h) which are conjectured to be equivalent, one in terms of a version of PT theory, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface, the specialization of n_beta(g,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-04.27.22

    Speaker: Venkatesan Guruswami, UC Berkeley

    Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

    Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.
    We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

    Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

    This is joint work with Xiaoyu He and Ray Li.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Michael Simkin

    Title: Threshold phenomena in random graphs and hypergraphs

    Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields.

    The model is defined as follows: Given a natural number $n$ and a parameter $p \in [0,1]$, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$, independent of all others. Despite their apparent simplicity, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena.

    A central feature is the appearance of threshold phenomena: For all monotone properties (e.g., connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e., with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Speaker: Freid Tong

    Title: The complex Monge-Ampere equation in Kahler geometry

    Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry, with a particular focus on the a priori C^0 estimates and their various applications. In the end, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.

  • Colloquium
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Gradient flows on totally nonnegative flag varieties

    9:30 am-10:30 am
    12/01/2024

    Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Kan Lin

    Title: China’s financial regulatory reform, financial opening-up, and Central Bank Digital Currency (CBDC)

    Abstract: In this talk, I will explain the overall situation of China’s financial industry and review the development of China’s financial regulatory system reform from 1949 to 2021. Then, I will explain the policies of the 3 stages of financial opening-up, 2001–08, 2008–18, 2018≠present. In particular, the latest round of opening-up from 2018 has brought great opportunities for foreign institutions. China has the world’s largest banking industry with assets totaling $53 trillion, and accounts for 1/3 of the growth in global insurance premiums over the next 10 years. I will also introduce the progress of research & development of China’s Central Bank Digital Currency (CBDC, or E-CNY). By October 2021, 140 million people had opened E-CNY wallets, and 1.6 million merchants could accept payments using eCNY wallets, including utilities, catering services, transportation, retail, and government services.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-03.24.2022-1583x2048

    Youtube Video

     

    Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.16.21-1-1

    Abstract: I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine (arxiv:2109.13323).

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 09.30.2022

    Algebraic Geometry in String Theory Seminar

    Speaker:  Mauricio Romo, Tsinghua University

    Title: GLSM, Homological projective duality and nc resolutions
    Abstract: Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.
  • Algebraic Geometry in String Theory Seminar
  • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
    9:30 am-5:00 pm
    12/01/2024-03/01/2019

    From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

    Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
    The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-05.18.22

    Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.07.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Sam Bardwell-Evans, Boston University
    Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
    Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.
  • Algebraic Geometry in String Theory Seminar
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Flip processes

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1

    Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by  $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.

    Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).

    These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).

    We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
    A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Gabriel Wong 

    Title: Universal relations between entanglement, symmetries, and entropy

    Abstract: Entanglement is an essential property of quantum systems that distinguishes them from classical ones.   It is responsible for the nonlocal character of quantum information and provides a resource for quantum teleportation and quantum computation. In this talk I will provide an introduction to quantum entanglement and explain the essential role it plays in two seemingly unrelated subjects: implementation of measurement-based quantum computation and microstate counting of black holes in quantum gravity.   Time permitting, I will also discuss attempts to characterize entanglement in string theory. A unifying theme that illuminates the entanglement structure of these diverse systems is the role of surface symmetries and (entanglement) edge modes. We will explain how these universal aspects of entanglement are captured in the framework of extended topological quantum field theory.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Hypergraph Matchings Avoiding Forbidden Submatchings

    9:30 am-10:30 am
    12/01/2024

    Abstract:  In 1973, Erdős conjectured the existence of high girth (n,3,2)-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős’ conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős’ conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth (n,q,r)-Steiner systems. We prove the approximate version of their conjecture.  This result follows from our general main results which concern finding perfect or almost perfect matchings in a hypergraph G avoiding a given set of submatchings (which we view as a hypergraph H where V(H)=E(G)). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when H is a hypergraph with small codegrees (for which high girth designs is a specific instance). Indeed, the coloring version of our result even yields an almost partition of K_n^r into approximate high girth (n,q,r)-Steiner systems.  If time permits, I will explain some of the other applications of our main results such as to rainbow matchings.  This is joint work with Luke Postle.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.14.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Daniel Pomerleano, UMass Boston

    Title: Singularities of the quantum connection on a Fano variety

    Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty.

    I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M, D).

  • Member Seminar
    9:30 am-11:00 am
    12/01/2024

    Member Seminar

    Speaker: Juven Wang

    Title: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass

    Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1,2,3,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765arXiv:2204.08393arXiv:2202.13498 and references therein.

  • Colloquium
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Daniel Junghans

    Title: AdS with Scale Separation

    Abstract: I will talk about Anti-de Sitter solutions in string theory with a parametric separation between the AdS curvature scale and the Kaluza-Klein scale. In particular, I will discuss recent progress on computing backreaction corrections in such solutions, and I will explain how to construct solutions without Romans mass that can be lifted to M-theory.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.28.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Ahsan Khan, IAS

    Title: 2-Categories and the Massive 3d A-Model

    Abstract: I will outline the construction of a 2-category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two, and three dimensions combined with a three-dimensional version of the Gaiotto-Moore-Witten web formalism.

     

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-GR-Seminar-03.24.22

    Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Vitor Cardoso, IST, Lisbon and The Niels Bohr Institute, Copenhagen

    Title: Testing GR with GWs

    Abstract: One of the most remarkable possibilities of General Relativity concerns gravitational collapse to black holes, leaving behind a geometry with light rings, ergoregions and horizons. These peculiarities are responsible for uniqueness properties and energy extraction mechanisms that turn black holes into ideal laboratories of strong gravity, of particle physics (yes!) and of possible quantum-gravity effects. I will discuss some of the latest progress in tests of General Relativity with black holes.

  • Colloquium
  • Seminars

    Seminars Colloquia & Seminar
    4/18/2019 General Relativity Seminar

    9:30 am-10:30 am
    12/01/2024
  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)
    3/2/2022Richard Kenyon (Yale University)
    3/9/2022Richard Tsai (UT Austin)
    3/23/2022Joel Cohen (University of Maryland)
    3/30/2022Rob Leigh (UIUC)
    4/6/2022Johannes Kleiner (LMU München)
    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
    4/20/2022TBA
    4/27/2022TBA
    5/4/2022Melody Chan (Brown University)
    5/11/2022TBA
    5/18/2022TBA
    5/25/2022Heeyeon Kim (Rutgers University)

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-03.17.2022-1-1544x2048-1

    Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)Title: Learning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    3/2/2022Richard Kenyon (Yale University)Title: Dimers and webs

    Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

    This is joint work with Dan Douglas and Haolin Shi.

    3/9/2022Yen-Hsi Richard Tsai (UT Austin)Title: Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space

    Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

    3/23/2022Joel Cohen (University of Maryland)Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths

    Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

    3/30/2022Rob Leigh (UIUC)Title: Edge Modes and Gravity

    Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

    4/6/2022Johannes Kleiner (LMU München)Title: What is Mathematical Consciousness Science?

    Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)Title: Quantisation in monoidal categories and quantum operads

    Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure.  But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups.

    The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

    In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts

    4/27/2022Venkatesan Guruswami (UC Berkeley)Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

    Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.

    We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

    Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

    This is joint work with Xiaoyu He and Ray Li.

    5/18/2022 David Nelson (Harvard)TitleStatistical Mechanics of Mutilated Sheets and Shells

    Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-01.26.2022

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Yingying Wu

    Title: Moduli Space of Metric SUSY Graphs

    Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties, followed by a discussion on the connection with the classical case.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Dan Kapec

    Title: Black Holes, 2D Gravity, and Random Matrices

    Abstract: I will discuss old and new connections between black hole physics, 2D quantum gravity, and random matrix theory. Black holes are believed to be very complicated, strongly interacting quantum mechanical systems, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model, but this result raises more questions than it answers. If time permits, I will discuss some extensions of these results and possible future directions.

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Cohomology of the moduli of Higgs bundles via positive characteristic

    9:30 am-8:30 pm
    12/01/2024

    Abstract: In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the character variety of the curve.  I will then explain how certain symmetries of this cohomology, which are predictions of this conjecture, can be constructed using techniques from non-abelian Hodge theory in positive characteristic.  Based on joint work with Mark de Cataldo, Junliang Shen, and Siqing Zhang.

  • Colloquium
  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Algebraic Geometry in String Theory 10.21.2022

    Algebraic Geometry in String Theory Seminar

    Speaker: Nicolo Piazzalunga, Rutgers

    Title: The index of M-theory

    Abstract: I’ll introduce the higher-rank Donaldson-Thomas theory for toric Calabi-Yau threefolds, within the setting of equivariant K-theory. I’ll present a factorization conjecture motivated by Physics. As a byproduct, I’ll discuss some novel properties of equivariant volumes, as well as their generalizations to the genus-zero Gromov-Witten theory of non-compact toric varieties.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The singularity probability of random symmetric matrices

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-12.07.2021

    Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-03.30.2022

    Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 12.08.22

    General Relativity Seminar

    Speaker: Allen Fang (Princeton)

    Title: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

    Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vector field techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-04.26.2022

    Abstract:   In “Mirror symmetry for log Calabi–Yau surfaces I,” given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y,D) with at worst du Val singularities. As a corollary, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 03.30.23

    General Relativity Seminar

    Speaker: Alejandra Castro (University of Cambridge)

    Title: Gravitational perturbations near to extreme Kerr

    Abstract: Gravitational perturbations of a black hole illustrate the invaluable synergy between theory, experiment, and numerical simulations in general relativity. A recent development in the theory side has been the identification of the relevant degrees of freedom describing the low energy physics driving a black hole away from extremality.  For simple cases, this low energy sector determines important aspects of the gravitational backreaction, and several properties that are key to our microscopic (quantum) understanding of black hole physics.
    In this talk I will discuss these developments in the context of the (near-)extreme Kerr black hole. In particular, I will revisit the spectrum of linear axisymmetric gravitational perturbations of this black hole. The aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. I will show that for Kerr the low-lying mode sector is subtle and intricate—features that their charged spherical symmetric cousins do not display. This unveils new clues on how to decode a microscopic, and holographic, understanding of the Kerr black hole.
  • Seminars

    Seminars Colloquia & Seminar
    8/4/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Sifan Yu, Vanderbilt University

    Title: Rough solutions of the relativistic Euler equations

    Abstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.

  • Seminars

    Seminars Colloquia & Seminar
    8/11/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/18/2020 Geometry and Physics Seminar

    9:30 am-11:30 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/19/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Conference
    9:30 am-5:00 pm
    12/01/2024-04/08/2022

    General Relativity Conference

    This conference will be held virtually on Zoom. Registration is required.
    Webinar Registration

    A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
    In-Person Registration

    Schedule | April 4–8, 2022

    Schedule (PDF)

    Monday, April 4, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amPieter Blue, University of Edinburgh, UK
    (virtual)
    Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge

    Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of the Einstein equation in this gauge, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975, Chrzanowski introduced the “outgoing radiation gauge”, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently, using a flow along null geodesics, we have constructed a new gauge such that, in this gauge, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge.

    This is joint work with Lars Andersson, Thomas Backdahl, and Siyuan Ma.

    10:30 am–11:30 amPeter Hintz, ETH Zürich
    (virtual)
    Title: Mode stability and shallow quasinormal modes of Kerr-de Sitter
    black holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe, such as our own, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question), mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which, depending on the scaling, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.
    11:30 am–12:30 pmLars Andersson, Albert Einstein Institute, Germany
    (virtual)
    Title: Gravitational instantons and special geometry

    Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

    12:30 pm–1:30 pmbreak
    1:30 pm–2:30 pmMartin Taylor, Imperial College London
    (virtual)
    Title: The nonlinear stability of the Schwarzschild family of black holes

    Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

    2:30 pm–3:30 pmPo-Ning Chen, University of California, Riverside
    (virtual)
    Title: Angular momentum in general relativity

    Abstract:
    The definition of angular momentum in general relativity has been a subtle issue since the 1960s, due to the ‘supertranslation ambiguity’. In this talk, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.
    3:30 pm–4:00 pmbreak
    4:00 pm–5:00 pmDan Lee, Queens College (CUNY)
    (hybrid: in person & virtual)
    Title: Stability of the positive mass theorem

    Abstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem, focusing on recent work with Kazaras and Khuri, in which we proved that if one assumes a lower Ricci curvature bound, then stability holds with respect to pointed Gromov-Hausdorff convergence.

     

    Tuesday, April 5, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amXinliang An, National University of Singapore
    (virtual)
    Title: Anisotropic dynamical horizons arising in gravitational collapse

    Abstract: Black holes are predicted by Einstein’s theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk, we will present several results in these directions. First, in a joint work with Qing Han, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second, in joint works with Dejan Gajic and Ruixiang Zhang, for the spherically symmetric Einstein-scalar field system, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism. If time permits, some results on fluid dynamics will also be addressed.

    10:30 am–11:30 amSergiu Klainerman, Princeton
    (virtual)
    Title: Nonlinear stability of slowly rotating Kerr solutions

    Abstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.

    11:30 am–12:30 pmSiyuan Ma, Sorbonne University
    (virtual)
    Title: Sharp decay for Teukolsky master equation

    Abstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmJonathan Luk, Stanford
    (virtual)
    Title: A tale of two tails

    Abstract: Motivated by the strong cosmic censorship conjecture, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).

    2:30 pm–3:30 pmGary Horowitz, University of California Santa Barbara
    (virtual)
    Title: A new type of extremal black hole

    Abstract: I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero, if quantum matter is added, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmLydia Bieri, University of Michigan
    (virtual)
    Title: Gravitational radiation in general spacetimes

    Abstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

     

    Wednesday, April 6, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amGerhard Huisken, Mathematisches Forschungsinstitut Oberwolfach
    (virtual)
    Title: Space-time versions of inverse mean curvature flow

    Abstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.

    10:30 am–11:30 amCarla Cederbaum, Universität Tübingen, Germany
    (virtual)
    Title: Coordinates are messy

    Abstract: Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M,g,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.

    11:30 am–12:30 pmStefanos Aretakis, University of Toronto
    (virtual)
    Title: Observational signatures for extremal black holes

    Abstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmJared Speck, Vanderbilt University
    (virtual)
    Title: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow

    Abstract: In the last two decades, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia, M. Disconzi, and J. Luk.

    2:30 pm–3:30 pmLan-Hsuan Huang, University of Connecticut
    (virtual)
    Title: Null perfect fluids, improvability of dominant energy scalar, and Bartnik mass minimizers

    Abstract: We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture.

    Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmDemetre Kazaras, Duke University
    (virtual)
    Title: Comparison geometry for scalar curvature and spacetime harmonic functions

    Abstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

     

    Thursday, April 7, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amPiotr Chrusciel, Universitat Wien
    (virtual)
    Title: Maskit gluing and hyperbolic mass

    Abstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.

    10:30 am–11:30 amGreg Galloway, University of Miami (virtual)Title:  Initial data rigidity and applications

    Abstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP, 2021), and look at some consequences.  In a note with Piotr Chruściel (CQG 2021), we showed how to use this result, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.

    11:30 am–12:30 pmPengzi Miao, University of Miami
    (virtual)
    Title: Some remarks on mass and quasi-local mass

    Abstract: In the first part of this talk, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello, and with H.C. Jang.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmYakov Shlapentokh Rothman, Princeton
    (hybrid: in person & virtual)
    Title: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations

    Abstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.

    2:30 pm–3:30 pmMarcelo Disconzi, Vanderbilt University
    (virtual)
    Title: General-relativistic viscous fluids.

    Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmMaxime van de Moortel, Princeton
    (hybrid: in person & virtual)
    Title: Black holes: the inside story of gravitational collapse

    Abstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models, the global structure of the black hole interior has largely remained unexplored.
    These questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.
    I will present my recent resolution of these problems in spherical gravitational collapse, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.

     

    Friday, April 8, 2022

    Time (ET)SpeakerTitle/Abstract
    9:30 am–10:30 amYe-Kai Wang, National Cheng Kun University, Taiwan
    (virtual)
    Title: Supertranslation invariance of angular momentum at null infinity in double null gauge

    Abstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing
    how Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen, Jordan Keller, Mu-Tao Wang, and Shing-Tung Yau.

    10:30 am–11:30 amZoe Wyatt, King’s College London
    (virtual)
    Title: Global Stability of Spacetimes with Supersymmetric Compactifications

    Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in
    supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.

    11:30 am–12:30 pmElena Giorgi, Columbia University
    (hybrid: in person & virtual)
    Title: The stability of charged black holes

    Abstract: Black hole solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

    12:30 pm–1:30 pmBreak
    1:30 pm–2:30 pmMarcus Khuri, Stony Brook University
    (virtual)
    Title: The mass-angular momentum inequality for multiple black holes

    Abstract
    : Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected, axisymmetric, maximal, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain, Chrusciel-Li-Weinstein, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from
    R^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han, G. Weinstein, and J. Xiong.
    2:30 pm–3:30 pmMartin Lesourd, Harvard
    (hybrid: in person & virtual)
    Title:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature

    Abstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau, Prof. D. A. Lee, and R. Unger.

    3:30 pm–4:00 pmBreak
    4:00 pm–5:00 pmGeorgios Moschidis, Princeton
    (virtual)
    Title: Weak turbulence for the Einstein–scalar field system.

    Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
    In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams.

  • Seminars

    Seminars Colloquia & Seminar
    8/20/2020 Quantum Matter

    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/23/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    BCFW recursion relations and non-planar positive geometry

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-04.12.22-1583x2048-1

    Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.

    **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

    All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

    LINK TO FORM

  • Seminars

    Seminars Colloquia & Seminar
    8/25/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/26/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    8/27/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Special Seminar
    9:30 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Michael Douglas

    Title: Knowledge Graph Embeddings and Inference

    Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.
    A popular KG representation method is graph embedding, which facilitates question answering, inferring missing edges, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning, network learning, and unstructured statistical inference, and describe experiments to measure the contributions of each mechanism.

    Joint work with M. Simkin, O. Ben-Eliezer, T. Wu, S. P. Chin, T. V. Dang and A. Wood.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/30/2020 Condensed Matters Seminar

    9:30 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/22/2020 Quantum Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker:An Huang

    Title: Quadratic reciprocity from a family of adelic conformal field theories

    Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories, and ensures that these Green’s functions satisfy an adelic product formula. In particular, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place, the desired holomorphic factorization follows from the global conformal symmetry.

  • Seminars

    Seminars Colloquia & Seminar
    6/24/2020 Quantum Matter Seminar

    9:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-02.10.2022-1544x2048-1

    Speaker: Mohamed Anber (Durham University)

    Title: The global structure of the Standard Model and new nonperturbative processes

    Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Matteo Parisi

    Title: Amplituhedra, Scattering Amplitudes and Triangulations

    Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

  • Geometry and Physics Seminar

    Geometry and Physics Seminar
    Geometry and Physics Seminar

    9:30 am-9:30 pm
    12/01/2024-12/22/2020
    unnamed-537x338

    During the summer of 2020, the CMSA will be hosting a new Geometry Seminar. Talks will be scheduled on Mondays at 9:30pm or Tuesdays at 9:30am, depending on the location of the speaker. This seminar is organized by Tsung-Ju Lee, Yoosik Kim, and Du Pei.

    To learn how to attend this seminar, please contact Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu).

    DateSpeakerTitle/Abstract
    6/2/2020
    9:30am ET
    Siu-Cheong Lau
    Boston University
    This meeting will be taking place virtually on Zoom.

    Speaker: Equivariant Floer theory and SYZ mirror symmetry

    Abstract: In this talk, we will first review a symplectic realization of the SYZ program and some of its applications. Then I will explain some recent works on equivariant Lagrangian Floer theory and disc potentials of immersed SYZ fibers. They are joint works with Hansol Hong, Yoosik Kim and Xiao Zheng.

    6/8/2020
    9:30pm ET
    Youngjin Bae (KIAS)This meeting will be taking place virtually on Zoom.

    TitleLegendrian graphs and their invariants

    Abstract: Legendrian graphs naturally appear in the study of Weinstein manifolds with a singular Lagrangian skeleton, and a tangle decomposition of Legendrian submanifolds. I will introduce various invariant of Legendrian graphs including DGA type, polynomial type, sheaf theoretic one, and their relationship. This is joint work with Byunghee An, and partially with Tamas Kalman and Tao Su.

    6/16/2020
    9:30am ET
    Michael McBreen (CMSA)This meeting will be taking place virtually on Zoom.

    Title: Loops in hypertoric varieties and symplectic duality

    Abstract: Hypertoric varieties are algebraic symplectic varieties associated to graphs, or more generally certain hyperplane arrangements. They make many appearances in modern geometric representation theory. I will discuss certain infinite dimensional or infinite type generalizations of hypertoric varieties which occur in the study of enumerative invariants, focusing on some elementary examples. Joint work with Artan Sheshmani and Shing-Tung Yau.

    6/22/2020
    9:30pm ET
    Ziming Ma (CUHK)This meeting will be taking place virtually on Zoom.

    Title: The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties

    Abstract: In this talk, we construct a \(dgBV algebra PV*(X)\) associated to a possibly degenerate Calabi–Yau variety X equipped with local thickening data. This gives a version of the Kodaira–Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi–Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi–Yau varieties X satisfying Hodge–deRham degeneracy property for cohomology of X, in the spirit of Kontsevich–Katzarkov–Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.

    6/30/2020
    9:30pm ET
    Sunghyuk Park (Caltech)This meeting will be taking place virtually on Zoom.

    Title: 3-manifolds, q-series, and topological strings

    Abstract: \(\hat{Z}\) is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients), which has interesting modular properties. While originally from physics, this invariant has been mathematically constructed for a big class of 3-manifolds, and conjecturally it can be extended to all 3-manifolds. In this talk, I will give a gentle introduction to \(\hat{Z}\) and what is known about it, as well as highlighting some recent developments, including the use of R-matrix, generalization to higher rank, large N-limit and interpretation as open topological string partition functions.

    7/7/2020
    9:30am ET
    Jeremy Lane  (McMaster University)This meeting will be taking place virtually on Zoom.

    TitleCollective integrable systems and global action-angle coordinates

    Abstract: A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates.  Moreover, the image of the moment map is a (non-simple) convex polytope.

    7/13/2020
    9:30pm ET
    Po-Shen Hsin (Caltech)This meeting will be taking place virtually on Zoom.

    TitleBerry phase in quantum field theory

    Abstract: We will discuss Berry phase in family of quantum field theories using effective field theory. The family is labelled by parameters which we promote to be spacetime-dependent sigma model background fields. The Berry phase is equivalent to Wess-Zumino-Witten action for the sigma model. We use Berry phase to study diabolic points in the phase diagram of the quantum field theory and discuss applications to deconfined quantum criticality and new tests for boson/fermion dualities in \((2+1)d\).

    7/20/2020
    9:30pm ET
    Sangwook Lee (KIAS)This meeting will be taking place virtually on Zoom.

    Title: A geometric construction of orbifold Jacobian algebras

    Abstract: We review the definition of a twisted Jacobian algebra of a Landau-Ginzburg orbifold due to Kaufmann et al. Then we construct an A-infinity algebra of a weakly unobstructed Lagrangian submanifold in a symplectic orbifold. We work on an elliptic orbifold sphere and see that above two algebras are isomorphic, and furthermore their structure constants are related by a modular identity which was used to prove the mirror symmetry of closed string pairings. This is a joint work with Cheol-Hyun Cho.

    7/27/2020 9:30pm ETMao Sheng (USTC)This meeting will be taking place virtually on Zoom.

    Title: Parabolic de Rham bundles: motivic vs periodic

    Abstract: Let \($C$\) be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over \($C$\) (with rational weights in parabolic structure). Many examples arise from geometry: let \($f: X\to U$\) be a smooth projective morphism over some nonempty Zariski open subset \($U\subset C$\). Then the Deligne–Iyer–Simpson canonical parabolic extension of the Gauss–Manin systems associated to \($f$\) provides such examples. We call a parabolic de Rham bundle \emph{motivic}, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory, to get a characterization of motivic parabolic de Rham bundles. In this talk, I introduce another subcategory of parabolic de Rham bundles, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan–Sheng–Zuo on Higgs-de Rham flows, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus–Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck–Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz’s work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture, we would like to single out the conjectural arithmetic Simpson correspondence, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.

    8/4/2020
    9:30am Et
    Pavel Safronov (University of Zurich)This meeting will be taking place virtually on Zoom.

    TitleKapustin–Witten TFT on 3-manifolds and skein modules

    Abstract: Kapustin and Witten have studied a one-parameter family of topological twists of \(4d N=4\) super Yang–Mills. They have shown that the categories of boundary conditions on a surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid–Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.

    8/11/2020
    9:30am
    Xujia Chen (Stonybrook)This meeting will be taking place virtually on Zoom.

    TitleLifting cobordisms and Kontsevich-type recursions for counts of real curves

    Abstract: Kontsevich’s recursion, proved in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger’s invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon’s recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon’s approach).

    8/18/2020
    9:30am ET
    Dongmin Gang (Asia Pacific Center for Theoretical Physics)This meeting will be taking place virtually on Zoom.

    Title: M-theoretic genesis of topological phases

    Abstract:  I will talk about a novel way of constructing \((2+1)d\) topological phases using M-theory. They emerge as macroscopic world-volume theories of M5-branes wrapped on non-hyperbolic 3-manifolds. After explaining the algorithm of extracting modular structures of the topological phase  from topological data of the 3-manifold, I will discuss the possibility of full classification of topological orders via the geometrical construction.

    8/25/2020
    9:30pm ET
    Mykola Dedushenko (Caltech)This meeting will be taking place virtually on Zoom.

    TitleAlgebras and traces at the boundary of \(4d N=4\) SYM

    Abstract: I will describe how the structure of supersymmetric boundary correlators in \(4d N=4\) SYM can be encoded in a class of associative algebras equipped with twisted traces. In the case of interfaces, this yields a new connection to integrability.

  • Seminars

    Seminars Colloquia & Seminar
    6/2/2020 Geometry Seminar

    9:30 am-10:30 am
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: In this talk, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian, over the torus fixed points, this representation is a Verma module. The vertex function, a K-theoretic enumerative invariant introduced by A. Okounkov, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application, this gives a proof of the invariance of the quantum q-difference module under variation of GIT.

  • Colloquium
    9:30 am-10:00 am
    12/01/2024

    Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Juven Wang

    Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model

    Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT), or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320.

    In the second part of my talk, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-02.17.2022-1544x2048

    Speaker: Andrea Grigoletto (SISSA & INFN)

    Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

    Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

  • Seminars

    Seminars Colloquia & Seminar
    6/25/2020 Condensed Matter Seminar

    9:30 am-11:00 am
    12/01/2024
  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-04.06.2022

    Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

  • Seminars

    Seminars Colloquia & Seminar
    7/7/2020 Geometry and Physics Seminar

    9:30 am-10:30 am
    12/01/2024
  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-04.07.2022-1583x2048-1

    Youtube Video

     

    Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.

    References:
    [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021)
    [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022)
    [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation.
    [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Shahar Hadar (University of Haifa)

    Title: Resolving the photon ring

    Abstract: In the past few years, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes, M87* and SgrA*. It is believed that within these images is embedded a fine, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of strong lensing by the black hole and thereby conveys information on its spacetime geometry, potentially providing a new independent avenue for tests of general relativity in the strong-field regime. In the talk I will briefly review the theory of the photon ring and its corresponding spacetime region, the photon shell, which governs the universal lensing structure. I will then describe some current efforts and future prospects for resolving the ring, which include both the construction of transformative new instruments and the development of novel analysis methods. Focusing on the latter, I will present an upcoming proposal to use spectro-temporal autocorrelations in signals emitted from black hole environs as a probe of strong lensing effects.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024

    This is the Fall 2020 – Spring 2022 Quantum Matter in Mathematics and Physics Archive page.

    To view current seminars, please visit the Fall 2022-Spring 2023 Quantum Matter Seminar Page

    As part of the program on Quantum Matter in Mathematics and Physics, the CMSA hosted two weekly seminars. The Quantum Matter/Quantum Field Theory seminar took place on Wednesdays from 10:30 – 12:00pm on Zoom.

    The Condensed Matter/Math Seminar took place on  Thursdays from 10:30 – 12:00pm on Zoom.  In addition to the Quantum Matter seminar, the CMSA  also hosted a related seminar series on  Strongly Correlated Quantum Materials and High-Temperature Superconductors.

    Videos are available at the Quantum Matter in Mathematics and Physics  Youtube Playlist

    Spring 2022

    DateSpeakerTitle/Abstract
    1/18/2022
    2:30–4:00 pm ET
    Aavishkar Patel (UC Berkeley)Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

    Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

    Video

    1/28/2022 2:30–4:00 pm ETMaria Tikhanovskaya (Harvard)Title: Maximal quantum chaos of the critical Fermi surface

    Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

    2/2/2022
    8:00 -9:30 pm ET
    Yunqin Zheng (IPMU & ISSP, U Tokyo)Title: Kramers-Wannier-like duality defects in higher dimensions

    Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

    2/3/2022
    11:30 – 1:00 pm ET
    Lu Li (U Michigan)Title:  Quantum Oscillations of Electrical Resistivity in an Insulator

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    2/9/2022
    8:00 –9:30 pm ET
    Yuji Tachikawa (Kavli IPMU, U Tokyo)Title: On the absence of global anomalies of heterotic string theories

    Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
    2/10/2022Mohamed Anber (Durham University)Title: The global structure of the Standard Model and new nonperturbative processes

    Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

    2/16/2022
    10:30 am–12:00 pm ET
    Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part I

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    2/17/2022
    9:30–11:00 am ET
    Andrea Grigoletto (SISSA & INFN)Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

    Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

    2/23/2022
    10:30 am–12:00 pm ET
    Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part II

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    2/24/2022
    8:00–9:30 pm ET
    Yohei Fuji (U Tokyo)Title: Bridging three-dimensional coupled-wire models and cellular topological states

    Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/1/2021Keisuke HarigayaTitle: Naturalness and muon anomalous magnetic moment

    Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

    Watch Video on Youtube

    9/2/2021Joseph Maciejko (University of Alberta)Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

    Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

    Watch Video on Youtube

    9/8/2021William Witczak-Krempa (U Montreal)Title: Cornering the universal shape of fluctuations and entanglement

    Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

    Ref: arXiv:2102.06223

    Watch Video on Youtube

    9/9/2021Sung-Sik Lee (McMaster University, Perimeter Institute)Title: Quantum gravity from quantum matter

    Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

    Watch Video on Youtube

    9/10/2021

    *special time: 3:30pm – 5:00pm ET*

    Ofri Telem (UC Berkeley)Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

    Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
    Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

    Watch Video on Youtube

    9/15/2021Liang Fu (MIT)Title: Three-particle mechanism for pairing and superconductivity

    Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

    [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
    [2] V. Crepel and L. Fu, arXiv:2103.12060
    [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

    Watch Video on Youtube

    9/16/2021Shiraz Minwalla (Tata Institute of Fundamental Research)Title: The Hilbert Space of large N Chern-Simons matter theories

    Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of  this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to  a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

    Watch Video on Youtube

    9/17/2021

    *special time 3:30 pm- 5 pm ET*

    Eslam Khalaf (Harvard)Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

    Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

    Watch Video on Youtube

    9/22/2021Daniel S Freed (U Texas)Title: Symmetry types in QFT and the CRT theorem

    Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

    Watch Video on Youtube

    9/23/2021Edward Shuryak (Stony Brook University)Title: Applications of instantons, sphalerons and instanton-dyons in QCD

    Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

    Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

    Watch Video on Youtube

    9/29/2021

    *special time 11:30 am- 1 pm ET*

    Nai Phuan Ong (Princeton University)Title: Oscillations in the thermal conductivity of a spin liquid*

    Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

    *Czajka et al., Nature Physics 17, 915 (2021).

    Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

    Watch Video on Youtube

    10/06/2021Gabriel Cuomo (SCGP)Title: Line defects in CFTs: renormalization group flows and semiclassical limits

    Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

    Watch Video on Youtube

    10/07/2021Ryan Thorngren (Harvard CMSA)Title: A tour of categorical symmetry

    Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

    Watch Video on Youtube

    10/07/2021

    *special time 8:30 pm- 10 pm ET*

    Nima Arkani-Hamed (IAS Princeton)Title: UV/IR and Effective Field Theory

    Watch Video on Youtube

    10/21/2021

    *special time 13:30 – 15:00 ET*

    Anton Kapustin (Caltech)Title: Electric-magnetic duality and the Geometric Langlands duality

    Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

    Watch Video on Youtube

    10/22/2021

    *special time 10:30am – 12:00 noon ET*

    Netta Engelhardt (MIT)Title:  Recent Holographic Developments on the Black Hole Information Problem

    Watch Video on Youtube

    10/29/2021

    *special time 2:15pm – 3:45pm ET*

    Eric Sharpe (Virginia Tech)Title: Anomaly resolution via decomposition

    Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

    Watch Video on Youtube

    10/29/2021

    *special time 4:00pm – 5:30pm*

    Biao Lian (Princeton)Title: Integrability and chaos of 1+1d chiral edge states

    Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

    Watch Video on Youtube

    11/03/2021
    *special time 2:00pm – 3:30pm ET*
    Clay Cordova (U Chicago)Title: Non-Invertible Duality Defects in 3+1 Dimensions

    Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

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    11/04/2021Yifan Wang (NYU)Title: Fusion Category Symmetries in Quantum Field Theory

    Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

    Watch Video on Youtube

    11/10/21
    *special time 10–11:30 am ET*
    Michael Stone (UIUC)Title: Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT

    Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature.  I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.

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    11/12/21
    *special time 2:30–4:00 pm ET*
    Jeongwan Haah (Microsoft)Title: A degeneracy bound for homogeneous topological order

    Watch Video on Youtube

    11/16/21
    *special time 3–4:30 pm ET*
    Jie Wang
    (Center for Computational Quantum Physics, Flatiron Institute, Simons Foundation)
    Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

    Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

    [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
    [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
    [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

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    11/18/2021 2:30–4:00 pm ETB. Andrei Bernevig (Princeton University)Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

    Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

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    11/24/21Shinsei Ryu (Princeton University)Title: Multipartitioning topological phases and quantum entanglement

    Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

    Watch Video on Youtube

    12/1/21
    10:00–11:30 am ET
    Daniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 1

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
    12/2/21 10:30–12:00 pm ETDaniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 2

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

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    12/8/21 10:30–12:00 pm ETFei Yan (Rutgers)Title: Defects, link invariants and exact WKB

    Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

    Watch Video on Youtube

    12/10/21 2:30–4:00 pm ETLukasz Fidkowski (U Washington)Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

    Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

    Watch Video on Youtube

    Summer 2021:

    DateSpeakerTitle/Abstract
    6/2/2021Juven Wang (Harvard CMSA)

    Video

    TitleUltra Unification:
    Quantum Fields Beyond the Standard Model
    Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
    6/3/2021Tian Lan (CUHK & U Waterloo)

    Video

    TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

    Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
    6/9/2021Yizhi You (Princeton U)

    Video

    TitleFracton critical point and Topological phase transition beyond renormalization

    Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
    6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)

    Video

    TitleMinimal nondegenerate extensions and an anomaly indicator

    Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

    6/16/2021Arkady Vainshtein (UMN)

    Video

    TitleUses of Wilson Operator Expansion in Gauge Theories

    Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

    It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

    6/17/2021Mikhail Shifman (UMN)

    Video

    TitleWhat can supersymmetry do that other field theory cannot
    7/7/2021Dung Nguyen (Brown)

    Video

    TitleFrom Fractional Quantum Hall to higher rank symmetry

    Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of  W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems.  Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
    7/8/2021

    8:00 – 9:30pm

    Jing-Yuan Chen (Tsinghua)

    Video

    TitleSolvable Lattice Hamiltonians with Fractional Hall Conductivity

    Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]

    7/14/2021Liujun Zou (Perimeter Institute)

    Video

    TitleStiefel liquids: Possible non-Lagrangian quantum criticality from intertwined orders

    Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.

    Ref: arXiv: 2101.07805.

    7/15/2021Nathanan Tantivasadakarn (Harvard)

    Video

    TitleHybrid Fracton Orders

    Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

    Based on 2102.09555 and 2106.03842

    7/21/2021Daniel Bulmash (UMD)TitleAnomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs

    Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.

    Ref: arXiv:2104.14567

    7/22/2021
    8:00pm ET
    Hong Yao (Tsinghua)TitleEmergent spacetime supersymmetry in topological phases of matter

    Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators.
    References:
    [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015)
    [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017)
    [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017)
    [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)

    7/28/2021Max Metlitski (MIT)Title: Boundary criticality of the O(N) model in d = 3 critically revisited.

    Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry.
    Based on arXiv:2009.05119.

    7/29/2021Ady Stern & David Mross (Weizmann)TitleThe nu=5/2 enigma: Recent insights from theory and experiment

    Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

    8/4/2021Nathan Benjamin (Princeton & Caltech)Title: Harmonic analysis of 2d CFT partition functions

    Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.

    8/5/2021Hans-Werner Hammer (TU Darmstadt)Title: Un-nuclear physics: conformal symmetry in nuclear reactions

    Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.

    8/11/2021Piers Coleman (Rutgers)Title: Order Fractionalization*

    Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

    8/12/2012Beni Yoshida (Perimeter Institute)Title: On the firewall puzzle

    Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.

    8/18/2021Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics
    Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
    8/19/2021Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)Title: “Probing the Standard Model of Particle Physics Using the Muon
    Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
    8/25/2021Hitoshi Murayama  (UC Berkely & IPMU)Title: Some Exact Results in QCD-like and Chiral Gauge Theories

    Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/20/2021Thomas Peter Devereaux (Stanford University)

    Video

    Title:  Numerical investigations of models of the cuprates

    Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

    I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

    1/21/2021
    8:30-10:00pm ET
    Masahito Yamazaki (IPMU)

    Video

    TitleConfinement as Analytic Continuation Beyond Infinity
    1/27/2021Luigi Tizzano  (SCGP)

    Video

    TitleInstantons, symmetries and anomalies in five dimensions

    Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

    1/28/2021Simon Catterall (Syracuse University)

    Video

    TitleChiral Fermions from Staggered Fields

    Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.

    2/3/2020Philip Phillips (University of Illinois Urbana-Champaign)

    Video

    TitleBeyond BCS: An Exact Model for Superconductivity and Mottness

    Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
    [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

    2/4/2021Diego Delmastro (Perimeter PI)

    Video

    Title: Domain Walls in 4d N=1 Supersymmetric Yang-Mills

    Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).

    2/10/2021Senthil Todadri (MIT)

    Video

    TitleStrange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

    Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.

    [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789
    [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

    2/11/2021Michael Hermele (University of Colorado Boulder)

    Video

    TitleFamilies of gapped systems and quantum pumps

    Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.

    2/17/2021Jaume Gomis (Perimeter PI)

    Video

    TitleGlobal Anomalies on the Hilbert Space

    Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

    2/18/2021Xiao-Gang Wen (MIT)

    Video

    TitleA solution to the chiral fermion problem

    Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

    2/24/2021Zhenghan Wang (Microsoft Station Q)

    Video

    Title:  A Riemann sum of quantum field theory:  lattice Hamiltonian realization of TQFTs

    Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics.  I will start with the conceptual origin of this model as requested by the organizer.  Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds.  In the end, I will mention lattice models that generalize the Haah codes in two directions:  general three manifolds and more than two qubits per site.

    If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum.  New lattice models in fracton physics raise an interesting question:  what kinds of quantum field theories are they approximating if their continuous limits exist?  Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.

    2/25/2021Justin Kaidi (SCGP)

    Video

    TitleExploring Non-Supersymmetric String Theory

    Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.

    3/3/2021Tim Hsieh (Perimeter PI)

    Video

    Title: Symmetry-protected sign problem and magic in quantum phases of matter

    Abstract:  We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
    3/4/2021Mohamed Anber (Clark University)

    Video

    TitleGeneralized ‘t Hooft anomalies in vector-like theories

    Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories.  Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics.  In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls.  This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.

    3/10/2021

    7:30pm ET

    Satoshi Yamaguchi (Osaka U)

    Video

    TitleSupersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases

    Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.

    3/11/2021Chao-Ming Jian (Cornell)

    Video

    Title: Entanglement Criticality in Random Gaussian Quantum Circuits

    Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.

    3/17/2021Silviu S. Pufu (Princeton)

    Video

    Title:  Exact symmetries and threshold states in two-dimensional models for QCD

    Abstract:  Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

    3/18/2021
    12:00 – 1:30pm ET
    Thomas Dumitrescu (UCLA)

    Video

    Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD

    Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint

    3/24/2021Emily Nardoni (UCLA)

    Video

    Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD: Part 2

    Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.

    3/25/2021Michael Levin (U Chicago)

    Video

    TitleAn introduction to string-net models

    Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.

    3/31/2021Dam Thanh Son (U Chicago)

    Video

    TitleSpin of the fractional quantum Hall magnetoroton through polarized Raman scattering

    Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.

    4/1/2021

    9:00am ET

    Naoto Nagaosa (Tokyo U.)

    Video

    Title: Applied physics of high-Tc theories

    Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

    4/7/2021Sakura Schafer-Nameki (University of Oxford)

    Video

    Title: Higher Form Symmetries in string/M-theory

    Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.

    4/8/2020

    1:00pm ET

    Anton Kapustin (Caltech)

    Video

    TitleChiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics
    Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
    4/14/2021Lakshya Bhardwaj (University of Oxford)

    Video

    TitleConfinement and 1-form Symmetries in 4d from 6d (2,0)

    Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
    4/15/2021Michael Creutz (Brookhaven National Laboratory)

    Video

    TitleQCD without diagrams

    Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.

    4/21/2021Sergei Gukov (Caltech)

    Video

    TitleExotic new animals in the CFT zoo: quasiparticles and anisotropic scaling
    4/22/2021Dung-Hai Lee (UC Berkeley)

    Video

    Title Non-abelian bosonization in two and three spatial dimensions and some applications
    Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
    4/28/2021Dominic Williamson (Stanford)

    Video

    Title1-form symmetry-protected topological phases and measurement-based quantum computation

    Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
    4/29/2021Fiona Burnell (University of Minnesota)

    Video

    TitleSubsystem-Symmetry protected phases of matter

    Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter.  These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states.  After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries.  I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.

    5/5/2021

    8:00pm ET

    Ioannis Papadimitriou (KIAS)

    Video

    TitleAnomalies and Supersymmetry

    Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.

    5/6/2021Weslei Bernardino Fontana (Boston University & Estadual)

    Video

    TitleChern-Simons-like theories for fracton phases

    Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.

    5/12/2021André-Marie Tremblay (University of Sherbrooke)

    Video

    Title: A unified theoretical perspective on the cuprate phase diagram

    Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

    5/13/2021Masataka Watanabe (Weizmann Institute of Science)

    Video

    TitleQuantum Information Theory of the Gravitational Anomaly

    Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].

    5/19/2021Herbert Neuberger (Rutgers)

    Video

    Title:  Construction of Lattice Chiral Gauge Theory

    Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided.
    The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.

    5/20/2021Steven Weinberg (UT Austin)

    Video

    TitleMassless Particles
    6/2/2021Juven Wang (Harvard CMSA)

    Video

    TitleUltra Unification:
    Quantum Fields Beyond the Standard Model
    Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
    6/3/2021Tian Lan (CUHK & U Waterloo)TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

    Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
    6/9/2021Yizhi You (Princeton U)TitleFracton critical point and Topological phase transition beyond renormalization

    Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
    6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)TitleMinimal nondegenerate extensions and an anomaly indicator

    Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

    6/16/2021Arkady Vainshtein (UMN)TitleUses of Wilson Operator Expansion in Gauge Theories

    Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

    It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

    6/17/2021Mikhail Shifman (UMN)TitleWhat can supersymmetry do that other field theory cannot
    8/11/2021Piers Coleman (Rutgers)TBA
    8/26/2021Daniel Harlow (MIT)Title: Symmetries in quantum field theory and quantum gravity
    TBAAdy Stern & David Mross (Weizmann)TBA

    Fall 2020:

    DateSpeakerTitle/Abstract
    9/2/2020Subir Sachdev (Harvard University)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

    Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
    describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

    9/3/2020
    9:30 – 11:00am
    Janet Ling Yan Hung (Fudan University)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleGapped Boundaries, Junctions via (fermionic) anyon condensation

    Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.

    9/9/2020Ying-Hsuan Lin (Caltech)

    Video

    This meeting will be taking place virtually on Zoom.

    Title:  Exotic Consistent (1+1)d Anomalies: A Ghost Story

    Abstract:  We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions.  On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm.  For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection.  Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines.  The holomorphic bc ghost system realizes all the exotic consistent anomalies.

    9/10/2020Maissam Barkeshli (Maryland)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleAbsolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions

    Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553

    9/16/2020Andreas Karch (UT Austin)

    Video

    This meeting will be taking place virtually on Zoom.

    TitleBranes, Black Holes and Islands

    Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.

    9/17/2020Roger Mong (University of Pittsburgh)

    Video

    TitleUniversal multipartite entanglement in quantum spin chains

    Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems.  Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations.  Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment.  The measures are based off of the entanglement of purification and the reflected entropy popular among holography.  For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases.  We conclude with a few remarks regarding applications to 2D phases.

    9/23/2020Subir Sachdev (Harvard University)

    Video

    TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders II

    Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

    9/24/2020
    12:00 – 2:30pm ET
    Inna Vishik (University of California, Davis)

    Video

    TitleUniversality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201

    Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.

    9/30/2020Jordan Cotler (Harvard)

    Video

    Title: Gravitational Constrained Instantons and Random Matrix Theory

    Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action.  We find these instantons in all spacetime dimensions, for AdS and dS.  Many can be written in closed form and are quadratically stable.  In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes.  We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.

    10/1/2020Omri Golan (Weizmann Institute of Science)

    Video

    Title: Intrinsic sign problems in topological matter

    Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions.  Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.

    10/7/2020Romain Vasseur (UMass Amherst)

    Video

    Title“Symmetry-enriched random critical points and topological phase transitions“

    Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.

    10/8/2020Justin Kulp (Perimeter Institute)

    Video

    TitleOrbifold Groupoids

    Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
    10/14/2020Yin-Chen He (Perimeter Institute)

    Video

    TitleNon-Wilson-Fisher Kinks of Conformal Bootstrap: Deconfined Phase Transition and Beyond

    Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.

    10/15/2020Louis Taillefer (University of Sherbrooke)

    Video

    TitleNew signatures of the pseudogap phase of cuprate superconductors

    Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

    10/21/2020Oleg Dubinkin (University of Illinois at Urbana–Champaign)

    Video

    Title: Multipole Insulators and Higher-Form symmetries

    Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.

    10/22/2020Paul Fendley (University of Oxford)

    Video

    TitleThe uses of lattice topological defects

    Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains.
    These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion.  One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.  I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.

    10/28/2020Patrick Lee (MIT)

    Video

    Title: The not-so-normal normal state of underdoped Cuprate

    Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

    10/29/2020Biao Lian (Princeton University)

    Video

    TitleSymmetry, Insulating States and Excitations of Twisted Bilayer Graphene with Coulomb Interaction

    Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.

    11/5/2020Zohar Ringel (Racah Institute of Physics)TitleThe information bottleneck: A numerical microscope for order parameters.

    Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.

    11/6/2020
    12:30pm
    Zhi-Xun Shen (Stanford University)

    Video

    TitleEssential Ingredients for Superconductivity in Cupper Oxide Superconductors

    Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
    Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
    magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
    (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
    experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

    [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
    [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
    [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
    [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
    [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
    [6] A. Lanzara et al., Nature 412, 510 (2001)
    [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
    [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
    [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
    [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
    [11] A.G. Loeser et al., Science 273, 325 (1996)
    [12] S. Chen et al., Science, 366, 6469 (2019)
    [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
    [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
    [15] Yu He et al., Science, 362, 62 (Oct. 2018)
    [16] Z. Chen, Y. Wang et al., preprint, 2020

    11/11/2020Abhishodh Prakash (ICTS)

    Video

    TitleAspects of fermionic SPT phases: boundary supersymmetry and unwinding

    Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
    11/12/2020Chandra Varma (University of California, Riverside)

    Video

    TitleLoop-Current Order and Quantum-Criticality in Cuprates

    This talk is organized as follows:
    1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
    2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
    3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
    4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.

    Time permitting,
    (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
    (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
    (iii) Problems.

    11/18/2020Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

    Video

    Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

    Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

    11/19/2020Eduardo Fradkin (University of Illinois at Urbana-Champaign)

    Video

    TitlePair Density Waves and Intertwined Orders in High Tc Superconductors

    Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

    11/25/2020Qimiao Si (Rice University)

    Video

    Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

    Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

    12/2/2020Andrey Chubukov (University of Minnesota)

    Video

    TitleInterplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

    Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

    12/3/2020David B. Kaplan  (University of Washington)

    Video

    Title: Domain Wall Fermions and Chiral Gauge theories: Topological Insulators in Particle Physics

    Abstract:  Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics.  I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter.  How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!)  remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
    12/9/2020David Hsieh (Caltech)

    Video

    Title:  Signatures of anomalous symmetry breaking in the cuprates 

    Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
    [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

    [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516
    .

    12/10/2020Xinan Zhou (Princeton PCTS)

    Video

    Title: An analytic bootstrap approach for CFTs on RP^d and CFTs with boundaries

    Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
    12/16/2020Zheng-Yu Weng (Tsinghua University)

    Video

    TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

    Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

    12/17/2020Steven Kivelson (Stanford University)

    Video

    Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

    Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
    12/22/2020David Tong (University of Cambridge)

    Video

    TitleGapped Chiral Fermions

    Abstract: I’ll describe some quantum field theories that gap fermions without breaking chiral symmetries.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    CMSA-Colloquium-04.13.22

    Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure. But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

    In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    3/2/2022Richard Kenyon (Yale University)
    3/9/2022Richard Tsai (UT Austin)
    3/23/2022Joel Cohen (University of Maryland)
    3/30/2022Rob Leigh (UIUC)
    4/6/2022Johannes Kleiner (LMU München)
    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
    4/20/2022TBA
    4/27/2022TBA
    5/4/2022Melody Chan (Brown University)
    5/11/2022TBA
    5/18/2022TBA
    5/25/2022Heeyeon Kim (Rutgers University)

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024

    Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

    April 20, 2022 | 9:30 – 11:00 am ET

    Title: Mechanism Design

    Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

    Talk chairs: Scott Kominers, Sergiy Verstyuk

    SLIDES | VIDEO

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. Higgs-Coulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wall-crossing results for GLSM and generalizes Landau- Ginzburg/Calabi-Yau correspondence. The talk is based on a joint work in progress with Melissa Liu.

  • Colloquium
    9:30 am-10:30 am
    12/01/2024
    02CMSA-Colloquium-03.02.2022

    Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

    This is joint work with Dan Douglas and Haolin Shi.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Title: Stable Big Bang formation for the Einstein equations

    Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Itamar Shamir

    Title: Geometry, Entanglement and Quasi Local Data

    Abstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Tropical Lagrangian multi-sections and locally free sheaves

    9:30 am-10:30 am
    12/01/2024

    Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-03.03.2022-1544x2048-1

    Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138

    Member Seminar

    Speaker: Martin Lesourd

    Title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds

    Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, and Prof. D. A. Lee.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    Some combinatorics of Wilson loop diagrams

    9:30 am-10:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands.

    **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

    All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

    LINK TO FORM

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 02.03.23

    General Relativity Seminar

    Speaker: Chiara Toldo (Harvard)

    Title: Near extremal de Sitter black holes and JT gravity

    Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

  • Quantum Matter
    9:30 am-10:30 am
    12/01/2024
    CMSA QMMP 1.30.23

    Quantum Matter Seminar

    Title: Group Invariant States as Many-Body Scars

    Speaker: Igor R. Klebanov (Princeton University)

    Abstract: Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies.  The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

     

    https://www.youtube.com/watch?v=O4xizOTzpL4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=18

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024

    Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

    April 22, 2022 | 9:30 – 11:00 am ET

    Title: Auction Theory

    Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

    Talk chairs: Scott Kominers, Sergiy Verstyuk

    SLIDES | VIDEO Answers to Questions from Talks 2 and 3

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Prashant Kocherlakota (BHI)

    Title: Testing spacetime geometry with images of supermassive compact objects: Current status and the future

    Abstract: Astrophysical black holes (BHs) are expected to be described by the Kerr solution of the Einstein equations. Several frameworks have recently been developed to parametrically deform the Kerr metric in significantly different ways, to enable formulations of tests of the no-hair theorems. Testing the viability status of alternative models – such as non-Kerr BHs from general relativity, BHs from alternative theories, wormholes, and other exotic objects – as descriptors of astrophysical objects has been of longstanding interest. The Event Horizon Telescope (EHT) recently imaged Sagittarius A* (Sgr A*), the supermassive compact object at the center of the Galaxy, making such tests possible. In such tests, the shadow critical curve (or simply shadow boundary), defined on the observer’s image plane, has gained prominence as the observable of interest. We will discuss how the EHT is able to extract information regarding the shadow of Sgr A* and the status of associated tests of the spacetime geometry in the strong-field regime. Future imaging measurements expect to detect the so-called photon ring, a strong-gravitational lensing feature that appears in the close vicinity of the critical curve, which houses higher-order images of the emission source. Time permitting, we will also discuss how these can be used to set up more stringent tests of the spacetime metric and gravity in the future.

     

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: Strominger-Yau-Zaslow conjecture is one of the guiding principles in mirror symmetry, which not only predicts the geometric structures of Calabi-Yau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricci-flat metrics. In this talk, we will explain how SYZ fibrations on log Calabi-Yau surfaces detect the non-standard semi-flat metric which generalized the semi-flat metrics of Greene-Shapere-Vafa-Yau. Furthermore, we will use the SYZ fibration on log Calabi-Yau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Dan Lee

    Title: Survey on stability of the positive mass theorem

    Abstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk, I will discuss various results related to this question.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    The longest induced path in a sparse random graph

    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-12.14.2021

    Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Speaker: Du Pei

    Title: Wall-crossing from Higgs bundles to vortices

    Abstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks.  In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.

  • Combinatorics Physics and Probability
    9:30 am-10:30 am
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-11.30.2021

    Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
    In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
    Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
    This work was done in collaboration with Renaud Lambiotte.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-04.19.2022

    Abstract:  In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong.

    In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

  • Combinatorics Physics and Probability
    9:30 am-10:30 am
    12/01/2024

    Speaker: Nima Arkani-Hamed, IAS

    Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes

  • Colloquium
    9:30 am-10:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

    Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    Video

    2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

    Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

    I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    2/8/2022Wenbin Yan (Tsinghua University)
    (special time: 9:30 pm ET)
    Title: Tetrahedron instantons and M-theory indices

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    Video

    2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

    Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
    between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
    and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

    In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    3/2/2022Richard Kenyon (Yale University)
    3/9/2022Richard Tsai (UT Austin)
    3/23/2022Joel Cohen (University of Maryland)
    3/30/2022Rob Leigh (UIUC)
    4/6/2022Johannes Kleiner (LMU München)
    4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
    4/20/2022TBA
    4/27/2022TBA
    5/4/2022Melody Chan (Brown University)
    5/11/2022TBA
    5/18/2022TBA
    5/25/2022Heeyeon Kim (Rutgers University)

    Fall 2021

    DateSpeakerTitle/Abstract
    9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

    Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

    11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

    Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
    11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

    Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
    I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

    12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

    Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

    12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

    Abstract: Tree decompositions are a powerful tool in both structural
    graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

    Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

    12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

    Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures.

    The talk is partially based on joint works with Si Li.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Puskar Mondal

    Title: Stability and convergence issues in mathematical cosmology

    Abstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized, one needs to study its stability properties. Therefore, I will briefly discuss the stability issue and its consequences (e.g., structure formation, etc).

  • Algebraic Geometry in String Theory Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA-Algebraic-Geometry-in-String-Theory-02.01.2022

    Abstract: We will consider the following problem: if (C,x_1,…,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,…,y_n, then how many maps f:C -> X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory, the answer may be expressed in terms of the quantum cohomology of X, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle, though in the presence of sufficient positivity, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem, including joint work with Farkas, Pandharipande, and Cela, as well as work of other authors.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 03.09.23

    General Relativity Seminar

    Speaker: Jose Luis Jaramillo (Bourgogne U.)

    Title: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture

    Abstract: Can we measure the ‘effective regularity’ of spacetime from the perturbation of quasi-normal mode (QNM) overtones? Black hole (BH) QNMs encode the resonant response of black holes under linear perturbations, their associated complex frequencies providing an invariant probe into the background spacetime geometry. In the late nineties, Nollert and Price found evidence of a BH QNM instability phenomenon, according to which perturbed QNMs of Schwarzschild spacetime migrate to new perturbed branches of different qualitative behaviour and asymptotics. Here we revisit this BH QNM instability issue by adopting a pseudospectrum approach. Specifically, we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator by adopting a hyperboloidal formulation of spacetime. Non-selfadjoint (more generally non-normal) operators suffer potentially of spectral instabilities, the notion of pseudospectrum providing a tool suitable for their study. We find evidence that perturbed Nollert & Price BH QNMs track the pseudospectrum contour lines, therefore probing the analytic structure of the resolvent, showing the following (in)stability behaviour: i) the slowest decaying (fundamental) mode is stable, whereas ii) (all) QNM overtones are ultraviolet unstable (for sufficiently high frequency). Building on recent work characterizing Burnett’s conjecture as a low-regularity problem in general relativity, we conjecture that (in the infinite-frequency limit) generic ultraviolet spacetime perturbations make BH QNMs migrate to ‘Regge QNM branches’ with a precise universal logarithmic pattern. This is a classical general relativity (effective) low-regularity phenomenon, agnostic to possible detailed (quantum) descriptions of gravity at higher-energies and potentially observationally accessible.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

  • Member Seminar
    9:30 am-10:30 am
    12/01/2024

    Member Seminar

    Speaker: Jue Liu

    Title: Instability of naked singularities in general relativity

    Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, which are called by naked singularities, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method, and it is this wild method that helps us to extend some results to the asymmetric cases.

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024
    CMSA GR Seminar 02.23.23

    General Relativity Seminar

    Speaker: Nikolaos Athanasiou (University of Crete, Greece)

    Title: Formation of trapped surfaces in the Einstein-Yang-Mills system

    Abstract: The purpose of this talk is to give an overview of a semi-global existence result and a trapped surface formation results in the context of the Einstein-Yang-Mills system. Adopting a “signature for decay rates” approach first introduced by An, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yield the desired semi-global existence result. Once semi-global existence has been established, we will explain how the formation of a trapped surface follows from a standard ODE argument. This is joint work with Puskar Mondal and Shing-Tung Yau.

  • Math Science Literature Lecture Series
    9:30 am-11:00 am
    12/01/2024

    Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

    April 18, 2022 | 9:30 – 11:00 am ET

    Title: Game Theory Basics and Classical Existence Theorems

    Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

    Talk chairs: Scott Kominers, Sergiy Verstyuk

    SLIDES | VIDEO

     

  • Quantum Matter
    9:30 am-11:00 am
    12/01/2024
    CMSA-QMMP-Seminar-04.14.22-1583x2048-1

    Youtube video

     

    Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields.  Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos.  Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).

    As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role.  Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times.  Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime.  This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole).  It also makes a number of testable predictions.

    (Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

  • General Relativity Seminar
    9:30 am-10:30 am
    12/01/2024

    Title: On the Observable Shape of Black Hole Photon Rings

    Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

  • Special Seminar
    9:50 am-10:50 am
    12/01/2024-04/26/2016

    The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

    DayNameTitle
    09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
    09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
    09-22-2015Teng FeiSome new solutions to the Strominger system
    09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
    10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
    10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
    10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
    10-27-2015Tom IlmanenFlow of curves by curvature in R^n
    11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
    11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
    11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
    11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
    12-01-2015Tom Ilmanen
    01-26-2016Mao ShengUniformization of p-adic curves
    02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
    02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
    02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
    02-23-2016Junbin LiConstruction of black hole formation spacetimes
    03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
    03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
    03-15-2016Spring Break 
    03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
    03-29-2016Piotr ChruscielMass of characteristic surfaces
    04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
    04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
    04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
    04-26-2016Andre NevesA path to Yau’s conjecture
  • Seminars
    9:50 am-10:50 am
    12/01/2024

    The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

    DateNameTitle
    09-03-2015Long JinScattering Resonances for Convex Obstacles
    09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
    09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
    09-24-2015Felix FinsterCausal fermion systems and the causal action principle
    10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
    10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
    10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
    10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
    10-29-2015Pin YuShock formations for 3 dimensional wave equations
    11-05-2015No talk 
    11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
    11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
    11-26-2015ThanksgivingNo seminar
    12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
    01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
    02-04-2016Pranav PanditCategorical Kähler Geometry
    02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
    02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
    02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
    03-03-2016Piotr ChruscielSingularities in general relativity
    03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
    03-17-2016Spring BreakNo Talk
    03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
    03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
    04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
    04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
    04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
    04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
    05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
    05-12-2016Stefano Bianchini
  • General Relativity Seminar
    10:00 am-11:00 am
    12/01/2024

    Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

  • Workshop
    10:00 am-5:00 pm
    12/01/2024-05/08/2022

    On May 6–8, 2022, the CMSA  hosted a second NSF FRG Workshop.

    This project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology), Computer Science (Scientific Computing and Complexity Theory), and domain sciences, from Data Sciences to Computational Biology.

    Scientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time, however, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing, searching, simulating, analyzing, and comparing shapes. These methods and tools can be applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition, and satellite image analysis.

    This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

    The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.


    Workshop on Discrete Shapes
    May 6–8, 2022

    Organizers:

    • David Glickenstein (University of Arizona)
    • Joel Hass (University of California, Davis)
    • Patrice Koehl (University of California, Davis)
    • Feng Luo (Rutgers University, New Brunswick)
    • Maria Trnkova (University of California, Davis)
    • Shing-Tung Yau (Harvard)

    Speakers:

    • Miri Ben-Chen (Technion)
    • Alexander Bobenko (TU Berlin)
    • John Bowers (James Madison)
    • Steven Gortler (Harvard)
    • David Gu (Stony Brook)
    • Anil Hirani (UIUC)
    • Yanwen Luo (Rutgers)
    • Peter Schroeder (Caltech)
    • Justin Solomon (MIT)
    • Tianqi Wu (Clark University)

    Contributed Talk Speakers:

    • Oded Stein (MIT)
    • Bohan Zhou (Dartmouth)

    Schedule
    Schedule (PDF)

    Friday, May 6, 2022

    10:00–10:05 amWelcome Opening
    10:05–10:55 amAnil N. HiraniTitle: Discrete vector bundles with connection

    Abstract: We have recently initiated a generalization of discrete exterior calculus to differential forms with values in a vector bundle. A discrete vector bundle with connection over a simplicial complex has fibers at vertices and transport maps on edges, just as in lattice gauge theory. The first part of this work involves defining and examining properties of a combinatorial exterior covariant derivative and wedge product. We find that these operators commute with pullback under simplicial maps of the base space. From these definitions emerges a combinatorial curvature. In the second part of this work we showed that the curvature behaves as one expects: it measures failure of parallel transport to be independent of the path, and is the local obstruction to a trivialization. For a bundle with metric, metric compatibility of the discrete connection is equivalent to a Leibniz rule.  Vanishing curvature is indeed equivalent to an appropriately defined discrete flat connection, and curvature obstructs trivializability. In this talk I will focus on just the first part, and talk about naturality of the discrete exterior covariant derivative and discrete wedge product using simple examples. Joint work with Daniel Berwick-Evans (UIUC) and Mark Schubel (Apple, Inc.).

    11:10–12:00 pmDavid GuTitle: Surface Quadrilateral Meshing Based on Abel-Jacobi Theory

    Abstract: Surface quadrilateral meshing plays an important role in many fields. For example, in CAD (computer-aided design), all shapes are represented as Spline surfaces, which requires structured quad-meshing; in CAE (computer-aided engineering), the surface tessellation greatly affects the accuracy and efficiency of numerical simulations. Although the research on mesh generation has a long history, it remains a great challenge to automatically generate structured quad-meshes with high qualities. The key is to find the governing equation for the singularities of the global structured quad-meshes.

    In this talk, we introduce our recent discovery:  the singularities of a quad-mesh are governed by the Abel theorem. We show that each quad-mesh determines a conformal structure and a meromorphic quadratic differential, the configuration of the mesh singularities can be described as the divisor of the differential. The quad-mesh divisor minus four times of the divisor of a holomorphic one-form is principal and satisfies the Abel theorem: its image under the Jacobi map is zero in the Jacobi variety.

    This leads to a rigorous and efficient algorithm for surface structured quadrilateral meshing. After determining the singularities, the metric induced by the quad-mesh can be computed using the discrete Yambe flow, and the meromorphic quartic differential can be constructed, the trajectories of the differentials give the quad-mesh. The method can be applied directly for geometric modeling and computational mechanics.

    12:00–2:00 pmLunch Break
    2:00–2:50 pm Justin SolomonTitle:  Geometry Processing with Volumes

    Abstract:  Many algorithms in geometry processing are restricted to two-dimensional surfaces represented as triangle meshes.  Drawing inspiration from simulation, medical imaging, and other application domains, however, there is a substantial demand for geometry processing algorithms targeted to volumes represented as tetrahedral meshes or grids.  In this talk, I will summarize some efforts in our group to develop a geometry processing toolkit specifically for volumes.  Specifically, I will cover our recent work on hexahedral remeshing via cuboid decomposition, volumetric correspondence, and minimal surface computation via geometric measure theory.

    3:00–3:20 pmOded SteinTitle: Optimization for flip-free parametrization

    Abstract: Parametrizations without flipped elements are desirable in a variety of applications such as UV mapping and surface/volume correspondence. Computing flip-free parametrizations can be challenging, and there are many different approaches to the problem. In this talk we will look at multiple strategies for flip-free parametrizations that are based on the optimization of continuous energies. Due to the nature of the problem, these energies are often nonconvex and unbounded, which is a challenge for optimization methods. We will also take a closer look at our recently developed method for computing flip-free parametrizations using the Alternating Direction Method of Multipliers (ADMM).

    3:20–4:00 pmBreak
    4:00–4:50 pmJohn BowersTitle: Koebe-Andre’ev-Thurston Packings via Flow

    Abstract: Recently, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation, flip-and-flow, that allows two tangency packings whose contact graphs differ by a combinatorial edge flip to be continuously deformed from one to the other while maintaining tangencies across all of their common edges. Starting from a canonical tangency circle packing with the desired number of circles a finite sequence of flip-and-flow operations may be applied to obtain a circle packing for any desired (proper) contact graph with the same number of circles.

    The full Koebe-Andre’ev-Thurston theorem generalizes the circle packing theorem to allow for neighboring circles to overlap by angles up to $\pi/2$. In this talk I will show that the Connelly-Gortler method can be extended to allow for circles to overlap to angles up to $\pi/2$. This results in a new proof of the general Koebe-Andre’ev-Thurston theorem for disk patterns on $\mathbb{S}^2$ as well as a numerical algorithm for computing them. The proof involves generalizing a notion of convexity for circle polyhedra that was recently used to prove the global rigidity of certain circle packings, which is then used to show that all convex circle polyhedra are infinitesimally rigid, a result of independent interest.

    5:00–5:30 pmMovies “conform!” & ”Koebe polyhedra”

     

    Saturday, May 7, 2022

    9:30–10:20 amAlexander BobenkoTitle: The Bonnet problem: Is a surface characterized by its metric and curvatures?

    Abstract: We consider a classical problem in differential geometry, known as the Bonnet problem, whether a surface is characterized by a metric and mean curvature function. Generically, the answer is yes. Special cases when it is not the case are classified. In particular, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas

    10:20–11:00 amBreak
    11:00–11:50 amMiri Ben ChenTitle: Surface Multigrid via Intrinsic Prolongation

    Abstract: The solution of a linear system is a required ingredient in many geometry processing applications, and multigrid methods are among the most efficient solution techniques. However, due to the unstructured nature of triangle meshes, mapping functions between different multigrid levels is challenging. In this talk I will present our recent work that uses an intrinsic prolongation operator as the main building block in a multigrid solver for curved triangle meshes. Our solver can be used as a black-box in any triangle-mesh based system that requires a linear solve, and leads to order of magnitude time-efficiency improvement compared to direct solvers.

    12:00–2:00 pmLunch Break
    2:00–2:50 pmSteven GortlerTitle: Reconstructing configurations and graphs from unlabeled distance measurements

    Abstract: Place a configuration of n  points (vertices) generically in R^d. Measure the Euclidean lengths of m point-pairs (edges). When is the underlying graph determined by these $m$ numbers (up to isomorphism)? When is the point configuration determined by these $m$ numbers (up to congruence)? This question is motivated by a number of inverse problem applications. In this talk, I will review what is known about this question.

    3:00–3:20 pmBohan ZhouTitle: Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs

    Abstract: Optimal transport has profound and wide applications since its introduction in 1781 by Monge. Thanks to the Benamou-Brenier formulation, it provides a meaningful functional in the image science like image and shape registrations. However, exact computation through LP or PDE is in general not practical in large scale, while the popular entropy-regularized method introduces additional diffusion noise, deteriorating shapes and boundaries. Until the recent work [Jacobs and Leger, A Fast Approach to Optimal Transport: the back-and-forth method, Numerische Mathematik, 2020], solving OT in a both accurate and fast fashion finally becomes possible. Multiple marginal optimal transport is a natural extension from OT but has its own interest and is in general more computationally expensive. The entropy method suffers from both diffusion noise and high dimensional computational issues. In this work with Matthew Parno, we extend from two marginals to multiple marginals, on a wide class of cost functions when those marginals have a graph structure. This new method is fast and does not introduce diffusion. As a result, the new proposed method can be used in many fields those require sharp boundaries. If time allows, we will illustrate by examples the faithful joint recover via MMOT of images with sharp boundaries, with applications on sea ice prediction.

    3:20–4:00 pmBreak
    4:00–4:50 pmPeter SchroederTitle: Constrained Willmore Surfaces

    Abstract: The Willmore energy of a surface is a canonical example of a squared curvature bending energy. Its minimizers are therefore of interest both in the theory of surfaces and in practical applications from physical and geometric modeling. Minimizing the bending energy alone however is insufficient. Taking a cue from univariate splines which incorporate an isometry constraint we consider Willmore minimizers subject to a conformality constraint. In this talk I will report on a numerical algorithm to find such constrained minimizers for triangle meshes.

    Joint work with Yousuf Soliman (Caltech), Olga Diamanti (UGraz), Albert Chern (UCSD), Felix Knöppel (TU Berlin), Ulrich Pinkall (TU Berlin).

    5:00–5:50 pmProblems and Application discussions

     

    Sunday, May 8, 2022

    9:00–9:50 amTianqi WuTitle: Convergence of discrete uniformizations

    Abstract: The theory of discrete conformality, based on the notion of vertex scaling, has been implemented in computing conformal maps or uniformizations of surfaces. We will show that if a Delaunay triangle mesh approximates a smooth surface, then the related discrete uniformization will converge to the smooth uniformization, with an error bounded linearly by the size of the triangles in the mesh.

    10:10–11:00 amYanwen LuoTitle:  Recent Progress in Spaces of Geodesic Triangulations of Surfaces

    Abstract:
    Spaces of geodesic triangulations of surfaces are natural discretization of the groups of surface diffeomorphisms isotopy to the identity. It has been conjectured that these spaces have the same homotopy type as their smooth counterparts. In this talk, we will report the recent progress in this problem. The key ingredient is the idea in Tutte’s embedding theorem. We will explain how to use it to identify the homotopy types of spaces of geodesic triangulations. This is joint work with Tianqi Wu and Xiaoping Zhu.
    11:10–12:00 pmProblems and Application discussions
    12:00–1:00 pmMovie“The Discrete Charm of Geometry”

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Meng Cheng (Yale)

    Title: Symmetry and many-body topology in mixed states

    Abstract: It is by now well-understood that gapped ground states of local Hamiltonians can be classified topologically, and the nontrivial states exhibit many interesting topological phenomena. In this talk I’ll discuss recent developments in generalizing the topological classification to mixed states. Global symmetry plays a key role in understanding phases in pure states. For mixed states, certain “weak” symmetries may hold “on average” for the entire ensemble, in contrast to “strong” symmetries respected by each state in the ensemble. I will show that the interplay between these two kinds of symmetries lead to a rich landscape of symmetry-protected mixed states, and can also be used to characterize mixed state topological order.

     

  • CMSA EVENT: Computational Biology Symposium
    10:00 am-4:00 pm
    12/01/2024
    Compbiotextlessfeature-600x338

    On May 3, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo.

    The symposium will begin at 10:00am ET. There will be a morning and afternoon session, with an hour break for lunch.

    Videos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.

    Confirmed participants:

    Schedule:

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/19/2021 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Swampland Seminar
    10:00 am-11:00 am
    12/01/2024

    Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Aleksey Cherman (UMN)

    Title: Exact lattice chiral symmetry in 2d gauge theory

    Abstract: Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory.  I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

  • Swampland Seminar
    10:00 am-11:00 am
    12/01/2024

    Swampland Seminar

    Speakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech)

    Title: Causality constraints on corrections to Einstein gravity

    Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

  • Quantum Matter
  • Seminars

    Seminars Colloquia & Seminar
    13/3/2018 Topology Seminar

    10:00 am-11:30 am
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/26/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/22/2018 Topology Seminar

    10:00 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 05.05.23 (2)

    Quantum Matter Seminar

    Speaker: Sona Najafi (IBM Quantum)

    Title: Detecting central charge in a superconducting quantum processor

    Abstract: Physical systems at the continuous phase transition point exhibit conformal symmetry rendering local scaling invariance. In two dimensions, the conformal group possesses infinite generators described by Virasoro algebra with an essential parameter known as a central charge. While the central charge manifests itself in a variety of quantities, its detection in experimental setup remains elusive. In this work, we utilize Shannon-Renyi entropy on a local basis of a one-dimensional quantum spin chain at a critical point. We first use a simulated variational quantum eigen solver to prepare the ground state of the critical transfer field Ising model and XXZ model with open and periodic boundary conditions and perform local Pauli X and Z basis measurements. Using error mitigation such as probabilistic error cancellation, we extract an estimation of the local Pauli observables needed to determine the Shannon-Renyi entropy with respect to subsystem size. Finally, we obtain the central charge in the sub-leading term of Shannon-Renyi entropy.

    https://www.youtube.com/watch?v=Os26XRahD0c&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=5

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024

    Speaker: Haoyu Guo (Harvard)

    Title: Transport in large-N critical Fermi surface

    Abstract:
     A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermion-scalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and show that a previously proposed mega^{-2/3} contribution to the optical conductivity at frequency mega has vanishing co-efficient. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity behaves like a Fermi liquid. Arxiv references: 2203.04990, 2207.08841

  • Topological Quantum Matter Seminar
    10:00 am-11:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 12.07.22

    Topological Quantum Matter Seminar

    Speaker: Vasil Rokaj (Harvard)

    Title: Controlling Quantum Matter with Quantum Cavity Fields

    Abstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free electron gas [5]. The exact analytic solution of the Sommerfeld model in the cavity will be presented as well as its fundamental properties. Then, in the second part of the talk, I will focus on a many-particle system of cold ions in a harmonic trap coupled to the cavity field. I will show how this system couples collectively to the cavity and that hybrid states between light and matter, known as polaritons, emerge. The formation of polaritons leads to the modification of the properties of the cold ions and enhances the localization of the many-body wave function [6]. Connections to experiments will be discussed as well.

    [1] F. Garcia-Vidal, C. Ciuti, T. W. Ebbesen, Science, 373, 178 (2021)

    [2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)

    [3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)

    [4] T. W. Ebbesen, Acc. Chem. Res. 49, 11, 2403–2412 (2016)

    [5] V. Rokaj, M. Ruggenthaler, F. G. Eich, A. Rubio, Phys. Rev. Research 4, 013012 (2022)

    [6] V. Rokaj, S.I. Mistakidis, H.R. Sadeghpour, arXiv:2207.03436 (2022)

  • Algebraic Geometry in String Theory Seminar
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Pre-talk Speaker: David Wu (Harvard Physics): 10:00-10:30 am

    Speaker: Damian van de Heisteeg, CMSA

    Title: Species Scale across String Moduli Spaces

    Abstract: String theories feature a wide array of moduli spaces. We propose that the energy cutoff scale of these theories – the so-called species scale – can be determined through higher-curvature corrections. This species scale varies with the moduli; we use it both asymptotically to bound the diameter of the field space, as well as in the interior to determine a “desert point” where it is maximized.

  • Joint Harvard-CUHK-YMSC Differential Geometry
    10:00 am-11:00 am
    12/01/2024

    Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or, Neumann) eigenvalues. Using the results on the Birkhoff conjecture, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks, which Kac proved to be uniquely determined, these are the only domains for which it is known that one can hear their shape.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Andreas Bauer  (Freie Universität Berlin)

    Title: Tensorial TQFT and disentangling modular Walker-Wang models

    Abstract: I will introduce simple “tensorial” definitions for many algebraic and categorical structures appearing in the classification of topological phases of matter. Such “tensorial TQFTs” will be defined as maps that associate tensors to geometric/topological objects of some type, subject to gluing axioms. Tensorial TQFTs are very directly related to microscopic physical models in terms of discrete path integrals. I will use those tensorial definitions to construct invertible boundaries which disentangle modular Walker-Wang models.

     

    https://www.youtube.com/watch?v=MJ8NRSrvihQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=12

  • Topological Quantum Matter Seminar
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Topological Seminar 11.16.22

    Topological Quantum Matter Seminar

    Speaker: Jérôme Faist  (ETH Zurich)

    Title: Vacuum fluctuations in cavities: breakdown of the topological protection in the integer Quantum Hall effect

    Abstract: When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling ΩR is such that the coupling energy becomes close to the one of the bare matter resonance ω0. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian.

    In a microcavity, the strength of the electric field caused by the vacuum fluctuations, to which the strength of the light-matter coupling ΩR is proportional, scales inversely with the cavity volume. One very interesting feature of the circuit-based metamaterials is the fact that this volume can be scaled down to deep subwavelength values in all three dimension of space.1 Using metamaterial coupled to two-dimensional electron gases under a strong applied magnetic field, we have now explored to which extend this volume can be scaled down and reached a regime where the stability of the polariton is limited by diffraction into a continuum of plasmon modes2.

    We have also used transport to probe the ultra-strong light-matter coupling3, and show now that the latter can induce a breakdown of the integer quantum Hall effect4. The phenomenon is explained in terms of cavity-assisted hopping, an anti-resonant process where an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity5. We are also evaluating a proposal suggesting that the value of the quantization voltage can be renormalized by the cavity6.

     

    1. Scalari, G. et al. Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial. Science 335, 1323–1326 (2012).
    2. Rajabali, S. et al. Polaritonic Nonlocality in Light Matter Interaction. Nat Photon 15, 690–695 (2021).
    3. Paravicini-Bagliani, G. L. et al. Magneto-Transport Controlled by Landau Polariton States. Nat. Phys. 15, 186–190 (2019).
    4. Appugliese, F. et al. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science 375, 1030–1034 (2022).
    5. Ciuti, C. Cavity-mediated electron hopping in disordered quantum Hall systems. Phys. Rev. B 104, 155307 (2021).
    6. Rokaj, V., Penz, M., Sentef, M. A., Ruggenthaler, M. & Rubio, A. Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance. Phys. Rev. B 105, 205424 (2022).

     

  • Quantum Matter
    10:00 am-11:00 am
    12/01/2024
    CMSA QMMP 03.10.23

    Quantum Matter Seminar

    Speaker: Yichen Huang (Harvard)

    Title: Quantum entropy thermalization

    Abstract: In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization.

    References: arXiv:2302.10165, 2209.09826; Joint work with Aram W. Harrow

     

    https://www.youtube.com/watch?v=8b4g9SEFn_Y&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=13

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Scalable Dynamic Graph Algorithms

    10:00 am-10:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    CMSA Interdisciplinary Science Seminar

    Speaker: Quanquan Liu, Northwestern University

    Title: Scalable Dynamic Graph Algorithms

    Abstract: The field of dynamic graph algorithms seeks to understand and compute statistics on real-world networks that undergo changes with time. Some of these networks could have up to millions of edge insertions and deletions per second. In light of these highly dynamic networks, we propose various scalable and accurate graph algorithms for a variety of problems. In this talk, I will discuss new algorithms for various graph problems in the batch-dynamic model in shared-memory architectures where updates to the graph arrive in multiple batches of one or more updates. I’ll also briefly discuss my work in other dynamic models such as distributed dynamic models where the communication topology of the network also changes with time (ITCS 2022). In these models, I will present efficient algorithms for graph problems including k-core decomposition, low out-degree orientation, matching, triangle counting, and coloring.

    Specifically, in the batch-dynamic model where we are given a batch of B updates, I’ll discuss an efficient O(B log^2 n) amortized work and O(log^2 n log log n) depth algorithm that gives a (2+\epsilon)-approximation on the k-core decomposition after each batch of updates (SPAA 2022). We also obtain new batch-dynamic algorithms for matching, triangle counting, and coloring using techniques and data structures developed in our k-core decomposition algorithm. In addition to our theoretical results, we implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyper-threading on 11 graphs of varying densities and sizes. Our experiments show improvements over state-of-the-art algorithms even on machines with only 4 cores (your standard laptop). I’ll conclude with a discussion of some open questions and potential future work that these lines of research inspire.

    Bio: Quanquan C. Liu is a postdoctoral scholar at Northwestern University under the mentorship of Prof. Samir Khuller. She completed her PhD in Computer Science at MIT where she was advised by Prof. Erik Demaine and Prof. Julian Shun. Before that, she obtained her dual bachelor’s degree in computer science and math also at MIT. She has worked on a number of problems in algorithms and the intersection between theory and practice. Her most recent work focuses on scalable dynamic and static graph algorithms as well as differentially private graph algorithms for problems including k-core decomposition, densest subgraphs, subgraph counting, matching, maximal independent set and coloring. She has earned the Best Paper Award at SPAA 2022, a NSF Graduate Research Fellowship, and participated in the 2021 EECS Rising Stars workshop. Outside of research, she is extensively involved in programming outreach as a coach for the USA Computing Olympiad (USACO) and as a trainer for the North America Programming Camp (NAPC).

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Margarita Davydova (MIT)

    Title: Floquet codes, automorphisms, and quantum computation

    Abstract: In this talk, I will introduce a new kind of measurement-based quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of low-weight measurements which simultaneously encode logical information and enable error correction.  We introduce a new class of quantum error-correcting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes.

    As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of time-like domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model.  This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes.

    The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two- and, rarely three-body measurements. Using adaptive two-body measurements, we can achieve a non-Clifford gate in 3+1d, making the first step towards universal quantum computation in this model.

    The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].

  • CMSA EVENT: Frontiers in Applied Mathematics and Computation
    10:00 am-2:00 pm
    12/01/2024-04/29/2020
    Frontiers In Applied Mathematics And Computation

    Together with the School of Engineering and Applied Sciences, the CMSA will be hosting a lecture series on the Frontiers in Applied Mathematics and Computation. Talks in this series will aim to highlight current research trends at the interface of applied math and computation and will explore the application of these trends to challenging scientific, engineering, and societal problems.

    Lectures will take place on March 25, April 1, and April 29, 2021.

    Speakers:

    • George Biros (U.T. Austin)
    • Laura Grigori (INRIA Paris)
    • Samory K. Kpotufe (Columbia)
    • Jonas Martin Peters (University of Copenhagen)
    • Joseph M. Teran (UCLA)

    The schedule below will be updated as talks are confirmed.

     

    Date/TimeSpeakerTitle/Abstract
    3/25/2021
    10:00 – 11:00am ET
    Joseph M. TeranTitle: Affine-Particle-In-Cell with Conservative Resampling and Implicit Time Stepping for Surface Tension Forces

    Abstract: The Particle-In-Cell (PIC) method of Harlow is one of the first and most widely used numerical methods for Partial Differential Equations (PDE) in computational physics. Its relative efficiency, versatility and intuitive implementation have made it particularly popular in computational incompressible flow, plasma physics and large strain elastoplasticity. PIC is characterized by its dual particle/grid (Lagrangian/Eulerian) representation of material where particles are generally used to track material transport in a Lagrangian way and a structured Eulerian grid is used to discretize remaining spatial derivatives in the PDE. I will discuss the importance of conserving linear and angular momentum when switching between these two representations and the recent Affine-Particle-In-Cell (APIC) extension to PIC designed for this conservation. I will also discuss a recent APIC technique for discretizing surface tension forces and their linearizations needed for implicit time stepping. This technique is characterized by a novel surface resampling strategy and I will discuss a generalization of the APIC conservation to this setting.

    4/1/2021
    9:00 – 10:00am ET
    George BirosTitle: Inverse biophysical modeling and its application to neurooncology

    Abstract: A predictive, patient-specific, biophysical model of tumor growth would be an invaluable tool for causally connecting diagnostics with predictive medicine. For example, it could be used for tumor grading, characterization of the tumor microenvironment, recurrence prediction, and treatment planning,  e.g., chemotherapy protocol or enrollment eligibility for clinical trials. Such a model also would provide an important bridge between molecular drivers of tumor growth and imaging-based phenotypic signatures, and thus,  help identify and quantify mechanism-based associations between these two. Unfortunately, such a predictive biophysical model does not exist. Existing models undergoing clinical evaluation are too simple–they do not even capture the MRI phenotype. Although many highly complex models have been proposed, the major hurdle in deploying them clinically is their calibration and validation.

    In this talk, I will discuss the challenges related to the calibration and validation of biophysical models, and in particular the mathematical structure of the underlying inverse problems. I will also present a new algorithm that localizes the tumor origin within a few millimeters.

    4/1/2021
    10:00 – 11:00am ET
    Samory K. KpotufeTitle: From Theory to Clustering

    Abstract: Clustering is a basic problem in data analysis, consisting of partitioning data into meaningful groups called clusters. Practical clustering procedures tend to meet two criteria: flexibility in the shapes and number of clusters estimated, and efficient processing. While many practical procedures might meet either of these criteria in different applications, general guarantees often only hold for theoretical procedures that are hard if not impossible to implement. A main aim is to address this gap.
    We will discuss two recent approaches that compete with state-of-the-art procedures, while at the same time relying on rigorous analysis of clustering. The first approach fits within the framework of density-based clustering, a family of flexible clustering approaches. It builds primarily on theoretical insights on nearest-neighbor graphs, a geometric data structure shown to encode local information on the data density. The second approach speeds up kernel k-means, a popular Hilbert space embedding and clustering method. This more efficient approach relies on a new interpretation – and alternative use – of kernel-sketching as a geometry-preserving random projection in Hilbert space.
    Finally, we will present recent experimental results combining the benefits of both approaches in the IoT application domain.
    The talk is based on various works with collaborators Sanjoy Dasgupta, Kamalika Chaudhuri, Ulrike von Luxburg, Heinrich Jiang, Bharath Sriperumbudur, Kun Yang, and Nick Feamster.

    4/29/2021
    12:00 – 1:00pm ET
    Jonas Martin PetersTitle: Causality and Distribution Generalization

    Abstract: Purely predictive methods do not perform well when the test distribution changes too much from the training distribution. Causal models are known to be stable with respect to distributional shifts such as arbitrarily strong interventions on the covariates, but do not perform well when the test distribution differs only mildly from the training distribution. We discuss anchor regression, a framework that provides a trade-off between causal and predictive models. The method poses different (convex and non-convex) optimization problems and relates to methods that are tailored for instrumental variable settings. We show how similar principles can be used for inferring metabolic networks. If time allows, we discuss extensions to nonlinear models and theoretical limitations of such methodology.

    4/29/2021
    1:00 – 2:00pm ET
    Laura GrigoriTitle: Randomization and communication avoiding techniques for large scale linear algebra

    Abstract: In this talk we will discuss recent developments of randomization and communication avoiding techniques for solving large scale linear algebra operations. We will focus in particular on solving linear systems of equations and we will discuss a randomized process for orthogonalizing a set of vectors and its usage in GMRES, while also exploiting mixed precision.  We will also discuss a robust multilevel preconditioner that allows to further accelerate solving large scale linear systems on parallel computers.

  • Math Science Literature Lecture Series
    10:00 am-11:30 am
    12/01/2024

    Zhengwei Liu (Tsinghua University)

    Title: Subfactors–in Memory of Vaughan Jones

    Abstract: Jones initiated modern subfactor theory in early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial, for which Jones won the Fields Metal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed.

    Talk chair: Arthur Jaffe

    Slides | Video 

  • Swampland Seminar
    10:00 am-11:30 am
    12/01/2024

    Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

  • Quantum Matter
    10:00 am
    12/01/2024
    CMSA QMMP 03.03.23

    Quantum Matter Seminar

    Speaker: Anna Hasenfratz (University of Colorado)

    Title: Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions
    Abstract: 4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the conformal phase is well established, very little is known about the nature of the phase transition or the strong coupling phase.
    Lattice QCD methods can predict the RG $\beta$ function, but the calculations are often limited by non-physical bulk phase transition that prevent exploring the strong coupling region of the phase diagram. Even the critical flavor number is controversial, estimates vary between $N_f=8$ and 14 for fundamental fermions.
    Using an improved lattice actions that include heavy Pauli-Villars (PV) type bosons to reduce ultraviolet fluctuations, I was able to simulate an SU(3) system with 8 fundamental flavors at much stronger renormalized coupling than previously possibly. The numerical results indicate a smooth phase transition from weak coupling to a strongly coupled phase.
    I investigate the critical behavior of the transition using finite size scaling. The result of the scaling analysis is not consistent with a first order phase transition, but it is well described by   Berezinsky-Kosterlitz-Thouless or BKT scaling. BKT scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that warrants further investigations.
    The strongly coupled phase appear to be chirally symmetric but gapped, suggesting symmetric mass generation (SMG). This could be the consequence of the lattice fermions used in this study. Staggered fermions in the massless limit are known to be anomaly free, allowing an SMG phase in the continuum limit.

     


    References:
    Phys.Rev.D 106 (2022) 1, 014513 • e-Print: 2204.04801
    Phys.Rev.D 104 (2021) 7, 074509 • e-Print: 2109.02790
    For anomalies and staggered fermion, see
    Phys.Rev.D 104 (2021) 9, 094504 • e-Print: 2101.01026
    https://www.youtube.com/watch?v=3jtNsFGszjE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=14
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Xiao-Gang Wen (MIT)

    Title: A 6-year journey: from gravitational anomaly to a unified theory of generalized symmetry

    Abstract: Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topological-order correspondence. I will also discuss some applications of emergent generalized symmetry.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/16/2020 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Swampland Seminar
    10:00 am-11:30 am
    12/01/2024
    Speakers: Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)
    Title4d strings at strong coupling
    As usual, the format will be 45 min talk + 30 min discussion, to encourage participation from the audience.
    Looking forward to seeing you there!
  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    General Relativity Program Minicourses

    10:00 am-1:00 pm
    12/01/2024-05/17/2022
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Minicourses

    General Relativity Program Minicourses

    During the Spring 2022 semester, the CMSA hosted a program on General Relativity.

    This semester-long program included four minicourses running in March, April, and May;  a conference April 4–8, 2022;  and a workshop from May 2–5, 2022.

     

    ScheduleSpeakerTitleAbstract
    March 1 – 3, 2022
    10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
    Dr. Stefan CzimekCharacteristic Gluing for the Einstein EquationsAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).
    March 22 – 25, 2022
    22nd & 23rd, 10:00 am – 11:30am ET
    24th & 25th, 11:00 am – 12:30pm ET
    Location: Hybrid. CMSA main seminar room, G-10.
    Prof. Lan-Hsuan HuangExistence of Static Metrics with Prescribed Bartnik Boundary DataAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is

    1. The conjecture and an overview of the results
    2. Static regular: a sufficient condition for existence and local uniqueness
    3. Convex boundary, isometric embedding, and static regular
    4. Perturbations of any hypersurface are static regular

    Video on Youtube: March 22, 2022

    March 29 – April 1, 2022 10:00am – 12:00pm ET, each day

    Location: Hybrid. CMSA main seminar room, G-10.

    Prof. Martin TaylorThe nonlinear stability of the Schwarzschild family of black holesAbstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.
    April 19 & 21, 2022
    10 am – 12 pm ET, each dayZoom only
    Prof. Håkan AndréassonTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.

    Video 4/19/2022

    Video 4/22/2022

    May 16 – 17, 2022
    10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
    Prof. Marcelo DisconziA brief overview of recent developments in relativistic fluidsAbstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.

    1. Set-up, review of standard results, physical motivation.
    2. The relativistic Euler equations: null structures and the problem of shocks.
    3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
    4. Relativistic viscous fluids.

    Video 5/16/2022

    Video 5/17/2022

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: John Baez (University of California, Riverside)

    Title: Two of my favorite numbers: 8 and 24

    Abstract: The numbers 8 and 24 play special roles in mathematics. The number 8 is special because of Bott periodicity, the octonions and the E8 lattice, while 24 is special for many reasons, including the binary tetrahedral group, the 3rd stable homotopy group of spheres, and the Leech lattice. The number 8 does for superstring theory what the number 24 does for bosonic string theory. In this talk, which is intended to be entertaining, I will overview these matters and also some connections between the numbers 8 and 24.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 05.12.23

    Quantum Matter Seminar

    Speaker: Carolyn Zhang (U Chicago)

    Title: Anomalies of (1+1)D categorical symmetries

    Abstract: We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $A$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the \emph{electric} Lagrangian algebra, that describes a phase with $A$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $A$. We observe that if there exists a different gapped boundary, given by a \emph{magnetic} Lagrangian algebra, then there exists a gapped phase where $A$ is not spontaneously broken at all, which means that $A$ is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $A$ being anomaly-free. As an application, we consider the Drinfeld centers of $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.

    https://www.youtube.com/watch?v=hSzBMYEY_q8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=4

  • Swampland Seminar
    10:00 am-11:00 am
    12/01/2024

    Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 06.30.23

    Quantum Matter Seminar

    Speaker: Marieke Van Beest (SCGP)

    Title: Monopoles, Scattering, and Generalized Symmetries

    Abstract: In this talk, we will discuss the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle, as they can carry fractional quantum numbers. We argue that such outgoing particles live in the twisted sector of a topological co-dimension 1 surface, which ends topologically on the monopole. This symmetry defect is often non-invertible, and as such the outgoing radiation not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory, which is a new prediction.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 06.26.23

    Quantum Matter Seminar

    Title: Chiral fermionic CFTs of central charge ≤ 16

    Abstract: We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac’s theorem and bosonization/fermionization. This talk will discuss the derivation of this result, its application to the classification of non-supersymmetric heterotic string theories, and along the way we’ll address some oft-overlooked subtleties of bosonization from the point of view of anomalies and topological phases.

  • Quantum Matter
    10:00 am-12:00 pm
    12/01/2024
    CMSA QMMP 06.13.23

    Quantum Matter Seminar

    Speaker: Brandon C. Rayhaun (C. N. Yang ITP, Stony Brook University)

    Title: Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality

    Abstract: Conformal field theories in (1+1)D are key actors in many dramas of physics and mathematics. Their classification has therefore been an important and long-standing problem. In this talk, I will explain the main ideas behind the classification of (most) “small” bosonic CFTs. Here, I use the adjective “small” informally to refer to theories with low central charge (less than 24) and few primary operators (less than 5). Time and attention permitting, I will highlight two applications of this result. First, I will describe how it can be used in tandem with bosonization and fermionization techniques to establish the classification of chiral fermionic CFTs with central charge less than 23. Second, I will showcase how it can be used to bootstrap generalized global symmetries using the concept of “symmetry/subalgebra duality.”

    Talk based on arXiv:2208.05486 [hep-th] (joint work with Sunil Mukhi) and arXiv:2303.16921 [hep-th].

    https://www.youtube.com/watch?v=NrOcsiUmSh0&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=1&t=2s

     

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 03.24.23

    Quantum Matter Seminar

    Speaker: Alexander Zlokapa, MIT

    Title: Traversable wormhole dynamics on a quantum processor

    Abstract: The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

     

    https://www.youtube.com/watch?v=iYkVuju_sP8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=11

  • CMSA EVENT: 2020 Big Data Conference (Virtual)
    10:00 am-2:05 pm
    12/01/2024-08/25/2020

    On August 24-25, 2020 the CMSA hosted our sixth annual Conference on Big Data. The Conference featured many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. The 2020 Big Data Conference took place virtually.

    Videos of the talks are available in this youtube playlist.

     

    Organizers: 

    • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
    • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
    • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Schedule:
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/1/2021 Math Physics

    10:00 am-11:00 am
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/22/2021 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Cheryne Jonay (Stanford)

    Title: A Physical Theory of Two-stage Thermalization

    Abstract: One indication of thermalization time is subsystem entanglement reaching thermal values. Recent studies on local quantum circuits reveal two exponential stages with decay rates $r_1$ and $r_2$ of the purity before and after thermalization. We provide an entanglement membrane theory interpretation, with $r_1$ corresponding to the domain wall free energy. Circuit geometry can lead to $r_1 < r_2$, producing a “phantom eigenvalue”. Competition between the domain wall and magnon leads to $r_2 < r_1$ when the magnon prevails. However, when the domain wall wins, this mechanism provides a practical approach for measuring entanglement growth through local correlation functions.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 04.28.23

    Quantum Matter Seminar

    Title: Fracton Self-Statistics

    Speaker: Hao Song (ITP-CAS)

    Abstract: Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating other excitations are called fractons. Here we address a fundamental open question — can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged, and show their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of abelian fracton orders. Finally, we show the existence of semionic or fermionic fracton self-statistics in some twisted variants of the checkerboard model and Haah’s code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.

    References: H Song, N Tantivasadakarn, W Shirley, M Hermele, arXiv:2304.00028.

    https://www.youtube.com/watch?v=TBAEif9XVww&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=6

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 04.21.23 (1)

    Quantum Matter Seminar

    Speaker: Prof. Subir Sachdev (Harvard)

    Title: A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order

    Abstract: Soon after the discovery of high-temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low-temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the “pseudogap metal” phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.
    As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.
    This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Mathias S. Scheurer, and S. S., arXiv:2302.07885

    https://www.youtube.com/watch?v=ueT28iMdjzE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=7

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/12/2021 Mathematical Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4/5/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/5/2021 Interdisciplinary Science Seminar

    10:00 am-11:00 am
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Pre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am

    Pre-talk Title: Introduction to the singularities of the MMP


    Speaker: Dori Bejleri (Harvard Math & CMSA)

    Title: Moduli of boundary polarized Calabi-Yau pairs

    Abstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher, H. Blum, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang.

     

     

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    20 Garden Street, Cambridge MA 02138
    CMSA QMMP 04.14.23

    Quantum Matter Seminar

    Speaker: Guanyu Zhu (IBM Quantum, T. J. Watson Research Center)

    Title: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries

    Abstract: Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects.

    References:
    1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua
    2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O&#39;Connor, Guanyu Zhu
    3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

     

    https://www.youtube.com/watch?v=APcDMMRI9VU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=8

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/8/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Mathematical Physics Seminar, Mondays

    10:00 am-11:00 am
    12/01/2024

    The seminar on mathematical physics will be held on Mondays from 10:00 – 11:00am ET on Zoom. Please email the seminar organizers to learn how toattend. This year’s Seminar will be organized by Yoosik Kim (yoosik@cmsa.fas.harvard.edu), Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu), and Yang Zhou (yangzhou@cmsa.fas.harvard.edu).

    Join the Math-Physics mailing list

    The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

    Spring 2021:

    DateSpeakerTitle/Abstract
    2/1/2021Choa Dongwook
    (KIAS)Video
    TitleFukaya category of Landau-Ginzburg orbifolds.

    Abstract: Landau-Ginzburg orbifold is just another name for a holomorphic function W with its abelian symmetry G. Its Fukaya category can be viewed as a categorification of a homology group of its Milnor fiber. In this introductory talk, we will start with some classical results on the topology of isolated singularities and its Fukaya-Seidel category. Then I will explain a new construction for such category to deal with a non-trivial symmetry group G. The main ingredients are classical variation map and the Reeb dynamics at the contact boundary. If time permits, I will show its application to mirror symmetry of LG orbifolds and its Milnor fiber. This is a joint work with C.-H. Cho and W. Jeong

    2/8/2021Jérémy Guéré (Fourier Institute)TitleCongruences on K-theoretic Gromov-Witten invariants

    Abstract: K-theoretic Gromov-Witten invariants of smooth projective varieties have been introduced by YP Lee, using the Euler characteristic of a virtual structure sheaf. In particular, they are integers. In this talk, I look at these invariants for the quintic threefold and I will explain how to compute them modulo 41, using the virtual localization formula under a finite group action, up to genus 19 and degree 40.

    2/15/2021Zhiwei Zheng (Max Planck Institute)

    Video

    Title: Some new results on automorphisms of hypersurfaces

    Abstract: It is natural to study automorphisms of hypersurfaces in projective spaces. In this talk, I will discuss a new approach to determine all possible orders of automorphisms of smooth hypersurfaces with fixed degree and dimension. Then we consider the specific case of cubic fourfolds, and discuss the relation with Hodge theory.

    2/22/2021Yu-Shen Lin (Boston University)

    Video

    TitleFull SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

    Abstract: Strominger–Yau–Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi–Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

    3/1/2021Carlos S. Shahbazi (Hamburg University)

    Video

    TitleMathematical supergravity and its applications to differential geometry.

    Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

    3/8/2021Miguel Moreira (ETH)

    Video

    TitleVirasoro constraints for stable pairs.

    Abstract: The theory of stable pairs (PT) with descendents, defined on a 3-fold X, is a sheaf theoretical curve counting theory. Conjecturally, it is equivalent to the Gromov-Witten (GW) theory of X via a universal (but intricate) transformation, so we can expect that the Virasoro conjecture on the GW side should have a parallel in the PT world. In joint work with A. Oblomkov, A. Okounkov, and R. Pandharipande, we formulated such a conjecture and proved it for toric 3-folds in the stationary case. The Hilbert scheme of points on a surface S might be regarded as a component of the moduli space of stable pairs on S x P1, and the Virasoro conjecture predicts a new set of relations satisfied by tautological classes on S[n] which can be proven by reduction to the toric case.

    3/15/2021Spring break
    3/22/2021Ying Xie (Shanghai Center for Mathematical Sciences)Title: Derived categories for Grassmannian flips

    Abstract: Flip is a fundamental surgery operation for constructing minimal models in higher-dimensional birational geometry. In this talk, I will introduce a series of flips from Lie theory and investigate their derived categories. This is a joint program with Conan Leung.

    3/29/2021Emanuel Scheidegger (Peking University)Title:  On the quantum K-theory of the quintic.

    Abstract: Quantum cohomology is a deformation of the cohomology of a projective variety governed by counts of stable maps from a curve into this variety. Quantum K-theory is in a similar way a deformation of K-theory but also of quantum cohomology, It has recently attracted attention in physics since a realization in a physical theory has been found. Currently, both the structure and examples in quantum K-theory are far less understood than in quantum cohomology.
    We will explain the properties of quantum K-theory in comparison with quantum cohomology, and we will discuss the examples of projective space and the quintic hypersurface in P^4.
    4/5/2021Gaëtan Borot (HU Berlin)

    Video

    TitleTopological recursion in 4d N = 2 supersymmetric gauge theories

    Abstract: According to the Alday-Gaiotto-Tachikawa conjecture (proved in this case by Schiffman and Vasserot), the instanton partition function in 4d N = 2 SU(r) supersymmetric gauge theory on P^2 with equivariant parameters \epsilon_1,\epsilon_2 is the norm of a Whittaker vector for W(gl_r) algebra. I will explain how these Whittaker vectors can be computed (at least perturbatively in the energy scale) by topological recursion for \epsilon_1 +\epsilon_2 = 0, and by a non-commutation version of the topological recursion in the Nekrasov-Shatashvili regime where \epsilon_1/\epsilon_2 is fixed. This is a joint work to appear with Bouchard, Chidambaram and Creutzig.

    4/12/2021Fei Yan (Rutgers)TitleNetworks and quantization

    Abstract: I will describe two quantization scenarios. The first scenario involves the construction of a quantum trace map computing a link “invariant” (with possible wall-crossing behavior) for links L in a 3-manifold M, where M is a Riemann surface C times a real line. This construction unifies the computation of familiar link invariant with the refined counting of framed BPS states for line defects in 4d N=2 theories of class S. Certain networks on C play an important role in the construction. The second scenario concerns the study of Schroedinger equations and their higher order analogues, which could arise in the quantization of Seiberg-Witten curves in 4d N=2 theories. Here similarly certain networks play an important part in the exact WKB analysis for these Schroedinger-like equations. At the end of my talk I will also try to sketch a possibility to bridge these two scenarios.

    4/19/2021Hazel Mak (Brown University)TitleBranching Rules and Young Tableaux Methods: 10D & 11D Supergravity

    Abstract: In this talk, I will review 4D, N = 1 off-shell supergravity. Then I present explorations to construct 10D and 11D supergravity theories in two steps. The first step is to decompose scalar superfield into Lorentz group representations which involves branching rules and related methods. Interpretations of component fields by Young tableaux methods will be presented. The second step is to implement an analogue of Breitenlohner’s approach for 4D supergravity to 10D and 11D theories.

    4/26/2021Owen Gwilliam (UMass. Amherst)

    Video

    TitleTopological-holomorphic field theories and their BV quantizations

    Abstract: Topological field theories and holomorphic field theories have each had a substantial impact in both physics and mathematics, so it is natural to consider theories that are hybrids of the two, which we call topological-holomorphic and denote as THFTs. Examples include Kapustin’s twist of N=2, D=4 supersymmetric Yang-Mills theory and Costello’s 4-dimensional Chern-Simons theory. In this talk about joint work with Rabinovich and Williams, I will define THFTs, describe several examples, and then explain how to quantize them rigorously and explicitly, by building on techniques of Si Li.  Time permitting, I will indicate how these results offer a novel perspective on the Gaudin model via 3-dimensional field theories.


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/14/2020Lino Amorim (Kansas State University)TitleNon-commutative Gromov-Witten invariants

    Abstract:  I will describe an analogue of Saito’s theory of primitive forms for Calabi-Yau A-infinity categories. Under some conditions on the Hochschild cohomology of the category, this construction recovers the (genus zero) Gromov-Witten invariants of a symplectic manifold from its Fukaya category. This includes many compact toric manifolds, in particular projective spaces.

    9/21/2020Yuhan Sun (Rutgers)Title: Displacement energy of Lagrangian 3-spheres

    Abstract:  We study local and global Hamiltonian dynamical behaviors of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that there is a one-parameter family of Lagrangian tori near S, which are nondisplaceable in X. When dim S = 3, we obtain a new estimate of the displacement energy of S, by estimating the displacement energy of a one-parameter family of Lagrangian tori near S.

    9/28/2020Shota Komatsu (CERN)Title: Wilson loops as matrix product states

    Abstract:  In this talk, I will discuss a reformulation of the Wilson loop in large N gauge theories in terms of matrix product states. The construction is motivated by the analysis of supersymmetric Wilson loops in the maximally super Yang–Mills theory in four dimensions, but can be applied to any other large N gauge theories and matrix models, although less effective. For the maximally super Yang–Mills theory, one can further perform the computation exactly as a function of ‘t Hooft coupling by combining our formulation with the relation to integrable spin chains.

    10/5/2020Ming Zhang (UBC)Title: Verlinde/Grassmannian correspondence and applications.

    Abstract: In the 90s’, Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten’s work by relating the $\text{GL}_{n}$ Verlinde numbers to the level $l$ quantum K-invariants of the Grassmannian $\text{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence.

    The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will discuss the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.  At the end of the talk, I will describe some applications of this correspondence.

    10/12/2020Cancelled -Columbus Day
    10/19/2020Ben Gammage (Harvard)Title3d mirror symmetry for abelian gauge groups

    Abstract: 3d mirror symmetry is a proposed duality relating a pair of 3-dimensional supersymmetric gauge theories. Various consequences of this duality have been heavily explored by representation theorists in recent years, under the name of “symplectic duality”. In joint work in progress with Justin Hilburn, for the case of abelian gauge groups, we provide a fully mathematical explanation of this duality in the form of an equivalence of 2-categories of boundary conditions for topological twists of these theories. We will also discuss some applications to homological mirror symmetry and geometric Langlands duality.

    10/26/2020Cancelled
    11/2/2020Haoyu Sun (Berkeley)TitleDouble-Janus linear sigma models and generalized quadratic reciprocity

    Abstract: We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d N=4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T^2 fibered over S^1) times a circle with an SL(2,Z) duality wall inserted on S^1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2,Z), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
    11/9/2020An Huang (Brandeis)Titlep-adic strings, Einstein equations, Green’s functions, and Tate’s thesis

    Abstract: I shall discuss a recent work on how p-adic strings can produce perturbative quantum gravity, and an adelic physics interpretation of Tate’s thesis.
    11/16/2020
    10:00am ET
    Matt Kerr (WUSTL)Title:  Differential equations and mixed Hodge structures

    Abstract: We report on a new development in asymptotic Hodge theory, arising from work of Golyshev–Zagier and Bloch–Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry.  The talk will focus exclusively on the Hodge/period-theoretic aspects through two main examples.
    Given a variation of Hodge structure M on a Zariski open in P^1, the periods of the limiting mixed Hodge structures at the punctures are interesting invariants of M.  More generally, one can try to compute these asymptotic invariants for iterated extensions of M by “Tate objects”, which may arise for example from normal functions associated to algebraic cycles. The main point of the talk will be that (with suitable assumptions on M) these invariants are encoded in an entire function called the motivic Gamma function, which is determined by the Picard-Fuchs operator L underlying M. In particular, when L is hypergeometric, this is easy to compute and we get a closed-form answer (and a limiting motive).  In the non-hypergeometric setting, it yields predictions for special values of normal functions; this part of the story is joint with V. Golyshev and T. Sasaki.

    11/23/2020

    11:30am ET

    Kyoung-Seog Lee (U of Miami)TitleDerived categories and motives of moduli spaces of vector bundles on curves

    Abstract: Derived categories and motives are important invariants of algebraic varieties invented by Grothendieck and his collaborators around 1960s. In 2005, Orlov conjectured that they will be closely related and now there are several evidences supporting his conjecture. On the other hand, moduli spaces of vector bundles on curves provide attractive and important examples of algebraic varieties and there have been intensive works studying them. In this talk, I will discuss derived categories and motives of moduli spaces of vector bundles on curves. This talk is based on joint works with I. Biswas and T. Gomez.

    11/30/2020Zijun Zhou (IPMU)Title: 3d N=2 toric mirror symmetry and quantum K-theory

    Abstract: In this talk, I will introduce a new construction for the K-theoretic mirror symmetry of toric varieties/stacks, based on the 3d N=2 mirror symmetry introduced by Dorey-Tong. Given the toric datum, i.e. a  short exact sequence 0 -> Z^k -> Z^n -> Z^{n-k} -> 0, we consider the toric Artin stack of the form [C^n / (C^*)^k]. Its mirror is constructed by taking the Gale dual of the defining short exact sequence. As an analogue of the 3d N=4 case, we consider the K-theoretic I-function, with a suitable level structure, defined by counting parameterized quasimaps from P^1. Under mirror symmetry, the I-functions of a mirror pair are related to each other under the mirror map, which exchanges the K\”ahler and equivariant parameters, and maps q to q^{-1}. This is joint work with Yongbin Ruan and Yaoxiong Wen.

    12/7/2020Thomas Grimm (Utrecht)TitleModuli Space Holography and the Finiteness of Flux Vacua

    Abstract: In this talk I describe a holographic perspective to study field spaces that arise in string compactifications. The constructions are motivated by a general description of the asymptotic, near-boundary regions in complex structure moduli spaces of Calabi-Yau manifolds using asymptotic Hodge theory. For real two-dimensional field spaces, I introduce an auxiliary bulk theory and describe aspects of an associated sl(2) boundary theory. The bulk reconstruction from the boundary data is provided by the sl(2)-orbit theorem of Schmid and Cattani, Kaplan, Schmid, which is a famous and general result in Hodge theory. I then apply this correspondence to the flux landscape of Calabi-Yau fourfold compactifications and discuss how this allows us, in work with C. Schnell, to prove that the number of self-dual flux vacua is finite

    For a listing of previous Mathematical Physics Seminars, please click here.

  • Seminars

    Seminars Colloquia & Seminar
    Social Science Applications Forum

    10:00 am-11:00 am
    12/01/2024

    During the Summer of 2020, the CMSA will be hosting a periodic Social Science Applications Seminar.

    The list of speakers is below and will be updated as details are confirmed.

    For a list of past Social Science Applications talks, please click here.
    DateSpeakerTitle/Abstract
    7/13/2020 10:00-11:00am ETLudovic Tangpi (Princeton)Please note, this seminar will take place online using Zoom.

    Title: Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls

    Abstract: This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in non-cooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space.
    For security reasons, you will have to show your full name to join the meeting.

    7/27/2020
    10:00pm
    Michael Ewens (Caltech)Please note, this seminar will take place online using Zoom.

    Title: Measuring Intangible Capital with Market Prices

    Abstract: Despite the importance of intangibles in today’s economy, current standards prohibit the capitalization of internally created knowledge and organizational capital, resulting in a downward bias of reported assets. As a result, researchers estimate this value by capitalizing prior flows of R&D and SG&A. In doing so, a set of capitalization parameters, i.e. the R&D depreciation rate and the fraction of SG&A that represents a long-lived asset, must be assumed. Parameters now in use are derived from models with strong assumptions or are ad hoc. We develop a capitalization model that motivates the use of market prices of intangibles to estimate these parameters. Two settings provide intangible asset values: (1) publicly traded equity prices and (2) acquisition prices. We use these parameters to estimate intangible capital stocks and subject them to an extensive set of diagnostic analyses that compare them with stocks estimated using existing parameters. Intangible stocks developed from exit price parameters outperform both stocks developed by publicly traded parameters and those stocks developed with existing estimates. (Joint work with Ryan Peters and Sean Wang.)

  • Mathematical Physics Seminar
    10:00 am-11:00 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

     

    Speaker: Carlos S. Shahbazi (Hamburg University)

    Title: Mathematical supergravity and its applications to differential geometry

    Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA QMMP 04.07.23

    Quantum Matter Seminar

    Speaker: Nishad Maskara (Harvard)

    Title: Enhancing Detection of Topological Order by Local Error Correction

    Abstract: The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator.  Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.

     

    https://www.youtube.com/watch?v=oWIelx6_taU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=9

  • Algebraic Geometry in String Theory Seminar
    10:00 am-11:00 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA AGST Seminar 04.03.2023

    Algebraic Geometry in String Theory Seminar

    Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse

    Title: Kähler-Einstein metrics on families of Fano varieties

    Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.

  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Nat Tantivasadakarn (Caltech)

    Title: From wave-function collapse and Galois solvability to the realization of non-Abelian topological order on a quantum device

    Abstract: I will review our recent set of theoretical works on efficiently preparing long range quantum entanglement with adaptive quantum circuits: the combination of measurements with unitary gates whose choice can depend on previous measurement outcomes. I will show that this additional ingredient can be leveraged to prepare the long sought-after non-Abelian topological phases with a circuit depth that is independent of system size. Using this framework, we uncover a complexity hierarchy of long-range entangled states based on the minimal number of measurement layers required to create the state. Moreover, we find that certain non-Abelian states that cannot be efficiently prepared with adaptive circuits have a surprising connection to the unsolvability of the quintic polynomial.

    Finally, I will describe our recent collaboration with Quantinuum where we present the first unambiguous realization of non-Abelian D4 topological order and demonstrate control of its anyons. In particular, we are able to detect a non-trivial braiding where three non-Abelian anyons trace out the Borromean rings in spacetime, a signature unique to non-Abelian topological order.

  • Mathematical Physics Seminar
    10:00 am-11:00 am
    12/01/2024

    Speaker: Yu-Shen Lin (Boston University)

    Title: Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

    Abstract: Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi-Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/15/2021 Math Physics Seminar

    10:00 am-11:00 am
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Quantum Matter Seminar

    Speaker: Abijith Krishnan (MIT)

    Title: A Plane Defect in the 3d O(N) Model

    Abstract: It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

     

    https://www.youtube.com/watch?v=6cDK3TJ_H8w&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=10

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    2/10/2021 Strongly Correlated Quantum Materials

    10:00 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:00 am-11:30 am
    12/01/2024
    CMSA QMMP 06.09.23

    Quantum Matter Seminar

    Speakers: Gerald Höhn (Kansas State University) & Sven Möller (University of Hamburg)

    Title: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24

    Abstract: We discuss the classfication of self-dual vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely chiral 2-dimensional fermionic conformal field theories with just one primary field.

    There are exactly 969 such SVOAs under suitable regularity assumptions and the assumption that the shorter moonshine module VB^# is the unique self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1 spaces vanish.

    We construct and classify the self-dual SVOAs by determining the 2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central charge 24 and also by realising them as simple-current extensions of a dual pair containing a certain maximal lattice VOA. We show that all SVOAs besides VB^# x F and potential fake copies thereof stem from elements of the Conway group Co_0, the automorphism group of the Leech lattice.

    By splitting off free fermions F, if possible, we obtain the classification for all central charges less than or equal to 24.
    Reference: G. Höhn, S. Möller, arXiv:2303.17190.

    https://www.youtube.com/watch?v=U0alYxX05xU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=2

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Previous Random Matrix & Probability Theory Seminars

    10:26 am-10:27 am
    12/01/2024

    Spring 2020:

    DateSpeakerTitle/Abstract
    2/26/2020Louigi Addario-Berry (McGill University)Title: Hipster random walks and their ilk 

    Abstract: I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.

    4/1/2020Ian Jauslin (Princeton)This meeting will be taking place virtually on Zoom.

    Title: A simplified approach to interacting Bose gases
    Abstract: I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.

    4/22/2020Martin Gebert (UC Davis)This meeting will be taking place virtually on Zoom.

    TitleLieb-Robinson bounds for a class of continuum many-body fermion systems

    Abstract: We introduce a class of UV-regularized two-body interactions for
    fermions in $\R^d$ and prove a Lieb-Robinson estimate for the dynamics
    of this class of many-body systems. As a step towards this result, we
    also prove a propagation bound of Lieb-Robinson type for continuum
    one-particle Schr\“odinger operators. We apply the propagation bound to
    prove the existence of a strongly continuous infinite-volume dynamics on
    the CAR algebra.

    4/29/2020Marcin Napiórkowski (University of Warsaw)This meeting will be taking place virtually on Zoom.

    TitleFree energy asymptotics of the quantum Heisenberg spin chain

    Abstract: Spin wave theory suggests that low temperature properties of the Heisenberg model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction. Based on joint work with Robert Seiringer.

    5/6/2020Antti Knowles (University of Geneva)TitleField theory as a limit of interacting quantum Bose gases

    Abstract: We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the mean-field limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions d = 1,2,3. For d > 1 the Gibbs measure is supported on distributions of negative regularity and we have to renormalize the interaction. The proof is based on a functional integral representation of the grand canonical Gibbs state, in which convergence to the mean-field limit follows formally from an infinite-dimensional stationary phase argument for ill-defined non-Gaussian measures. We make this argument rigorous by introducing a white-noise-type auxiliary field, through which the functional integral is expressed in terms of propagators of heat equations driven by time-dependent periodic random potentials. Joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.
    5/13/2020Sven Bachmann (University of British Columbia)TitleQuantized quantum transport and Abelian anyons

    Abstract: I’ll discuss recent developments in the study of quantized quantum transport, focussing on the quantum Hall effect. Beyond presenting an index taking rational values, and which is the Hall conductance in the adapted setting, I will explain how the index is intimately paired with the existence of quasi-particle excitations having non-trivial braiding properties.

    5/20/2020Kristina Schubert (TU Dortmund)TitleFluctuation Results for General Ising Models — Block Spin Ising Models and Random Interactions

    Abstract: Starting from the classical Curie-Weiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins in which the vertices are divided into a finite number of blocks and where pair interactions are given according to their blocks. The magnetization is then the vector of magnetizations within each block, and we are interested in its behaviour and in particular in its fluctuations. On the other hand, we consider Ising models on Erdős-Rényi random graphs. Here, I will also present results on the fluctuations of the magnetization.

     

    Fall 2019:

    DateSpeakerTitle/Abstract
    9/11/2019Subhabrata SenTitle: Sampling convergence for random graphs: graphexes and multigraphexes

    Abstract: We will look at structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs, Chayes, Cohn and Veitch ’17). Sam- pling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We will introduce this framework and motivate the components of a graphex. Subsequently, we will discuss the graphex limit for several well-known sparse random (multi)graph models. This is based on joint work with Christian Borgs, Jennifer Chayes, and Souvik Dhara.

    9/25/2019Jeff Schenker (Michigan State)Title: An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states  

    Abstract: Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one — “entanglement breaking’’ – channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh)

    10/3/2019

     

    Thursday

    4:30pm

    Jian Ding (UPenn)Title: Distances associated with Liouville quantum gravity

    Abstract: I will review some recent progresses on distances associated with Liouville quantum gravity, which is a random measure obtained from exponentiating a planar Gaussian free field.

    The talk is based on works with Julien Dubédat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne, Ofer Zeitouni and Fuxi Zhang in various combinations.

    10/9/2019Ruth Williams (UCSD)Title: Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

    Abstract: Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy. It has been a standing problem to prove stability of this general model when the average load on the system is less than the network’s capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and indicate how to prove stability of the fluid model under mild conditions.

    This talk is based on joint work with Yingjia Fu.

    10/11/2019Cancelled
    10/16/2019Wei-Kuo Chen (University of Minnesota)Title: The generalized TAP free energy

    Abstract: Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag.

    10/23/2019Souvik Dhara (MIT)Title: A new universality class for critical percolation on networks with heavy-tailed degrees

    Abstract: The talk concerns critical behavior of percolation on finite random networks with heavy-tailed degree distribution. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdős-Rényi random graph. Subsequently, there has been a surge in the literature identifying two universality classes for the critical behavior depending on whether the asymptotic degree distribution has a finite or infinite third moment.

    In this talk, we will present a completely new universality class that arises in the context of degrees having infinite second moment. Specifically, the scaling limit of the rescaled component sizes is different from the general description of multiplicative coalescent given by Aldous and Limic (1998). Moreover, the study of critical behavior in this regime exhibits several surprising features that have never been observed in any other universality classes so far.

    This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden.

    10/30/2019Aram Harrow (MIT)Title: Random quantum circuits, phase transitions and complexity

    Abstract: Random unitary dynamics are a toy model for chaotic quantum dynamics and also have applications to quantum information theory and computing. Recently, random quantum circuits were the basis of Google’s announcement of “quantum computational supremacy,” meaning performing a task on a programmable quantum computer that would difficult or infeasible for any classical computer. Google’s approach is based on the conjecture that random circuits are as hard to classical computers to simulate as a worst-case quantum computation would be. I will describe evidence in favor of this conjecture for deep random circuits and against this conjecture for shallow random circuits. (Deep/shallow refers to the number of time steps of the quantum circuit.) For deep random circuits in Euclidean geometries, we show that quantum dynamics match the first few moments of the Haar measure after roughly the amount of time needed for a signal to propagate from one side of the system to the other. In non-Euclidean geometries, such as the Schwarzschild metric in the vicinity of a black hole, this turns out not to be always true. I will also explain how shallow quantum circuits are easier to simulate when the gates are randomly chosen than in the worst case. This uses a simulation algorithm based on tensor contraction which is analyzed in terms of an associated stat mech model.

    This is based on joint work with Saeed Mehraban (1809.06957) and with John Napp, Rolando La Placa, Alex Dalzell and Fernando Brandao (to appear).

    11/6/2019Bruno Nachtergaele (UC Davis)TitleThe transmission time and local integrals of motion for disordered spin chains

    Abstract:  We investigate the relationship between zero-velocity Lieb-Robinson bounds and the existence of local integrals of motion (LIOMs) for disordered quantum spin chains. We also study the effect of dilute random perturbations on the dynamics of many-body localized spin chains. Using a notion of transmission time for propagation in quantum lattice systems we demonstrate slow propagation by proving a lower bound for the transmission time. This result can be interpreted as a robustness property of slow transport in one dimension. (Joint work with Jake Reschke)

    11/13/2019Gourab Ray (University of Victoria)Title: Logarithmic variance of height function of square-iceAbstract: A homomorphism height function on a finite graph is a integer-valued function on the set of vertices constrained to have adjacent vertices take adjacent integer values. We consider the uniform distribution over all such functions defined on a finite subgraph of Z^2 with predetermined values at some fixed boundary vertices. This model is equivalent to the height function of the six-vertex model with a = b = c = 1, i.e. to the height function of square-ice. Our main result is that in a subgraph of Z^2 with zero boundary conditions, the variance grows logarithmically in the distance to the boundary. This establishes a strong form of roughness of the planar uniform homomorphisms.

     

    Joint work with: Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran Raoufi.

    11/20/2019Vishesh Jain (MIT)Title: A combinatorial approach to the quantitative invertibility of random matrices.

     

    Abstract: Abstract: Let $s_n(M_n)$ denote the smallest singular value of an $n\times n$ random matrix $M_n$. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood–Offord theory or net arguments) for obtaining upper bounds on the probability that $s_n(M_n)$ is smaller than $\eta \geq 0$ for quite general random matrix models. Such estimates are a fundamental part of the non-asymptotic theory of random matrices and have applications to the strong circular law, numerical linear algebra etc. In several cases of interest, our approach provides stronger bounds than those obtained by Tao and Vu using inverse Littlewood–Offord theory.

     

     

     

    2018-2019

    DateSpeakerTitle/Abstract
    9/28/2018

    *Friday, 10:00am*

    Yash Deshpande (MIT)Title: Estimating low-rank matrices in noise: phase transitions from spin glass theory

    Abstract: Estimating low-rank matrices from noisy observations is a common task in statistical and engineering applications. Following the seminal work of Johnstone, Baik, Ben-Arous and Peche, versions of this problem have been extensively studied using random matrix theory. In this talk, we will consider an alternative viewpoint based on tools from mean field spin glasses. We will present two examples that illustrate how these tools yield information beyond those from classical random matrix theory. The first example is the two-groups stochastic block model (SBM), where we will obtain a full information-theoretic understanding of the estimation phase transition. In the second example, we will augment the SBM with covariate information at nodes, and obtain results on the altered phase transition.

    This is based on joint works with Emmanuel Abbe, Andrea Montanari, Elchanan Mossel and Subhabrata Sen.

    10/3/2018Ian Jauslin (IAS)Title: Liquid Crystals and the Heilmann-Lieb model

    Abstract: In 1979, O.Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb.

    10/10/2018Afonso Bandeira (NYUTitle: Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment

    Abstract: Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions and orientations; Cryo-Electron Microscopy (Cryo-EM) imaging where projections of a molecule density are taken from unknown rotations, and several others.

    One fundamental example of this type of problems is Multi-Reference Alignment: Given a group acting in a space, the goal is to estimate an orbit of the group action from noisy samples. For example, in one of its simplest forms, one is tasked with estimating a signal from noisy cyclically shifted copies. We will show that the number of observations needed by any method has a surprising dependency on the signal-to-noise ratio (SNR), and algebraic properties of the underlying group action. Remarkably, in some important cases, this sample complexity is achieved with computationally efficient methods based on computing invariants under the group of transformations.

    10/17/2018

    3:30pm

    Thomas Chen (UT Austin)Title: Dynamics of a heavy quantum tracer particle in a Bose gas

    Abstract: We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R^3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit where N tends to infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. This is joint work with Avy Soffer (Rutgers University).

    10/24/2018

    *Room G02*

    Tselil Schramm (Harvard/MIT)Title: (Nearly) Efficient Algorithms for the Graph Matching Problem in Correlated Random Graphs

    Abstract: The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known.

    Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng.

    10/30/2018

    *Tuesday

    10:30am

    SC 507*

    Lauren Williams (Harvard)Title: Introduction to the asymmetric simple exclusion process (from a combinatorialist’s point of view)

    Abstract: The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, subject to the condition that there is at most one particle per site. This model was introduced in 1970 by biologists (as a model for translation in protein synthesis) but has since been shown to display a rich mathematical structure. There are many variants of the model — e.g. the lattice could be a ring, or a line with open boundaries. One can also allow multiple species of particles with different “weights.” I will explain how one can give combinatorial formulas for the stationary distribution using various kinds of tableaux. I will also explain how the ASEP is related to interesting families of orthogonal polynomials, including Askey-Wilson polynomials, Koornwinder polynomials, and Macdonald polynomials.

    11/7/2018Willhelm Schlag (Yale)Title: on the Bourgain-Dyatlov fractal uncertainty principle

    Abstract: We will present the Bourgain-Dyatlov theorem on the line, it’s connection with other uncertainty principles in harmonic analysis, and my recent partial progress with Rui Han on the problem of higher dimensions.

    11/14/2018David Gamarnik (MIT)Title: Two Algorithmic Hardness Results in Spin Glasses and Compressive Sensing.

    Abstract: I will discuss two computational problems in the area of random combinatorial structures. The first one is the problem of computing the partition function of a Sherrington-Kirkpatrick spin glass model. While the the problem of computing the partition functions associated with arbitrary instances is known to belong to the #P complexity class, the complexity of the problem for random instances is open. We show that the problem of computing the partition function exactly (in an appropriate sense) for the case of instances involving Gaussian couplings is #P-hard on average. The proof uses Lipton’s trick of computation modulo large prime number, reduction of the average case to the worst case instances, and the near uniformity of the ”stretched” log-normal distribution.

    In the second part we will discuss the problem of explicit construction of matrices satisfying the Restricted Isometry Property (RIP). This challenge arises in the field of compressive sensing. While random matrices are known to satisfy the RIP with high probability, the problem of explicit (deterministic) construction of RIP matrices eluded efforts and hits the so-called ”square root” barrier which I will discuss in the talk. Overcoming this barrier is an open problem explored widely in the literature. We essentially resolve this problem by showing that an explicit construction of RIP matrices implies an explicit construction of graphs satisfying a very strong form of Ramsey property, which has been open since the seminal work of Erdos in 1947.

    11/28/2018Sean O’ Rourke (UC Boulder)Title: Universality and least singular values of random matrix products

    Abstract: We consider the product of m independent iid random matrices as m is fixed and the sizes of the matrices tend to infinity.  In the case when the factor matrices are drawn from the complex Ginibre ensemble, Akemann and Burda computed the limiting microscopic correlation functions.  In particular, away from the origin, they showed that the limiting correlation functions do not depend on m, the number of factor matrices. We show that this behavior is universal for products of iid random matrices under a moment matching hypothesis.  In addition, we establish universality results for the linear statistics for these product models, which show that the limiting variance does not depend on the number of factor matrices either. The proofs of these universality results require a near-optimal lower bound on the least singular value for these product ensembles.

    12/5/2018

    *Room G02*

    Omer Angel (UBC)Title: balanced excited random walks

    Abstract: I will present results on the scaling limit and asymptotics of the balanced excited random walk and related processes. This is a walk the that moves vertically on the first visit to a vertex, and horizontally on every subsequent visit. We also analyze certain versions of “clairvoyant scheduling” of random walks.

    Joint work with Mark Holmes and Alejandro Ramirez.

    2/7/2019

    Science Center 530

    Ramis Movassagh (IMB Research)Title: Generic Gaplessness, and Hamiltonian density of states from free probability theory

    Abstract: Quantum many-body systems usually reside in their lowest energy states. This among other things, motives understanding the gap, which is generally an undecidable problem. Nevertheless, we prove that generically local quantum Hamiltonians are gapless in any dimension and on any graph with bounded maximum degree.

    We then provide an applied and approximate answer to an old problem in pure mathematics. Suppose the eigenvalue distributions of two matrices M_1 and M_2 are known. What is the eigenvalue distribution of the sum M_1+M_2? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions. We will describe FPT and show examples of its powers for approximating physical quantities such as the density of states of the Anderson model, quantum spin chains, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly (provably NP-hard). Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in fresh new contexts.

    2/14/2019Nike Sun (MIT)Title: Capacity lower bound for the Ising perceptron

    Abstract: The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results.

    2/21/2019Michael Loss (Georgia Tech)Title: Some results for functionals of Aharonov-Bohm type

    Abstract: In this talk I present some variational problems of Aharonov-Bohm type, i.e., they include a  magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a  variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.

    3/6/2019

    4:15pm

    Science Center 411

    Ilya Kachkovskiy (Michigan State University)Title: Localization and delocalization for interacting 1D quasiperiodic particles.

    Abstract: We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large coupling localization depends on symmetries of the single-particle potential. If the potential has no cosine-type symmetries, then we are able to show large coupling localization at all energies, even if the interaction is not small (with some assumptions on its complexity). If symmetries are present, we can show localization away from finitely many energies, thus removing a fraction of spectrum from consideration. We also demonstrate that, in the symmetric case, delocalization can indeed happen if the interaction is strong, at the energies away from the bulk spectrum. The result is based on joint works with Jean Bourgain and Svetlana Jitomirskaya.

    3/14/2019

    5:45pm

    Science Center 232

    Anna Vershynina (University of Houston)Title: How fast can entanglement be generated in quantum systems?

    Abstract: We investigate the maximal rate at which entanglement can be generated in bipartite quantum systems. The goal is to upper bound this rate. All previous results in closed systems considered entanglement entropy as a measure of entanglement. I will present recent results, where entanglement measure can be chosen from a large class of measures. The result is derived from a general bound on the trace-norm of a commutator, and can, for example, be applied to bound the entanglement rate for Renyi and Tsallis entanglement entropies.

    3/28/2019

    Room G02

    Xuwen Chen (University of Rochester)Title: The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics

    Abstract: We derive the 3D energy-critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. We develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false sharp trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new HUFL (hierarchical uniform frequency localization) property for the GP hierarchy and use it to prove a new type of uniqueness theorem.

    4/4/2019Paul Bourgade (NYU)Title: Log-correlations and branching structures in analytic number theory

    Abstract: Fyodorov, Hiary and Keating have predicted the size of local maxima of L-function along the critical axis, based on analogous random matrix statistics. I will explain this prediction in the context of the log-correlated universality class and branching structures. In particular I will explain why the Riemann zeta function exhibits log-correlations, and outline the proof for the leading order of the maximum in the Fyodorov, Hiary and Keating prediction. Joint work with Arguin, Belius, Radziwill and Soundararajan.

    4/9/2019

    Tuesday

    12:00pm

    Room G02

    Giulio Biroli (ENS Paris)Title: Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices

    Abstract: I consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. I will show how to obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $\theta>1$, in large deviations characterized by a small value of $u$, i.e. $u<1-1/\theta$, the second-largest eigenvalue pops out from the Wigner semi-circle and the associated eigenvector orients in the direction corresponding to the rank-one perturbation. These results can be generalized to the Wishart Ensemble, and extended to the first $n$ eigenvalues and the associated eigenvectors.

    Finally, I will discuss motivations and applications of these results to the study of the geometric properties of random high-dimensional functions—a topic that is currently attracting a lot of attention in physics and computer science.

    4/11/2019Rui Han (Georgia Tech)Title: Spectral gaps in graphene structures

    Abstract: We present a full analysis of the spectrum of graphene in magnetic fields with constant flux through every hexagonal comb. In particular, we provide a rigorous foundation for self-similarity by showing that for irrational flux, the spectrum of graphene is a zero measure Cantor set. We also show that for vanishing flux, the spectral bands have nontrivial overlap, which proves the discrete Bethe-Sommerfeld conjecture for the graphene structure. This is based on joint works with S. Becker, J. Fillman and S. Jitomirskaya.

    4/25/2019Benjamin Fehrman (Oxford)Title:  Pathwise well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

    Abstract:  We present a pathwise well-posedness theory for stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise.  Such equations arise in the theory of mean field games, approximate the Dean-Kawasaki equation in fluctuating fluid dynamics, describe the fluctuating hydrodynamics of the zero range process, and model the evolution of a thin film in the regime of negligible surface tension.  Motivated by the theory of stochastic viscosity solutions, we pass to the equation’s kinetic formulation, where the noise enters linearly and can be inverted using the theory of rough paths. The talk is based on joint work with Benjamin Gess.

    4/30/2019TBATBA
    5/2/2019Jian Ding (UPenn)TBA

    2017-2018

    Date…………Name…………….Title/Abstract
    2-16-20183:30pm

    G02

    Reza Gheissari (NYU)Dynamics of Critical 2D Potts ModelsAbstract: The Potts model is a generalization of the Ising model to $q\geq 3$ states with inverse temperature $\beta$. The Gibbs measure on $\mathbb Z^2$ has a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the phase transition is continuous while when $q>4$, the phase transition is discontinuous and the disordered and ordered phases coexist.

    We will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat bath/Metropolis) for the 2D Potts model, where the mixing time on an $n \times n$ torus should transition from $O(\log n)$ at high temperatures to $\exp(c_\beta n)$ at low temperatures, via a critical slowdown at $\beta_c(q)$ that is polynomial in $n$ when $q \leq 4$ and exponential in $n$ when $q>4$.

    2-23-20183:30pm

    G02

    Mustazee Rahman (MIT)On shocks in the TASEPAbstract: The TASEP particle system runs into traffic jams when the particle density to the left is smaller than the density to the right. Macroscopically, the particle density solves Burgers’ equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP shock whereby we identify the microscopic fluctuations around the shock by using exact formulas for the correlation functions of TASEP and its KPZ scaling limit. The resulting laws are related to universal laws of random matrix theory.

    For the curious, here is a video of the shock forming in Burgers’ equation:

    4-20-20182:00-3:00pmCarlo Lucibello(Microsoft Research NE)The Random Perceptron Problem: thresholds, phase transitions, and geometryAbstract: The perceptron is the simplest feedforward neural network model, the building block of the deep architectures used in modern machine learning practice. In this talk, I will review some old and new results, mostly focusing on the case of binary weights and random examples. Despite its simplicity, this model provides an extremely rich phenomenology: as the number of examples per synapses is increased, the system undergoes different phase transitions, which can be directly linked to solvers’ performances and to information theoretic bounds. A geometrical analysis of the solution space shows how two different types of solutions, akin to wide and sharp minima, have different generalization capabilities when presented with new examples.  Solutions in dense clusters generalize remarkably better,  partially closing the gap with Bayesian optimal estimators.  Most of the results I will present were first obtained using non rigorous techniques from spin glass theory and many of them haven’t been rigorously established yet,  although some big steps forward have been taken in recent years.
    4-20-20183:00-4:00pmYash Despande(MIT)Phase transitions in estimating low-rank matricesAbstract: Low-rank perturbations of Wigner matrices have been extensively studied in random matrix theory; much information about the corresponding spectral phase transition can be gleaned using these tools. In this talk, I will consider an alternative viewpoint based on tools from spin glass theory, and two examples that illustrate how these they yield information beyond traditional spectral tools. The first example is the stochastic block model,where we obtain a full information-theoretic picture of estimation. The second example demonstrates how side information alters the spectral threshold. It involves a new phase transition that interpolates between the Wigner and Wishart ensembles.
    DateNameTitle/Abstract
    9-27-17Herbert Spohn, Technische Universität MünchenHydrodynamics of integrable classical and quantum systems

    Abstract:  In the cold atoms community there is great interest in developing Euler-type hydrodynamics for one-dimensional integrable quantum systems, in particular with application to domain wall initial states.  I provide some mathematical physics background and also compare with integrable classical systems.

    10-23-17

    *12:00-1:00pm, Science Center 232*

     Madhu Sudan, Harvard SEASGeneral Strong Polarization

    A recent discovery (circa 2008) in information theory called Polar Coding has led to a remarkable construction of error-correcting codes and decoding algorithms, resolving one of the fundamental algorithmic challenges in the field. The underlying phenomenon studies the “polarization” of a “bounded” martingale. A bounded martingale, X_0,…,X_t,…  is one where X_t in [0,1]. This martingale is said to polarize if Pr[lim_{t\to infty} X_t \in {0,1}] = 1. The questions of interest to the results in coding are the rate of convergence and proximity: Specifically, given epsilon and tau > 0 what is the smallest t after which it is the case that Pr[X_t in (tau,1-tau)] < epsilon? For the main theorem, it was crucial that t <= min{O(log(1/epsilon)), o(log(1/tau))}. We say that a martingale polarizes strongly if it satisfies this requirement. We give a simple local criterion on the evolution of the martingale that suffices for strong polarization. A consequence to coding theory is that a broad class of constructions of polar codes can be used to resolve the afore-mentioned algorithmic challenge.

    In this talk I will introduce the concepts of polarization and strong polarization.  Depending on the audience interest I can explain why this concept is useful to construct codes and decoding algorithms, or explain the local criteria that help establish strong polarization (and the proof of why it does so).

    Based on joint work with Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, and Atri Rudra.

    10-25-17

    *2:00-4:00pm*

    Subhabrata Sen (Microsoft and MIT)

    Noga Alon,(Tel Aviv University)

    Subhabrata Sen, “Partitioning sparse random graphs: connections with mean-field spin glasses”

    Abstract: The study of graph-partition problems such as Maxcut, max-bisection and min-bisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cut-sizes on sparse Erd\ ̋{o}s-R\'{e}nyi and random regular graphs.

    Based on joint work with Aukosh Jagannath.

    Noga Alon, “Random Cayley Graphs”

    Abstract: The study of random Cayley graphs of finite groups is related to the  investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given  group with a prescribed number of generators.  Several intriguing questions that remain open will be mentioned as well.

    11-1-17

    *2:00-4:00pm*

    Kay Kirkpatrick (Illinois)

    and

    Wei-Ming Wang (CNRS)

    Kay Kirkpatrick, Quantum groups, Free Araki-Woods Factors, and a Calculus for Moments

     Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to free Araki-Woods factors, and cases where we have surprisingly good rates of convergence. This is joint work with Michael Brannan. Time permitting, we’ll mention another quantum central limit theorem for Bose-Einstein condensation and work in progress.

    Wei-Min Wang, Quasi-periodic solutions to nonlinear PDE’s

    Abstract: We present a new approach to the existence of time quasi-periodic solutions to nonlinear PDE’s. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a Lagrangian approach to KAM theory, as suggested by J. Moser.

    11-8-17Elchanan MosselOptimal Gaussian Partitions.

    Abstract: How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution.

    The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory.

    I will survey the little we know about this problem and the major open problems in the area.

    11-10-17

    *12pm SC 232*

    Zhe Wang (NYU)A Driven Tagged Particle in One-dimensional Simple Exclusion Process

    Abstract: We study the long-time behavior of a driven tagged particle in a one-dimensional non-nearest- neighbor simple exclusion process.  We will discuss two scenarios when the tagged particle has a speed. Particularly, for the ASEP, the tagged particle can have a positive speed even when it has a drift with negative mean; for the SSEP with removals, we can compute the speed explicitly. We will characterize some nontrivial invariant measures of the environment process by using coupling arguments and color schemes.

    11-15-17

    *4:00-5:00pm*

    *G02*

    Daniel Sussman (BU)Multiple Network Inference: From Joint Embeddings to Graph Matching

    Abstract: Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiple-network framework remains a relatively under-explored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, face-to-face interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, we’ll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching.

    11-20-17

    *Monday

    12:00-1:00pm*

     Yue M. Lu

    (Harvard)

    Asymptotic Methods for High-Dimensional Inference: Precise Analysis, Fundamental Limits, and Optimal Designs
    Abstract: Extracting meaningful information from the large datasets being compiled by our society presents challenges and opportunities to signal and information processing research. On the one hand, many classical methods, and the assumptions they are based on, are simply not designed to handle the explosive growth of the dimensionality of the modern datasets. On the other hand, the increasing dimensionality offers many benefits: in particular, the very high-dimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will mention recent work on exploiting such blessings of dimensionality via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widely-used spectral method for nonconvex signal recoveries; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and mean-field limits to analyze nonconvex optimization algorithms for high-dimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with high-dimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices.
    11-29-17David Gamarink (MIT)(Arguably) Hard on Average Constraint Satisfaction Problems

    Abstract: Many combinatorial optimization problems defined on random instances such as random graphs, exhibit an apparent gap between the optimal value, which can be estimated by non-constructive means, and the best values achievable by fast (polynomial time) algorithms. Through a combined effort of mathematicians, computer scientists and statistical physicists, it became apparent that a potential and in some cases a provable obstruction for designing algorithms bridging this gap is an intricate geometry of nearly optimal solutions, in particular the presence of chaos and a certain Overlap Gap Property (OGP), which we will introduce in this talk. We will demonstrate how for many such problems, the onset of the OGP phase transition indeed nearly coincides with algorithmically hard regimes. Our examples will include the problem of finding a largest independent set of a graph, finding a largest cut in a random hypergrah, random NAE-K-SAT problem, the problem of finding a largest submatrix of a random matrix, and a high-dimensional sparse linear regression problem in statistics.

    Joint work with Wei-Kuo Chen, Quan Li, Dmitry Panchenko,  Mustazee Rahman, Madhu Sudan and Ilias Zadik.

    12-6-17

    *2:00-4:00pm*

    Philippe Rigollet (MIT)

    2-3 pm

    &

    Ankur Moitra (MIT)

    3-4 pm

    Philippe Rigollet (MIT), Exact Recovery in the Ising Block Model 

    Abstract: Over the past fifteen years, the problem of learning Ising models from independent samples has been of significant interest in the statistics, machine learning, and statistical physics communities. Much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models, primarily in the case where the interaction graph is sparse. In parallel, stochastic blockmodels have played a more and more preponderant role in community detection and clustering as an average case model for the minimum bisection model. In this talk, we introduce a new model, called Ising blockmodel for the community structure in an Ising model. It imposes a block structure on the interactions of a dense Ising model and can be viewed as a structured perturbation of the celebrated Curie-Weiss model. We show that interesting phase transitions arise in this model and leverage this probabilistic analysis to develop an algorithm based on semidefinite programming that recovers exactly the community structure when the sample size is large enough. We also prove that exact recovery of the block structure is actually impossible with fewer samples.

    This is joint work with Quentin Berthet (University of Cambridge) and Piyush Srivastava (Tata Institute).

    Ankur Moitra (MIT), A New Approach to Approximate Counting and Sampling 

    Abstract: Over the past sixty years, many remarkable connections have been made between statistical physics, probability, analysis and theoretical computer science through the study of approximate counting. While tight phase transitions are known for many problems with pairwise constraints, much less is known about problems with higher-order constraints.
    Here we introduce a new approach for approximately counting and sampling in bounded degree systems. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random. In our setting, the solution space is not even connected and we introduce alternatives to the usual Markov chain paradigm.

    12-14-17TBD
    DateNameTitle
    09-16-2015Scott Aaronson, MITBosonSampling and the Permanents of Gaussian Matrices
    09-23-2015Xin Sun, MITAlmost sure multi fractal spectrum of SLE
    09-28-2015Li-Cheng Tsai, StanfordKPZ equation limit of interacting particle systems
    09-30-2015Kyle Luh, YaleRandom Matrices: l1 Concentration and Dictionary Learning with Few Samples
    10-07-2015Martin Zirnbauer, Cologne/Simons CenterBott periodicity and the “Periodic Table” of topological insulators and superconductors
    10-14-2015Benjamin Schweinhart, Harvard CMSAUniversality Conjectures for Curvature Flow on Graphs
    10-21-2015Nicholas Cook, UCLA
    10-28-2015Vu-Lan Nguyen, Université Paris DiderotVariants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer
    11-04-2015Vadim Gorin, MITLargest eigenvalues in random matrix beta-ensembles: structures of the limit.
    11-18-2015Louis-Pierre Arguin, CUNYThe maximum of the characteristic polynomial of random unitary matrices 
    11-19-2015Nicholas Zygouras, Univ. of WarwickFrom disorder relevance to the 2d Stochastic Heat Equation
    11-25-2015ThanksgivingNo seminar
    12-02-2015Eero Saksman (Helsinki)The uniqueness of Gaussian multiplicative chaos revisited
    12-04-2015Guillaume Barraquand, ColumbiaRandom walks in Beta random environment
    01-27-2016Louigi Addario-Berry, McGillSlowdown of the front for branching Brownian motion with decay of mass
    02-03-2016Antti Knowles, ETH ZurichAn optimal rotational invariant estimator for general covariance matrices
    02-10-2016No Seminar this week
    02-17-2016Florent Bekerman, MITTransport Methods and Universality for beta-matrix models
    02-24-2016Aukosh Jagannath, Courant InstituteThe Parisi variational problem
    03-02-2016No Seminar this weekTwo next week
    03-09-2016Adam Marcus, PrincetonPolynomials and (finite) free probability
    03-11-2016Hao Shen, ColumbiaThe Sine-Gordon stochastic PDE and regularity structures
    03-16-2016Spring Recess
    03-23-2016Zeev Rudnick, Tel-Aviv and IASQuantum chaos, eigenvalue statistics and the Fibonacci sequence
    03-30-2016Nikolai Makarov, CaltechRandom normal matrices with hard edge spectrum
    04-06-2016Timo Seppalainen, WisconsinVariational formulas and Busemann functions for random paths in a random medium
    04-11-2016 (Science Center 530)Milton D. Jara, IMPAAround the strong KPZ universality conjecture
    04-20-2016Mark Rudelson, MichiganDelocalization of eigenvectors of random matrices
    04-27-2016Marek Biskup, UCLALocal limit theory for extreme values of 2D Discrete Gaussian Free Field
    05-04-2016No Talk
    05-11-2016 (2:30-3:30pm, Room G10)Laure Saint-Raymond, École Normale SupérieureFluctuating dynamics for a 2D rarified gas of hard disks
    06-01-2016Jun Yin, University of WisconsinGeneralized Circular Law
    06-08-2016Paul Bourgade, NYUExtremes of random matrices and log-correlated fields
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    During the 2021–22 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Aghil Alaee, Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form.

    The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    2/10/2022Tin Yau Tsang (UC Irvine)Title: Dihedral ridigity and mass

    Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

    2/17/2022Shiraz Minwalla
    (Tata Institute of Fundamental Research, Mumbai)
    Title: Black Hole dynamics at Large D

    Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

    2/24/2022Achilleas Porfyriadis
    (Harvard Black Hole Initiative)
    Title: Extreme Black Holes: Anabasis and Accidental Symmetry

    Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2) transformation properties of the spherically symmetric linear perturbations of
    AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of  AdS_2.

    3/10/2022David Fajman (University of Vienna)Title: The Einstein-flow on manifolds of negative curvature

    Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.
    3/21/2022Prof. Arick Shao (Queen Mary University of London)Title: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

    Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

    In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

    This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

    3/24/2022Qian Wang, University of OxfordTitle: Rough solutions of the $3$-D compressible Euler equations

    Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

    3/28/2022Emanuele Berti, Johns Hopkins UniversityTitle: Black Hole Spectroscopy

    Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

    4/7/2022CMSA General Relativity Conference
    4/14/2022Chao Liu, Huazhong University of Science and TechnologyTitle: Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4

    Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

    4/21/2022Jinhua Wang,
    Xiamen University
    Title: Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system

    Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

    4/28/2022Allen Fang, Sorbonne UniversityTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

    Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/10/2021

    (10:30am – 11:30am (Boston time)

    Philippe G. LeFloch, Sorbonne University and CNRSTitle: Asymptotic localization, massive fields, and gravitational singularities

    Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

    9/17/2021

    (10:30am – 11:30am (Boston time)

    Igor Rodnianski, Princeton UniversityTitle: Stable Big Bang formation for the Einstein equations

    Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

    9/24/2021

    (10:30am – 11:30am (Boston time)

    Alex LupsascaTitle: On the Observable Shape of Black Hole Photon Rings

    Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

    10/1/2021

    (10:30am – 11:30am (Boston time)

    Zhongshan An, University of ConnecticutTitle: Static vacuum extensions of Bartnik boundary data near flat domains

    Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

    10/8/2021

    (10:30am – 11:30am (Boston time)

    Xiaoning Wu, Chinese Academy of SciencesTitleCausality Comparison and Postive Mass

    Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

    10/15/2021

    (10:30am – 11:30am (Boston time)

    Jiong-Yue Li, Sun Yat-Sen UniversityTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations

    Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

    10/22/2021

    (11:00am – 12:30pm (Boston time)

    Roberto Emparan, University of BarcelonaTitleThe Large D Limit of Einstein’s Equations

    Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

    10/28/2021Jorge Santos, University of CambridgeTitle: The classical interior of charged black holes with AdS asymptotics

    Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

    11/4/2021
    at 10 am ET
    Elena Giorgi, Columbia UniversityTitle: The stability of charged black holes

    Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

    11/11/2021
    *9:30 am ET*
    Siyuan Ma, Sorbonne UniversityTitle: Sharp decay for Teukolsky equation in Kerr spacetimes

    Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

    11/19/2021

    (10:30–11:30 am ET)

    Nishanth Gudapati, Clark UniversityTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes

    Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

    12/2/2021Professor Geoffrey Comp
    ére, Université Libre de Bruxelles
    Title: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger

    Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

    12/16/2021Xinliang An, University of SingaporeTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation

    Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker: Yifan Wang (NYU)

    Title: Fusion Category Symmetries in Quantum Field Theory

    Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti

    ble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

  • Swampland Seminar
    10:30 am-12:00 pm
    12/01/2024

    During the 2021-22 academic year, the CMSA will be co-hosting a seminar on Swampland, with the Harvard Physics Department, organized by Miguel Montero, Cumrun Vafa, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend, please subscribe here.

    Talks will be posted on the Swampland Seminars YouTube channel. The schedule below will be updated as talks are confirmed.

    Spring 2022

    DateSpeakerTitle/Abstract
    1/31/2022Rafael Álvarez-García (DESY Hamburg)Title: Membrane Limits in Quantum Gravity
    2/7/2022Du Pei (Harvard CMSA)Title: Holomorphic CFTs and topological modular forms

    Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

    2/28/2022 Tom Rudelius (UC, Berkeley)Title: Generalized Global Symmetries and the Weak Gravity Conjecture
    3/7/2022Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)Title: 4d strings at strong coupling
    3/21/2022Patrick Draper (Univ. of Illinois) and Alvaro Herraez (IPhT Saclay).Open Mic Discussion
    Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)
    3/28/2022Fernando Quevedo (Cambridge)Title: On renormalisation group induced moduli stabilisation and brane-antibrane inflation

    Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

    4/5/2022Simon Caron-Huot (McGill University) and Julio Parra (Caltech)Title: Causality constraints on corrections to Einstein gravity

    Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

    4/11/2022Timm Wrase and Eduardo Gonzalo (Lehigh)Title: Type IIB flux compactifications with $h^{1,1}=0$

    Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

    4/18/2022José Calderón (IFT Madrid)Open mic Swampland Discussion

    Topic: Cobordism

    5/9/2022Georges Obie (Harvard)Title: Inflation and light Dark Matter constraints from the Swampland

    Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

    Fall 2021

    DateSpeakerTitle/Abstract
    9/13/2021John Stout (Harvard)Title: Decoding Divergent Distances

    Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

    9/20/2021Manki Kim (MIT)Title: Small Cosmological Constants in String Theory

    Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

    9/27/2021Eran Palti (Ben Gurion)Title: Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

    Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

    10/18/2021Thomas Van Riet (KU Leuven)Title: The Festina Lente Bound

    Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for  phenomenology, both top-down and bottom-up.

    10/25/2021Joe Conlon (Oxford)Title: Exploring the Holographic Swampland

    Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

    11/01/2021Pieter Bomans (Princeton)Title: Bubble instability of mIIA on AdS_4 x S^6

    Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

    11/15/2021Nima Arkani-Hamed (IAS), and Gary Shiu (UW-Madison) This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be Swampland constraints, Unitarity and Causality. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.
    11/22/2021Thomas Grimm (Utrecht University)Title: Taming the Landscape

    Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

    11/29/2021Timm Wrase (Lehigh University)Title: Scale separated AdS vacua?

    Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

    12/6/2021Lars Aalsma (University of Wisconsin-Madison)Title: Extremal Black Hole Corrections from Iyer-Wald

    Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024

    Speaker: Michail Savvas, UT Austin

    Title: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds

    Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
    In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

    Organizer: Seminars
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    peaker: Ady Stern & David Mross (Weizmann)

    Speaker: Ady Stern & David Mross (Weizmann

    Title: The nu=5/2 enigma: Recent insights from theory and experiment

    Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:30 pm
    12/01/2024

     

    Nathanan Tantivasadakarn (Harvard)

    Video

    TitleHybrid Fracton Orders

    Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

    Based on 2102.09555 and 2106.03842

     

     

     

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024
    CMSA-QMMP-12.01.21-1544x2048

    Speaker: Daniel Harlow (MIT)

    Title: Symmetry in quantum field theory and quantum gravity 1

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

  • Quantum Matter
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-11.24.21-1583x2048

    Speaker: Shinsei Ryu (Princeton University)

    Title: Multipartitioning topological phases and quantum entanglement

    Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024

    Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
    In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    2/3/2021 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/23/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    02/21/2020 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    3/3/2020 Quantum Matter Seminar

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    12/01/2024
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    3/06/2020 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    3/9/2020 Special Seminar

    10:30 am-11:30 am
    12/01/2024
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    3/10/2020 Special Seminar

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    12/01/2024
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    3/11/2020 Quantum Matter Seminar

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    12/01/2024
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    3/25/2020 Quantum Matter seminar

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    12/01/2024
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    3/27/2020 General Relativity Seminar

    10:30 am-11:30 am
    12/01/2024
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    4/3/2020 General Relativity Seminar

    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    4/16/2020 Condensed Matter Seminar

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    12/01/2024
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    4/22/2020 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    4/29/2020 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    4/29/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
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    4/30/2020 Condensed Matter Seminar

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    12/01/2024
  • Seminars

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    5/4/2020 Condensed Matter Seminar

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    12/01/2024
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    5/4/2020 Mathematical Physics Seminar

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    12/01/2024
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    5/6/2020 Quantum Matter Seminar

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    12/01/2024
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    5/7/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    5/13/2020 Quantum Matter Seminar

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    12/01/2024
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    5/14/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Seminars

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    5/20/2020 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    5/21/2020 Condensed Matter Seminar

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    12/01/2024
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    12/01/2024
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    4/26/2019 Topology

    10:30 am-12:40 pm
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    10:30 am-12:00 pm
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    10:30 am-11:30 am
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    10:30 am-12:00 pm
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    11/27/2019 Quantum Matter Seminar

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    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
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    2/06/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
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    6/18/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    7/9/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/16/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/17/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 am
    12/01/2024-12/23/2020
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    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 am
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    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker:  Jaume Gomis (Perimeter PI)

    Title: Global Anomalies on the Hilbert Space

    Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers” that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker:  Xiao-Gang Wen (MIT)

    Title: A solution to the chiral fermion problem

    Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

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    12/01/2024-02/25/2021
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    12/01/2024
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    Mathematical Physics Seminar
    12/7/2020 Math Physics Seminar

    10:30 am-11:30 am
    12/01/2024
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    10:30 am-12:00 am
    12/01/2024-03/18/2021

    Speaker: Silviu Pufu (Princeton University)

    Title: Exact symmetries and threshold states in two-dimensional models for QCD

    Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of confinement in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

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    10:30 am-12:00 pm
    12/01/2024
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    12/01/2024
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    12/01/2024
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    12/01/2024
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    12/01/2024
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    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    5/12/2021 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
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    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/9/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
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    7/15/2020 Quantum Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
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    4/15/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
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    7/16/2020 Condensed Matter Seminar

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    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    unnamed-3-600x338

    In the 2020-2021 academic year, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom.

    Cuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator, several fascinating phases emerge, including a d-wave superconductor, a pseudo-gap metal, and strange metal. After intensive studies from experimental, theoretical, and numerical communities for more than three decades, remarkable progress has been made, but basic questions remain:

    1. What is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling, spin fluctuations, or resonating-valence-bonds?
    2. How do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters, or do we need an unconventional picture involving fractionalization?
    3. Is the strange metal at optimal doping associated with a quantum critical point? And if so, what is the driving force of this phase transition?

    The cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics, such as quantum spin liquids, topological order, and non-Fermi liquids. In the coming years, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series, we hope to accelerate this process by bringing together deeper conversations between experimental, theoretical, and numerical experts with different backgrounds and perspectives.

    The Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar.

    Seminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard).

    Scientific program advisors: Professor Subir Sachdev (Harvard), Professor Patrick Lee (MIT).

    In order to learn how to attend this series, please fill out this form.

    For more information, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu)

    Spring 2022

    April 20, 2022 | 11:30 – 1:00 pm ET

    Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)

    Title: Superconductivity in infinite-layer nickelates

    Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.


    February 3, 2022 | 11:30 – 1:00 pm ET

    Lu Li (U Michigan)

    Title: Quantum Oscillations of Electrical Resistivity in an Insulator

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    2020 – 2021

    September 2, 2020 | 10:30am ET

    Sachdev
    Subir Sachdev (Harvard)

    TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

    Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
    describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

    Video

    September 23, 2020 | 10:30am ET

    Sachdev
    Subir Sachdev (Harvard)

    Title: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II

    Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

    Video

    September 24, 2020 | 12:00pm ET

    hqdefault
    Inna Vishik (University of California, Davis)

    Title: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video

    October 15, 2020 | 10:30am ET

    unnamed
    Louis Taillefer (Université de Sherbrooke)

    TitleNew signatures of the pseudogap phase of cuprate superconductors

    Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

    Video

    October 28, 2020 | 10:30am ET

    lee_patrick
    Patrick Lee (MIT)

    Title: The not-so-normal normal state of underdoped Cuprate

    Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

    Video

    November 6, 2020 |12:30pm ET

    Shen
    Zhi-Xun Shen (Stanford University)

    Title: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors

    Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
    Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
    magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
    (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
    experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

    [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
    [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
    [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
    [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
    [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
    [6] A. Lanzara et al., Nature 412, 510 (2001)
    [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
    [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
    [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
    [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
    [11] A.G. Loeser et al., Science 273, 325 (1996)
    [12] S. Chen et al., Science, 366, 6469 (2019)
    [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
    [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
    [15] Yu He et al., Science, 362, 62 (Oct. 2018)
    [16] Z. Chen, Y. Wang et al., preprint, 2020

    Video

    November 12, 2020 |10:30am ET

    Chandra-Varma
    Chandra Varma (Visting Professor, University of California, Berkeley.
    Emeritus Distinguished Professor, University of California, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:
    1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
    2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
    3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
    4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting,
    (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
    (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
    (iii) Problems.Video

    November 18, 2020 |10:30am ET

    download
    Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

    Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

    Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

    Video

    November 19, 2020 |10:30am ET

    Fradkin
    Eduardo Fradkin (University of Illinois at Urbana-Champaign)

    Title: Pair Density Waves and Intertwined Orders in High Tc Superconductors

    Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

    Video

    November 25, 2020 |10:30am ET

    Si-1coborc
    Qimiao Si (Rice University)

    Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

    Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

    December 2, 2020 |10:30am ET

    Chubukov
    Andrey Chubukov (University of Minnesota)

    Title: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

    Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

    December 9, 2020 |10:30am ET

    Hsieh
    David Hsieh (Caltech)

    Title:  Signatures of anomalous symmetry breaking in the cuprates  

    Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
    [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

    [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516

    December 16, 2020 |10:30am ET

    weng
    Zheng-Yu Weng (Tsinghua University)

    TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

    Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

    December 17, 2020 |10:30am ET

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    Steven Kivelson (Stanford University)

    Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

    Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.

    January 20, 2021 |10:30am ET

    Devereaux
    Thomas Peter Devereaux (Stanford University)

    Title:  Numerical investigations of models of the cuprates

    Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

    I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

    February 3, 2021 |10:30am ET

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    Philip Phillips (University of Illinois Urbana-Champaign)

    Title: Beyond BCS: An Exact Model for Superconductivity and Mottness

    Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
    [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

    February 10, 2021 |10:30am ET

    todadri_senthil
    Senthil Todadri (MIT)

    Title: Strange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

    Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
    [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.07896
    [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

    April 1, 2021 |9:00am ET

    weng
    Naoto Nagaosa (University of Tokyo)

    TitleApplied physics of high-Tc theories

    Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

    April 22, 2021 |10:30am ET

    lee
    Dung-Hai Lee (UC Berkeley)

    Title: “Non-abelian bosonization in two and three spatial dimensions and some applications”

    Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.

    May 12, 2021 |10:30am ET

    weng
    André-Marie Tremblay (Université de Sherbrooke)

    Title: A unified theoretical perspective on the cuprate phase diagram

    Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

    August 11, 2021 |10:30am ET

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    Piers Coleman (Rutgers)

    Title: Order Fractionalization*

    Abstract: I will discuss the interplay of spin fractionalization with broken
    symmetry. When a spin fractionalizes into a fermion, the resulting particle
    can hybridize or pair with the mobile electrons to develop a new kind of
    fractional order parameter. The concept of “order fractionalization” enables
    us to extend the concept of off-diagonal order to encompass the formation of
    such order parameters with fractional quantum numbers, such as spinorial
    order[1].
    A beautiful illustration of this phenomenon is provided by a model
    which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This
    model explicitly exhibits order fractionalization and is expected to undergo a
    discrete Ising phase transition at finite temperature into an
    order-fractionalized phase with gapless Majorana excitations.
    The broader implications of these considerations for Quantum
    Materials and Quantum Field Theory will be discussed.
    Work done in collaboration with Yashar Komijani, Anna Toth and Alexei
    Tsvelik.
    [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018).
    [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

    September 15, 2021 |10:30am ET

    0049_7858_headshot-scaled-aspect-ratio-420-334-2-scaled-840x668-c-default
    Liang Fu (MIT)

    Title: Three-particle mechanism for pairing and superconductivity

    Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

    [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
    [2] V. Crepel and L. Fu, arXiv:2103.12060
    [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

    September 29, 2021 |11:30am ET (special time)

    Ong
    Nai Phuan Ong (Princeton University)

    Title:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al., Nature Physics 17, 915 (2021).Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

    Date TBA |10:30am ET

    image_normal
    Suchitra Sebastian (University of Cambridge)

    Title: TBA

    Date TBA |10:30am ET

    hoffman
    Jenny Hoffman (Harvard University)

    Title: TBA

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/14/2020 Mathematical Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/21/2020 Math-Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    9/23/2020 Strongly Correlated Quantum Materials Series

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/1/2020 Quantum Matter seminar

    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/05/2020 Math Physics Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/25/2020 Strongly Correlated Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/19/2020 Math Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    10/28/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/9/2020 Math-Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/12/2020 Condensed Matter Seminar

    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/18/2020 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/19/20 Strongly Correlated Quantum Materials

    10:30 am-12:00 pm
    12/01/2024
  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-12.02.21-1544x2048-1

    Speaker: Daniel Harlow (MIT)

    Title: Symmetry in quantum field theory and quantum gravity 2

    Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/2/2020 Math-Physics Seminar

    10:30 am-11:30 am
    12/01/2024
  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Xueyang Song (MIT)

    Title: Phase transitions out of quantum Hall states in moire TMD bilayers

    Abstract: Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\’e Transition Metal Dichalcogenide (TMD) bilayers, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth.  At filling -2/3, we describe a direct transition between the FQAH state and a Charge Density Wave (CDW) insulator. The critical theory resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by  Barkeshli and McGreevy.   Crucially we show that translation symmetry alone is enough to enable a second order CFL-FL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order.  A striking signature is a universal jump of resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFL-FL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist.  We also present a critical theory for the CFL to FL transition at filling -3/4.  Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-04.06.2022-1583x2048-1

    Youtube Video

     

    Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024
    CMSA QMMP 02.17.23

    Quantum Matter Seminar

    Speaker: Rahul Sahay (Harvard)

    Title: Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics

    Abstract: While many-body quantum systems can in principle host exotic quantum spin liquid (QSL) states, realizing them as ground states in experiments can be prohibitively difficult. In this talk, we show how non-equilibrium dynamics can provide a streamlined route toward creating QSLs. In particular, we show how a simple Hamiltonian parameter sweep can dynamically project out condensed anyons from a family of initial product states (e.g. dynamically “un-Higgs”), yielding a QSL-like state. We christen such states “quantum spin lakes” which, while not thermodynamically large QSLs, enable their study in NISQ-era quantum simulators. Indeed, we show that this mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. Time permitting, we will discuss how our theory motivates a tree tensor network-based numerical tool—reliant on our theory—that quantitatively reproduces the experimental data two orders of magnitude faster than conventional brute-force simulation methods. Finally, we will highlight that even spin liquid states that are unstable in equilibrium—namely, 2 + 1D U(1) spin liquid states—can be robustly prepared by non-equilibrium dynamics.

     

    https://www.youtube.com/watch?v=ECT9nozk2SY&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=15

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Professor Harvey Reall (University of Cambridge) 

    Title: The second law of black hole mechanics in effective field theory

    Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs.

    Video
  • Quantum Matter
    10:30 am-12:30 pm
    12/01/2024

    Speaker: Kenichi Konishi (UNIPI.IT)

    Title: Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: Recent developments

    Abstract: After many years of efforts, still very little is known today about the physics of strongly-coupled chiral gauge theories in four dimensions, in spite of an important role they might play in the physics of fundamental interactions beyond the standard SU(3)xSU(2)xU(1) model. This is in stark contrast with the vectorlike gauge theories for which we have many solid results, thanks to some exact theorems, to the lattice simulation studies, to the Seiberg-Witten exact solution of N=2 supersymmetric gauge theories, and last, but not the least, to the real-world strong-interaction phenomenology and experimental tests of Quantum Chromodynamics.

    The purpose of this seminar is to discuss the results of our recent efforts to improve the understanding of the strongly-coupled chiral gauge theories. Among the main tools of analysis are the consideration of anomalies. We use both the conventional ’t Hooft anomaly-matching ideas, and new, more stringent constraints coming from the generalized anomalies involving some higher-form symmetries. Also, the so-called strong anomalies, little considered in the context of chiral gage theories, are found to carry significant implications.

    As the playground we study several classes of SU(N) gauge theories, the so-called Bars-Yankielowicz models, the generalized Georgi-Glashow models, as well as a few other simple theories with the fermions in complex, anomaly-free representations of the color SU(N).

    Color-flavor-locked dynamical Higgs phase and dynamical Abelianization, emerge, among others, as two particularly interesting possible phases the system can flow into in the infrared, depending on the matter fermion content of the model.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Sheldon Katz, UIUC

    Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants

    Abstract:  A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3.  These X are nodal CY threefolds which do not admit a projective small resolution.  B-model techniques can be applied to compute GV invariants up to g \le 32.  This raises the question: what is the geometric meaning of these invariants?

    Evidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by Kuznetsov.  One of these moduli stacks is a stacky small resolution X’ of X itself.  This leads to another geometric interpretation of the invariants as being associated with moduli of sheaves on X’ twisted by a Brauer class.  Geometric computations based on these working definitions always agree with the B-model computations.

    This talk is based on joint work with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe.

     

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    Virtual and in 20 Garden Street, Room G10

    Speaker: Seth Koren (University of Chicago)

    Title: Baryon Minus Lepton Number BF Theory for the Cosmological Lithium Problem

    Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+  3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    unnamed-file

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024

    Topological Quantum Matter Seminar

    Speaker: Amanda Young, UIUC

    Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential

    Abstract: Haldane pseudopotentials were first introduced as Hamiltonian models for the fractional quantum Hall effect, and it has been long expected that they should exhibit the characteristic properties of this exotic phase of matter, including a spectral gap above the ground state energy. We will discuss recent work that verified this gap conjecture for a truncated version of the 1/3-filled Haldane pseudopotential in the cylinder geometry. Numerical evidence suggested that for open boundary conditions the gap of the truncated model closes as the cylinder radius converges to zero and that this closure is due to the presence of edge modes; in contrast, for periodic boundary conditions, the gap remains robustly order one in the same radius limit. The standard scheme for applying spectral gap estimating techniques to the model with periodic boundary conditions, though, produces a lower bound on the bulk gap that still reflects the energy of the edge modes. To obtain an estimate on the bulk gap that reflects its true behavior, a new gap estimating strategy was developed. By customizing the spectral gap method to key invariant subspaces of the Hamiltonian, we are able to successfully avoid the edge states and produce a more accurate lower bound on the bulk gap. In this talk, we discuss this invariant subspace strategy for proving bulk gaps in the presence of edge states. This is based off joint work with S. Warzel.

     

     

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-04.28.22-1583x2048

    Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    Superconductivity in infinite-layer nickelates

    10:30 am-1:00 pm
    12/01/2024
    CMSA-Strongly-Correlated-Quantum-Materials-and-High-Temperature-Superconductors-04.20.21-1583x2048

    Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Thorsten Schimannek (Utrecht University)

    Title: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants

    Abstract: The physics of M-theory and Type IIA strings on a projective nodal CY 3-folds is determined by the geometry of a small resolution, even if the latter is not Kähler. We will demonstrate this explicitly in the context of a family of Calabi-Yau double covers of P^3. Using conifold transitions, we prove that the exceptional curves in any small resolution are torsion while M-theory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary Gopakumar-Vafa invariants, that is associated to the singular Calabi-Yau and captures the enumerative geometry of the non-Kähler resolutions. We further argue that twisted circle compactifications of the 5d theory are dual to IIA compactifications on the nodal CY 3-fold with a flat but topologically non-trivial B-field. As a result, the torsion refined invariants are encoded in the topological string partition functions with different choices for the global topology of a flat B-field.

    The talk is based on 2108.09311, 2212.08655 (with S. Katz, A. Klemm, and E. Sharpe) and 2307.00047 (with S. Katz).

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: An Huang (Brandeis)

    Pre-talk Speaker: TBA: 10:00-10:30 am

    Title: A p-adic Laplacian on the Tate curve

    Abstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.30.2022-1583x2048-1

    Youtube Video

     

    Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy.  This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport.  We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation.  Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem.  The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories.  Our techniques generalize to other RG flow equations beyond Polchinski’s.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 09.15.22

    General Relativity Seminar
    Title: The Gregory-Laflamme instability of black strings revisited
     
    Abstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string.
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA GR Seminar 04.27.23

    General Relativity Seminar

    Speaker: Philippe G. LeFloch, Sorbonne University and CNRS

    Title: The localized seed-to-solution method for the Einstein constraints

    Abstract: I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set, we define a “localized seed-to-solution” map, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly, as we prove it, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis, we discover the notion of ‘asymptotic modulators’, as we call them, or “correctors” to the standard ADM invariants.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.23.2022-1583x2048

    Youtube Video

     

    Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.16.2022-1544x2048-1

    Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv  2201.00903.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024

    Speaker: Petr Hořava (UC Berkeley)

    Title: Topological Quantum Gravity and the Ricci Flow – Part I

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-02.16.2022-1544x2048

    Speaker: Petr Hořava (UC Berkeley)

    Title: Topological Quantum Gravity and the Ricci Flow – Part I

    Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Jonah Herzog-Arbeitman, Princeton University

    Title: Exact Results in Flat Band Hubbard Models

    Abstract: Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multi-orbital case: the mean-field theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and low-energy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution reveals the importance of quantum geometry in escaping (some of) BCS phenomenology within a tractable and nontrivial strong coupling theory.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.09.2022-1544x2048-1

    Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Pre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am

    Speaker: Kai Xu (CMSA)

    Title: Motivic decomposition of moduli space from brane dynamics

    Abstract: Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-03.02.2022-1544x2048

    Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Ho Tat Lam, MIT

    Title: Dipolar and modulated symmetry protected topological phases

    Abstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-02.24.2022-1544x2048-1

    Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Maksym Fedorchuk (Boston College)

    Title: CM-minimizers and standard models of Fano fibrations over curves

    Abstract: A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of K-stable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CM-minimizers without base change. In answering this question, we arrive at a theory of Koll\’ar stability for fibrations over one-dimensional bases, and standard models of Fano fibrations. I will explain the joint work with Hamid Abban and Igor Krylov in which we show that the CM-minimizers for del Pezzo fibrations are Corti’s standard models and related work in progress on quartic threefold hypersurfaces.

     

  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024

    Quantum Matter Seminar

    Speaker: Ho Tat Lam (MIT)

    Title: Non-invertible Symmetry Enforced Gaplessness

    Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

     

    https://www.youtube.com/watch?v=A-47aZ4HS1k&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=16

  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: David Favero, University of Minnesota

    Title: Gauged Linear Sigma Models and Cohomological Field Theories

    Abstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker.  Gauged Linear Sigma Models (GLSMs)  serve as a means of interpolating between Kahler geometry and singularity theory.  In enumerative geometry, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.   In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs.  Furthermore, we proved that these invariants form a Cohomological Field Theory.   In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss the construction of these general invariants.  Briefly, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”.  This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Professor Oscar Dias (University of Southampton)

    Title: Strong Cosmic Censorship

    Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally, I will discuss some possibilities (quantum effects, non-smooth initial data,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

  • Topological Quantum Matter Seminar
    10:30 am-11:30 am
    12/01/2024

    Topological Quantum Matter Seminar

    Speaker: Shenghan Jiang, Kavli Institute for Theoretical Sciences UCAS

    Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States

    Abstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has been established that topological insulator phases persist as stable phases. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wavefunctions for numerical simulations is highly desirable.
    In this talk, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions, we write down tensor equations, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems.

     

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Naqing Xie (Fudan University)

    Title: Gravitational Wave, Angular Momentum, and Supertranslation Ambiguity
    Abstract: The supertranslation ambiguity of angular momentum is a long-standing and conceptually important issue in general relativity. Recently, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However, in the compact binary coalescence community, supertranslation ambiguity is often ignored. We have shown that, in the linearised theory of gravitational wave, the new angular momentum coincides with the classical definition at the quadrupole level. This talk is based on a recent joint work with Xiaokai He and Xiaoning Wu.
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar

    General Relativity Seminar

    Speaker: Nikolaos Athanasiou
    Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
    Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.
  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Sergei Dubovsky (New York University)
    Title: Love Symmetry of Black Holes
    Abstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2,ℝ) symmetry in the suitably defined near zone approximation. We show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2,ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2,ℝ) representations. It is this highest-weight property that forces the static Love numbers to vanish. We show that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. The Love symmetry also exhibits a peculiar UV/IR mixing.
  • Quantum Matter
    10:30 am-11:30 am
    12/01/2024
    CMSA QMMP 02.03.23

    Quantum Matter Seminar

    Speaker: Han Yan (Rice U)

    Title: Fracton orders in hyperbolic space and its excitations with fractal mobility

    Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.

    Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

     

    https://www.youtube.com/watch?v=ekfKNCKzZyE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=17

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA GR Seminar 09.29.22

    General Relativity Seminar

    Speaker: Marcelo Disconzi, Vanderbilt University

    Title: Generalrelativistic viscous fluids
    Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.
  • Algebraic Geometry in String Theory Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Andrew Harder, Lehigh University

    Pre-talk Speaker: TBA: 10:00-10:30 am

    Title: Deformations of Landau-Ginzburg models and their fibers

    Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

  • Quantum Matter
    10:30 am-12:00 pm
    12/01/2024
    CMSA-QMMP-12.08.21-1544x2048

    Speaker: Fei Yan (Rutgers)

    Title: Defects, link invariants and exact WKB

    Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024

    General Relativity Seminar

    Speaker: Pengyu Le (BIMSA)

    Title: Asymptotic geometry of null hypersurface in Schwarzschild spacetime and null Penrose inequality

    Abstract: Null Penrose inequality is an important case of the well-known Penrose inequality on a null hypersurface. It conjectures the relation between the area of the outmost marginally trapped surface and the Bondi mass at null infinity. Following the proposal of Christodoulou and Sauter, we employ the perturbation method to study the asymptotic geometry of null hypersurfaces at null infinity in a perturbed vacuum Schwarzshild spacetime. We explain how to apply this perturbation theory to prove null Penrose inequality on a nearly spherically symmetric null hypersurface in a perturbed vacuum Schwarzschild spacetime.

  • General Relativity Seminar
    10:30 am-11:30 am
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Uri Kol, CMSA

    Title: Duality in Einstein’s Gravity

    Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-02-2016 Random Matrix & Probability Theory Seminar

    10:32 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    10:36 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-07-16 Mathematical Physics Seminar

    10:38 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar

    Special Seminar
    11-04-16 Special Seminar

    10:42 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    10:43 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-09-2016 Random Matrix & Probability Theory Seminar

    10:44 am
    12/01/2024

    No additional detail for this event.

  • Program
    10:44 am-11:04 am
    12/01/2024-06/12/2021
    CMSA-2-600x338

    The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

    Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

    In this course, we will start with an introduction to computer programming, algorithm, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

    The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

    This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard related perks (such as a place to live if you are in Boston over the summer.)

    However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

    If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited to 10 people, so don’t wait too long to apply.

  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Quantum Matter Seminar

    10:45 am-12:45 pm
    12/01/2024
  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Birational geometry

    10:45 am-12:15 pm
    12/01/2024
    Lecture_Shokurov-pdf

    Vyacheslav V. Shokurov (Johns Hopkins University)

    Title: Birational geometry

    Abstract: About main achievements in birational geometry during the last fifty years.

    Talk chair: Caucher Birkar

    Video

  • Seminars
    10:46 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    10:56 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    10:57 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-14-16 Mathematical Physics Seminar

    10:58 am
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Rodrigo Silva, University of Maryland

    Title: Quantization of causal diamonds in 2+1 dimensional gravity

    Abstract: We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with a fixed boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that has the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required — in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham’s group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

     

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Black Hole Formation

    11:00 am-12:00 pm
    12/01/2024
    Lecture_Bieri-pdf

    Lydia Bieri (University of Michigan)

    Title: Black Hole Formation

    Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the dynamical mathematical structures of the Einstein equations. Black holes are related to the presence of trapped surfaces in the spacetime manifold. Christodoulou proved that in the regime of pure general relativity and for arbitrarily dispersed initial data, trapped surfaces form through the focusing of gravitational waves provided the incoming energy is large enough in a precisely defined way. The proof combines new ideas from geometric analysis and nonlinear partial differential equations as well as it introduces new methods to solve large data problems. These methods have many applications beyond general relativity. D. Christodoulou’s result was generalized in various directions by many authors. It launched mathematical activities going into multiple fields in mathematics and physics. In this talk, we will discuss the mathematical framework of the above question. Then we will outline the main ideas of Christodoulou’s result and its generalizations, show relations to other questions and give an overview of implications in other fields.

    Video

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Michael Freedman

    11:00 am-12:30 pm
    12/01/2024
    20bottfeatureplain-1

    20bottfeatureplain
    On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.

    This will be the third annual lecture series held in honor of Raoul Bott.

    Lecture 1
    October 4th, 11:00am (Boston time)
    Title: The Universe from a single Particle

    Abstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.

    Video

    Lecture 2
    October 5th, 11:00am (Boston time)
    Title: Controlled Mather Thurston Theorems.

    Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374  

    Video

     

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Shuaijie Qian (Harvard CMSA)

    Title: Some non-concave dynamic optimization problems in finance

    Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present our recent work on some non-concave dynamic optimization problems, where the concavification principle may not hold and the resulting value function is indeed non-concave.

    The first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation, where the average tax basis and the average mining cost serves as an approximation, respectively. This approximation results in a non-concave value function, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover, the penalty method still works and converges to the value function.

    The second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints, which makes the concavification principle invalid, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous, we introduce a new definition of viscosity solution, prove the corresponding comparison principle, and show that a monotone, stable, and consistent finite difference scheme converges to the solution of the utility maximization problem.

     

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Mauricio Romo

    Title: Quantum trace and length conjecture for hyperbolic knot

    Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Diandian Wang(Harvard University)

    Title: Pole skipping, quasinormal modes, shockwaves and their connection to chaos

    Abstract: A chaotic quantum system can be studied using the out-of-time-order correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function — that seems to also know things: things like the Lyapunov exponent and the butterfly velocity, which are important quantifiers of the OTOC. Then I will talk about a systematic way of deriving pole-skipping conditions for general holographic CFTs dual to classical bulk theories and how to use this framework to derive a few interesting statements including: (1) theories with higher spins generally violate the chaos bound; (2) the butterfly velocity calculated using pole skipping agrees with that calculated using shockwaves for arbitrary higher-derivative gravity coupled to ordinary matter; (3) shockwaves are related to a special type of quasinormal modes. As we will see, the techniques are entirely classically gravitational, which I will go through with a certain level of details.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Maria Rodriguez (Utah)

    Title: Tidal Squeezing of Black Holes

    Abstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Chethan Krishnan (IISc Bangalore)

    Title: A Smooth Horizon without a Smooth Horizon

    Abstract: I will talk about some work that is about to appear, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls, fuzzballs, Type I algebras,…)

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Alejandro Poveda

    Title: Compactness and Anticompactness Principles in Set Theory

    Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.

  • Seminars

    Seminars Colloquia & Seminar
    3/30/2020 Math Physics Seminar

    11:00 am-12:00 pm
    12/01/2024
  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    17 Oxford St, Cambridge, MA 02138

    Swampland Seminar

    Location: Jefferson Physical Laboratory, Seminar room J356

    Speaker: Markus Dierigl (LMU Munich)

    Title: IIB Explored – Dualities, Bordisms, and the Swampland

    Abstract: In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries, we discuss which defects need to be included to break them completely. Interestingly, we find many backgrounds that are well-known in the F-theory literature, such as [p,q]-7-branes, non-Higgsable clusters, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications, which I will discuss in more detail.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Damian van de Heisteeg

    Title: Light states in the interior of CY moduli spaces

    Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Lionel Mason (Oxford)

    Title: Geometry at Strong coupling for amplitudes/Wilson loops

    Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024

    General Relativity Seminar

    Speaker: Andras Vasy (Stanford)

    Title: The Feynman propagator and self-adjointness

    Abstract: In this talk I will discuss the Feynman and anti-Feynman inverses for wave operators on certain Lorentzian manifolds; these are two inverses which from a microlocal analysis perspective are more natural than the standard causal (advanced/retarded) ones. For instance, for the spectral family of the wave operator, these are the natural inverses when the spectral parameter is non-real. Indeed, I will explain that these connect to the self-adjointness of the wave operator, and the positivity properties that follow.

     

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Fernando Marchesano (IFT Madrid)

    Title: EFT strings and emergence

    Abstract: We revisit the Emergence Proposal in 4d N=2 vector multiplet sectors that arise from  type II string Calabi-Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA compactifications, where EFT strings arise from NS5-branes wrapping internal four-cycles, and consider a set of infinite-distance moduli-space limits that can be classified in terms of a scaling weight w=1,2,3. It has been shown before how one-loop threshold effects of an infinite tower of BPS particles made up of D2/D0-branes generate the asymptotic behaviour of  the gauge kinetic functions along limits with $w=3$. We extend this result to w=2 limits, by taking into account D2-brane multi-wrapping numbers. In w=1 limits the leading tower involves EFT string oscillations, and one can reproduce the behaviour of both weakly and strongly-coupled U(1)’s independently on whether the EFT string is critical or not, by assuming that charged modes dominate the light spectrum.

  • Seminars

    Seminars Colloquia & Seminar
    5/8/2020 General Relativity Seminar

    11:00 am
    12/01/2024
  • Active Matter Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter

    Active Matter Seminar
    Speaker: Shenshen Wang, UCLA
    Title:  Limit and potential of adaptive immunity
    Abstract: The adaptive immune system is able to learn from past experiences to better fit an
    unforeseen future. This is made possible by a diverse and dynamic repertoire of cells
    expressing unique antigen receptors and capable of rapid Darwinian evolution within an
    individual. However, naturally occurring immune responses exhibit limits in efficacy,
    speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical
    frameworks we developed to (1) explore functional impacts of non-equilibrium antigen
    recognition, and (2) identify conditions under which natural selection acting local in time
    can find adaptable solutions favorable in the long run, through exploiting environmental
    variations and functional constraints.
  • Seminars

    Seminars Colloquia & Seminar
    5/15/2020 General Relativity Seminar

    11:00 am
    12/01/2024
  • Probability Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA Probability Seminar 03.09.23

    Probability Seminar

    Speaker: Jean-Christophe Mourrat (ENS Lyon)

    Title: On the free energy of spin glasses with multiple types

    Abstract: In the simplest spin-glass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups, which we can visualize as forming two layers, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there, and some partial progress.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Member Seminar
    Speaker: Shai Chester
    Title: Derivation of AdS/CFT for Vector Models

    Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories, and at finite temperature.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Ben McKenna

    Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance

    Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Jake McNamara (Caltech)
    Title: Parity and Cobordism
    Abstract: The swampland cobordism conjecture provides a convenient way to discuss conserved charges associated with the topology of spacetime. However, much of the power of the cobordism conjecture comes from a mathematical black box: the Adams spectral sequence. In this talk, I will give physical meaning to this black box through a concrete example: domain walls arising from the spontaneously breaking of parity symmetry, which arise in particle physics in Nelson-Barr models. I will argue that parity domain walls are exactly stable, and interpret this stability as the result of an unusual type of gauge symmetry that can only occur in gravitational theories.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-16-2016 Random Matrix & Probability Theory Seminar

    11:00 am
    12/01/2024

    No additional detail for this event.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Jie Wang

    Title: Kahler geometry in twisted materials

    Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making many-body states less stable in flatbands.

    In this talk, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform, but still exhibit exact properties such as model wavefunctions, density algebra, exact parent Hamiltonians. I will discuss both the theory of ideal flatband, its experimental realization in Dirac materials as well as implications.

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar 

    Speaker: Zhigang Yao

    Title: Principal flow, sub-manifold and boundary

    Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold, a manifold passing through the center of the data, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find, use and interpret the principal sub-manifold, by which a principal boundary can be further defined for data sets on manifolds.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Swampland Seminar
    Speaker: Aasmund Folkestad (MIT)
    Title: The Penrose Inequality as a Constraint on Low Energy Quantum Gravity
    Abstract: In this talk, I argue that the Penrose inequality (PI) can be used to constrain low energy theories compatible AdS/CFT, and possibly also quantum gravity in flat space. Focusing on AdS/CFT, it is shown that the PI can be violated for minimally coupled scalar fields, and I produce exclusion plots on couplings that respect the PI. I also present numerical evidence that top-down scalar theories and supersymmetric theories respect the PI. Finally, similar to the Breitenlohner-Freedman bound, I give a necessary condition for the stability AdS that constrains coupling constants (beyond the scalar mass).
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/28/2020 Mathematical Physics Seminar

    11:00 am-12:00 pm
    12/01/2024
  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: David Andriot (Annecy, LAPTH)

    Title: String theory scalar potentials and their critical points

    Abstract: Positive scalar potentials in string effective theories could provide an origin to Dark Energy, responsible for the accelerated expansion of our universe today or during inflation. It is thus crucial to characterize these scalar potentials, namely their slope, their critical points (de Sitter solutions) and the associated stability, as also advocated by the Swampland Program. We will present such characterizations. Going further, we will also discuss negative scalar potentials, and make related observations on anti-de Sitter solutions, in particular on a new mass bound, as well as comments on scale separation.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Paul-Konstantin Oehlmann(Northeastern)

    Title: Anomalies of Discrete Gauge Symmetries and their Cancellation in 6D F-theory

    Abstract: We consider 6D SUGRAs with a discrete gauge group G, engineered via F-theory compactifications on genus-one fibered threefolds. We argue that group G suffers from Dai-Freed anomalies that can be canceled via a discrete Green-Schwarz mechanism. We comment on the ambiguity to assign this GS term in the 7D Anomaly theory which leads to choices that are not all compatible with F-theory.

    In F-theory we then deduce this Anomaly coefficient explicitly by computing the elliptic genera of the non-critical strings that couple to the 6D two-form fields: Their 2D worldsheet theories inherits a G Flavor symmetries whose t’Hooft anomaly cancels the 6D Dai-Freed anomaly in the bulk via inflow. This talk is based on work in preparation together with Markus Dierigl and Thorsten Schimmanek.

  • CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
    11:00 am-8:45 pm
    12/01/2024-05/09/2021
    Summer,Warm,Sun,Light,Forest,Aerial,View

    This workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom

    The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data.

    This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

    The first half of the workshop will feature talks aimed at graduate students, newcomers, and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications.

    For the discussions, we are soliciting open problems in mathematical theory and applications of shape analysis. You are encouraged to post problems by sending an email to geometricproblemsfrg@gmail.com.

    We invite junior researchers to present a short talk in the workshop. The session will be held on Friday, May 7th or Saturday, May 8th at 4pm and are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks, the organizers will review the submissions and let you know if you have been selected. If you are interested please send your title and abstract to tianqi@cmsa.fas.harvard.edu by the end of May 2nd.

     

    Organizers:

    • David Glickenstein, University of Arizona
    • Joel Hass, University of California, Davis
    • Patrice Koehl, University of California, Davis
    • Feng Luo, Rutgers University, New Brunswick
    • Tianqi Wu, Harvard University
    • Shing-Tung Yau, Harvard University

    Featured lectures:

    • Christopher Bishop, Stony Brook
    • Keenan Crane, Carnegie Mellon

    Speakers include:

    • Miri Ben-Chen, Technion – Israel Institute of Technology
    • Alexander Bobenko, Technische Universität Berlin, Germany
    • Ulrike Buecking, Free University, Germany
    • Nadav Dym, Duke University
    • Ivan Izmestiev, Vienna University of Technology
    • Yanwen Luo, Rutgers
    • Stephan Tillmann, The University of Sydney
    • Max Wardetzky, University of Goettingen
    • Xu Xu, Wuhan University
  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics

    Title: Quantum magnet chains and Kashiwara crystals

    Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva, Joel Kamnitzer, and Alex Weekes.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Swampland Seminar
    Speaker: Samir Mathur (Ohio State)
    Title: The story of the information paradox
    Abstract:  In 1975 Hawking argued that black hole evaporation would lead to a loss of unitarity in quantum theory.  The small corrections theorem made Hawking’s argument into a precise statement: if semiclassical physics hold to leading order in any gently curved region of spacetime, then there can be no resolution to the paradox. In string theory, whenever people have been able to construct microstates explicutly, the states turned out to be horizon sized objects (fuzzballs) with no horizon; such a structure of microstates resolves the information paradox since their is no pair creation at a vacuum horizon. There have been a set of parallel attempts to resolve the paradox (with ideas involving wormholes, islands etc) where the horizon is smooth in some leading approximation. An analysis of such models however indicated that in each case the exact quantum gravity theory would either have to be nonunitary or to have dynamics at infinity that is conflict with usual low energy physics in the lab.
  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Swampland Seminar 01.30.23

    Swampland Seminar

    Speaker: Ignatios Antoniadis (LPTHE Paris)
    Title: Swampland program, extra dimensions and supersymmetry breaking
    Abstract: I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalisation of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.
  • Colloquium
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 04.03.2023

    Colloquium

    Speaker: Luca Iliesiu, Stanford

    Title: Black hole microstate counting from the gravitational path integral

    Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Swampland Seminar 04.10.23

    Swampland Seminar

    Speaker: Seung-Joo Lee (IBS Daejeon)

    Title: Swampland bounds on the abelian gauge sectors

    Abstract: In this talk we will derive various bounds on the 0-form and the 1-form abelian gauge sectors of gravitational effective theories in 6 dimensions with minimal supersymmetry. We will start by considering 6-dimensional F-theory vacua with at least one tensor multiplets, to bound for them the number of the (0-form) U(1) gauge factors as well as the cyclic orders of the 1-form discrete gauge factors. While the two abelian gauge sectors may look rather independent, we will observe that both are heavily constrained by the solitonic heterotic strings present in the spectrum, which provide a common intuition for the derived bounds. Building upon the heterotic intuition, we will also try extending the arena to address analogous bounds for all F-theory vacua in 6 dimensions and even beyond. If time permits, several applications and future directions of research will be discussed at the end of the talk.

  • Math Science Literature Lecture Series
    11:00 am-12:30 pm
    12/01/2024

    Sergiu Klainerman (Princeton University)

    Title: Nonlinear stability of Kerr black holes for small angular momentum

    Abstract: According to a well-known conjecture,  initial data sets,  for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon)   which approaches  (globally)  a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $|a|/m $ sufficiently small. The work, ArXiv:2104.11857v1,  also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr,  with Szeftel and Elena Giorgi,  which I will also describe.

    Talk chair: Lydia Bieri 

    Video

  • Member Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin

    Title: Explicit Ramsey Graphs and Two Source Extractors

    Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    Jefferson Hall Room 368, 17 Oxford St, Cambridge, MA 02138

    Swampland Seminar

    Speaker: Thomas Grimm (Utrecht U.)

    Title: The Tameness of Quantum Field Theories

    Abstract: Tameness is a generalized notion of finiteness that is restricting the geometric complexity of sets and functions. The underlying mathematical foundation lies in tame geometry, which is built from o-minimal structures introduced in mathematical logic. In this talk I formalize the connection between quantum field theories and logical structures and argue that the tameness of a quantum field theory relies on its UV definition. I quantify our expectations on the tameness of effective theories that can be coupled to quantum gravity and on CFTs. In particular, I present tameness conjectures about CFT observables and propose universal constraints that render spaces of CFTs to be tame sets. I then highlight the relation of these conjectures to other swampland conjectures, e.g., by arguing that the tameness of CFT observables restricts having parametrical gaps in the operator spectrum.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Swampland Seminar 03.27.23

    Swampland Seminar

    Speaker: Valerio De Luca (UPenn)

    Title: Recent developments on the tidal Love numbers of black holes

    Abstract: Tidal Love numbers describe the deformability of compact objects under the presence of external tidal perturbations, and are found to be exactly zero for black holes in pure General Relativity. This property is however fragile, since they receive corrections from higher-order derivative terms in the theory. We show that the tidal deformability of neutral black holes is constrained by the Weak Gravity Conjecture.

  • Swampland Seminar
    11:00 am-12:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Swampland Seminar

    Speaker: Alvaro Herraez (Saclay)

    Title: The Emergence Proposal in Quantum Gravity and the Species Scale

    Abstract: The Emergence Proposal claims that in Quantum Gravity the kinetic terms of the fields in the IR emerge from integrating out (infinite) towers of particles up to the QG cutoff. After introducing this proposal in the context of the Swampland Program, I will explain why it is natural to identify this QG cutoff with the Species Scale, motivating it by direct computation in the presence of the relevant towers. Then, I will present evidence for this proposal by directly studying how it is realized in different string theory setups, where the kinetic terms of scalars, p-forms and even scalar potentials can be shown to emerge after integrating out such towers.

     

     

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024

    General Relativity Seminar

    Speaker: Daniel Kolb (Max Planck Institute)

    Title: Quasi-Local Mass in a Binary Black Hole Merger

    Abstract: One of the major open problems in classical general relativity is how one should define the mass of a finite region of space. In this talk, we will investigate a promising definition proposed by Wang and Yau in 2009. A closed 2-surface bounding the region of interest is embedded isometrically into Minkowski space. The mass is then calculated by comparing the extrinsic geometries. The Wang-Yau mass has many desirable properties, but it has previously not been calculated for surfaces in dynamical spacetimes. To remedy this, we will discuss how the Wang-Yau mass can be computed in practice and extend the definition to surfaces important in black hole dynamics: their quasi-local horizons. Finally, we look at how this mass behaves in a merger of black holes.

  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: David Kubiznak (Charles University)

    Title: Remarkable symmetries of rotating black holes

    Abstract: It is well known that the Kerr geometry admits a non-trivial Killing tensor and its ‘square root’ known as the Killing-Yano tensor. These two objects stand behind Carter’s constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object — the principal Killing-Yano tensor — generates a tower of explicit and hidden symmetries responsible for integrability of geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes described by the `magic square’ version of the Lense-Thirring solution, giving rise to a geometrically preferred spacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.

  • General Relativity Seminar
  • General Relativity Seminar
  • General Relativity Seminar
  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    General Relativity Seminar

    Speaker: Leo Stein (Mississippi)

    Title: Resolving memory in numerical relativity, and fixing BMS frames for modeling

    Abstract: Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE), and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames, we can extract well-defined remnant quantities, perform precision ringdown modeling, and build complete surrogate waveform models that capture memory effects.

  • Seminars

    Seminars Colloquia & Seminar
    3-2-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    12/01/2024-03/03/2018
  • Seminars

    Seminars Colloquia & Seminar
    2-16-2018 Mirror Symmetry Seminar

    11:00 am
    12/01/2024
  • General Relativity Seminar
    11:00 am-12:00 pm
    12/01/2024
    20 Garden Street, Cambridge MA 02138

    General Relativity Seminar

    Speaker: David Fajman (Vienna)

    Title: Fluid stabilization in slowly expanding cosmological spacetime

    Abstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.

     

    Talk via Zoom, broadcast in G10

     

  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    4-13-2018 Mirror Symmetry Seminar

    11:00 am-12:00 am
    12/01/2024-04/14/2018
  • Seminars

    Seminars Colloquia & Seminar
    10/19/2018 Mirror Symmetry Seminar

    11:00 am-11:00 pm
    12/01/2024
  • General Relativity Seminar
  • Seminars

    Seminars Colloquia & Seminar
    02-09-2018 Mirror Symmetry Seminar

    11:00 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2-23-2018 Mirror Symmetry Seminar

    11:00 am
    12/01/2024
  • Member Seminar
    11:01 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-21-16 Mathematical Physics Seminar

    11:02 am
    12/01/2024

    No additional detail for this event.

  • Algebraic Geometry in String Theory Seminar
    11:02 am-12:02 pm
    12/01/2024

    Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    11:03 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:03 am-11:04 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:04 am
    12/01/2024

    The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

    Spring 2020

    DateSpeakerTitle/Abstract
    1/29/2020David Yang (Harvard)

    Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

    2/5/2020Scott Aaronson (UT Austin)

    Video

    Title: Gentle Measurement of Quantum States and Differential Privacy

    Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
    of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

    Based on joint work with Guy Rothblum (arXiv:1904.08747)

    2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

    Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

    2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

    Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

    2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

    Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
    3/4/2020

    4:45 – 5:45pm

    Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

    Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

    In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

    3/11/2020

    Postponed

    Jose Scheinkman

    (Columbia)

    This colloquium will be rescheduled at a later date. 

    Title: Menu Costs and the Volatility of Inflation

    Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

    3/12/2020

    4:00 – 5:00pm

    Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

    Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

    Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

    Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

    3/25/2020Cancelled
    4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

    Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

    Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

    4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

    Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

    Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
    explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
    fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

    4/15/2020
    Lars Andersson (Max-Planck Institute for Gravitational Physics)
    This meeting will be taking place virtually on Zoom.

    Title: Stability of spacetimes with supersymmetric compactifications

    Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

    4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow in high codimension

    Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

    4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

    Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

    Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

    5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

    Title: Energy, Mass and Radiation in General Spacetimes

    Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

    5/13/2020Mikhail Lukin (Harvard)

    Video

    This meeting will be taking place virtually on Zoom.

    Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

    Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

    5/20/2020This meeting will be taking place virtually on Zoom.

    Fall 2019

    DateSpeakerTitle/Abstract
    9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

    Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

    ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

    ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

    ◦ The natural Nullstellensatz are falling into place.

    The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

    9/25/2019Pavel Etingof (MIT)

     

    Title: Double affine Hecke algebras

    Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

    10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

    Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

    10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

     

    Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

     

    Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

    John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

    Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

    Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

    Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

    10/16/2019Aram Harrow (MIT)

    Video

    Title: Monogamy of entanglement and convex geometry

    Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

    10/23/2019No talk
    10/30/2019Nima Arkani-Hamed (IAS)

    Video

    Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
    11/6/2019Kevin Costello (Perimeter Institute)

    Video

    Title: A unified perspective on integrability

     

    Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

    11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

    Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

    11/20/2019Xi Yin (Harvard)

    Video

    Title: An Introduction to the Non-Perturbative Bootstrap

    Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

    11/25/2019

    Monday

    Madhu Sudan (Harvard)
    Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

    In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

    Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

    12/4/2019Xiao-Gang Wen (MIT)
    Video
    Title: Emergence of graviton-like excitations from a lattice model

    Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

    2018-2019

    DateSpeakerTitle/Abstract
    9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

    Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

    10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

    Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

    10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

    Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

    10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

    Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

    In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

    10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

    Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

    11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

    Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

    11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

    Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

    11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

    Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

    12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

    Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

    Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

    12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

    Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

    1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

    Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

    2/7/2019

    *Thursday*

    Ulrich Mueller (Princeton)Title: Inference for the Mean

    Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

    2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

    Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

    2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

    Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

    [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

    2/27/2019

    2:30pm

    Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

    Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

    3/6/2019

    2:30pm

    Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

    Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

    3/13/2019

    5:15pm

    Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

    Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

    3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

    Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

    3/27/2019

    5:15pm

    Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

    Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

    4/3/2019

    2:30pm

    Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

    Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

    4/10/2019

    2:30pm

    Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

    Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

    Paper

    Online Appendix

    4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

    Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

    .

    [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

    [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

    [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

    4/24/2019Shengwu Li (Harvard)
    Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
    Date…………SpeakerTitle
    02-09-2018 *Friday       Fan Chung

    (UCSD)

    Sequences: random, structured or something in between

    There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

    testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

    02-14-2018Zhengwei Liu

    (Harvard Physics)

    A new program on quantum subgroups

    Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

    02-21-2018Don Rubin

    (Harvard)

    Essential concepts of causal inference — a remarkable history

    Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

    02-26-2018 *MondayTom Hou

    (Caltech)

    Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

    Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

    03-07-2018Richard Kenyon

    (Brown)

    Harmonic functions and the chromatic polynomial

    Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

    03-14-2018
    03-21-2018
    03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

    Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

    We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
    [Based on joint work with Song Mei and Phan-Minh Nguyen]

    03-30-2018
    04-04-2018Ramesh Narayan 

    (Harvard)

    Black Holes and Naked Singularities

    Abstract: Black Hole solutions in General Relativity contain Event Horizons and
    Singularities. Astrophysicists have discovered two populations of
    black hole candidates in the Universe: stellar-mass objects with
    masses in the range 5 to 30 solar masses, and supermassive objects
    with masses in the range million to several billion solar
    masses. There is considerable evidence that these objects have Event
    Horizons. It thus appears that astronomical black hole candidates are
    true Black Holes. Direct evidence for Singularities is much harder to
    obtain since, at least in the case of Black Holes, the Singularities
    are hidden inside the Event Horizon. However, General Relativity also
    permits Naked Singularities which are visible to external
    observers. Toy Naked Singularity models have been constructed, and
    some observational features of accretion flows in these spacetimes
    have been worked out.

    04-11-2018Pablo Parrilo

    (MIT)

    Graph Structure in Polynomial Systems: Chordal Networks

    Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

    04-18-2018Washington Taylor

    (MIT)

    On the fibration structure of known Calabi-Yau threefolds

    Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

    04-25-2018 Xi Yin

    (Harvard)

    How we can learn what we need to know about M-theory

    Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

    05-02-2018
    05-09-2018

    2016-2017

    DateNameTitle/Abstract
    01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

    Title: Spectral graph theory of cognitive maps

    Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

    02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

    Sean_Eddy

    Title: Biological sequence homology searches: the future of deciphering the past 

    Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

    02-08-17Matthew Headrick, Brandeis University

    matthew_headrick

    Title: Quantum entanglement, classical gravity, and convex programming: New connections

    Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

    02-15-17Masahito Yamazaki, IMPU

    Masahito Yamazaki

     Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

    Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

    Video

    02-22-17Steven Rayan, University of Saskatchewan

    Title: Higgs bundles and the Hitchin system

    Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

    Video

    03-01-17Jun Liu, Harvard University

    Jun liu

    Title: Expansion of biological pathways by integrative Genomics

    Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

    Based on the joint work with Yang Li and the Vamsi Mootha lab.

    Video

    03-08-17Gabor Lippner, Northeastern University

    ---

    Title: Evolution of cooperation in structured populations

    Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

    In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
    03-15-17 Spring Break: No session
    03-22-17Gunther Uhlmann, University of Washington

    guntherUhlman

    Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
    waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
    The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
    We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
    03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

    Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

    NOTE: This talk will begin at 4:00pm

    04-05-17Gongjie Li, Harvard University

    GongjieLi

    Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

    Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

    Video

    04-12-17Shlomo Razamat, Israel Institute of Technology

    ShlomoRazamat

    Title: Complicated four-dimensional physics and simple mathematics

    Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

    Video

    04-19-17Cumrun Vafa, Harvard University

    CumrunVafa

    Title: String Swampland

    Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

    04-27-17Mehran Kardar, MIT

    MehranKardar

    Title: Levitation by Casimir forces in and out of equilibrium

    Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

    Note: This talk will begin at 3:00pm

    05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

    Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
    similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
    have led to substantial progress in protein structural and functional
    predictions.

    Note:  This talk will begin at 4:00pm

    05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

    Abstract: A deterministic or random system with a conservation law is often used to
    approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

    Note: This talk will be held in the Science Center, Room 507

    05-10-17
    05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

    Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

    05-24-17 NO COLLOQUIUM
    05-31-17Peter Michor, University of Vienna

     Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

    Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

    DateNameTitle
    09-09-16

    Bong Lian, Brandeis

    portrait

    Title: Riemann-Hilbert Problem and Period Integrals

    Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

    09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

    Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

    09-21-16Prof. L. Mahadevan, Harvard SEAS

    Mahadevan_200x300

    Title: “Morphogenesis: Biology, Physics and Mathematics”

    Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

    09-28-16Hong Liu, MIT

    liu_hong

    Title: A new theory of fluctuating hydrodynamics

    Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

    We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

    Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

    10-05-16

    Alexander LogunovTel-Aviv University

    alex

    Title: Zeroes of harmonic functions and Laplace eigenfunctions

     Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

    10-12-16 Conan Nai Chung Leung, CUHK

    conan_profile

    Title:  Coisotropic A-branes and their SYZ transform

    Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

    10-19-16Vaughan Jones, UC Berkeley

    vj6

    Title: Are the Thompson groups any good as a model for Diff(S^1)?

    Abstract. The Thompson groups are by definition groups of piecewise linear
    diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
    be conjugated to a group of smooth diffeomorphisms. That’s the good news.
    The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
    procedure analogous to the constructions of the central extension of Diff(S^1)?
    I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

     10-26-16

    Henry Cohn, Microsoft

    ????????????????????????????????????

    Sums of squares, correlation functions, and exceptional geometric structures

    Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

    11-02-16

    Christian Borgs, Microsoft

    Borgs

    Title:  Graphon processes and limits of   sparse graph sequences

    Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

    In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

    11-09-16

    TIME CHANGE: 4PM

    Norden E. HuangNational Central University, (Taiwan)

    member1_clip_image003

    Title: On Holo-Hilbert Spectral Analysis

    Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

    11-16-16Tristan Collins, Harvard University

    image

    TIME CHANGE: 3:30PM

    Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

    Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

    11-22-16 TUESDAY

    TIME CHANGE: 4-5PM

    Xiangfeng Gu, Stonybrook

    Title: Differential Geometric Methods for Engineering Applications

    Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

    11-30-16

    TIME CHANGE: 4:20PM

    Sharad Ramanathan, Harvard MCB & SEAS

    Ramanathan.Sharad_200x300

    Title: Finding co-ordinate systems to monitor the development of mammalian embryos
     12-07-16

    Valentino Tosatti, Northwestern

    Title: Metric limits of hyperkahler manifolds

    Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

     12-14-16

    2015-2016

    DateNameTitle
    09-02-2015Madhu SudanRobust low-degree testing
    09-09-2015Mithat Unsal
    What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
    09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
    09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
    09-30-2015Leslie ValiantHolographic Algorithms
    10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
    10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
    10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
    10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
    11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
    11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
    11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
    11-25-2015ThanksgivingNo seminar
    12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
    12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
    01-27-2016Conan LeungSome modern aspects of Morse theory 
    02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
    02-10-2016Chun Peng Wang
    02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
    02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
    03-02-2016Lydia BieriMathematical General Relativity
    03-09-2016Piotr ChruscielThe mathematics of gravitation
    03-16-2016Spring BreakNo Talk
    03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
    03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
    04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
    04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
    04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
    04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
    04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
    05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
    05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
  • Colloquium
    11:05 am-11:06 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:07 am-11:08 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:08 am-11:09 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-22-2016 Random Matrix & Probability Theory Seminar

    11:12 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-07-2016 Random Matrix & Probability Theory Seminar

    11:16 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-05-16 Mathematical Physics Seminar

    11:17 am
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
    11:19 am
    12/01/2024-11/14/2019
    Dynamics-12-x-18-683x1024

    On November 12-14, 2019 the CMSA will be hosting a workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Biological cells are the fundamental units of life, and predictive modeling of cellular dynamics is essential for understanding a myriad of biological processes and functions. Rapid advances in technologies have made it possible for biologists to measure many variables and outputs from complex molecular and cellular networks with various inputs and environmental conditions. However, such advances are far ahead of the development of mathematical theory, models and methods needed to secure a deep understanding of how high-level robust behaviors emerge from the interactions in complex structures, especially in dynamic and stochastic environments. This workshop will bring together mathematicians and biological scientists involved in developing mathematical theories and methods for understanding, predicting and controlling dynamic behavior of molecular and cellular networks. Particular emphasis will be placed on efforts directed towards discovering underlying biological principles that govern function, adaptation and evolution, and on the development of associated mathematical theories.

    Organizers: Jeremy Gunawardena (Harvard) and Ruth Williams (University of California, San Diego)

    A limited amount of funding is available to help in defraying the travel costs of early career researchers, women, and underrepresented minorities, participating the workshop. Early career researchers are researchers who received their Ph.D. in 2014 or later, or who are Ph.D. students expecting to complete their Ph.D. by the end of 2020.

    To apply, please send a CV, a statement of why you wish to attend, and, if you are a grad student, a letter of support from your advisor to Sarah LaBauve at slabauve@math.harvard.edu

    All applications received by 5pm, EDT, October 28, 2019 will receive full consideration.

    Speakers: 

    Videos from the workshop can be found in the Youtube playlist.

  • Seminars
    11:21 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:21 am-11:22 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-14-2016 Random Matrix & Probability Theory Seminar

    11:22 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    11:24 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    11:25 am
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Learning from health data in the million genome era
    11:26 am
    12/01/2024

    On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

    Speakers: 

    • Heidi Rehm, Ph.D.
      Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
    • Saiju Pyarajan, Ph.D.
      Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
    • Tianxi Cai, Sci.D
      John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
    • Susan Redline, M.D., M.P.H
      Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
    • Avinash Sahu, Ph.D.
      Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
    • Peter J. Park, Ph.D.
      Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
    • David Roberson
      Community Engagement Manager, Seven Bridges

    Registration & Schedule

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    9/29/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    4/20/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    12/15/2020 Computer Science for Math

    11:30 am-12:30 pm
    12/01/2024
  • Quantum Matter
    11:30 am-1:00 pm
    12/01/2024

    Quantum Matter Seminar

    Speaker: Daniel S. Freed (U Texas)

    Title: Topological symmetry in field theory

    Abstract: Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries,” “higher symmetries,” “noninvertible symmetries,” etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory. This is joint work with Constantin Teleman and Greg Moore.

     

    https://www.youtube.com/watch?v=y5uHfqVGunA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=26

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Quantum Field Theory Seminar

    11:30 am-12:00 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/24/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    Quantum Oscillations of Electrical Resistivity in an Insulator

    11:30 am-1:00 pm
    12/01/2024
    CMSA-QMMP-02.03.2022

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    9/22/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    9/15/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    10/6/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    Rank-Based Independence Testing in Near Linear Time

    11:30 am-12:30 pm
    12/01/2024

    Speaker: Chaim Even-Zohar (Alan Turing Institute, London)

    Title: Rank-Based Independence Testing in Near Linear Time

    Abstract: In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.
    We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.

    Joint work with Calvin Leng.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    10/20/2020 Computer Science for Math

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    5/11/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/3/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    4/6/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    10/27/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    01-30-2017 Mathematical Physics Seminar

    11:30 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/23/2020 Mathematical Physics Seminar

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/17/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/2/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/23/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    3/2/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Quantum Matter
    11:30 am-1:00 pm
    12/01/2024

    Speaker: Lu Li (U Michigan)

    Title: Quantum Oscillations of Electrical Resistivity in an Insulator

    Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    11/10/2020 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    3/9/2021 Computer Science for Mathematicians

    11:30 am-12:30 am
    12/01/2024-03/10/2021
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    3/23/2021 Computer Science for Mathematicians

    11:30 am-12:30 pm
    12/01/2024
  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/9/2021 Computer Science for Math

    11:30 am-12:30 pm
    12/01/2024
  • Seminars
    11:32 am
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    11:33 am-1:33 pm
    12/01/2024

    Title: Symmetry types in QFT and the CRT theorem

    Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-06-2017 Mathematical Physics Seminar

    11:33 am
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    02-13-2017, Mathematical Physics Seminar

    11:34 am
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    11:35 am
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
    11:36 am
    12/01/2024-10/30/2019
    Space-Time-poster-5

    As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

    Everyone is welcome to attend the lectures.

    The master class workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Photos of the event

    Organizers:

  • Member Seminar
    11:37 am
    12/01/2024

    Hansol Hong, Harvard

    Title: Homological Mirror Functors

    Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

  • Colloquium
    11:39 am-11:40 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:40 am-11:41 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    11:42 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:43 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:45 am
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    11:47 am-1:47 pm
    12/01/2024

    Title: Applications of instantons, sphalerons and instanton-dyons in QCD

    Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

    Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

  • Quantum Matter
    11:48 am-1:48 pm
    12/01/2024

    Title: Oscillations in the thermal conductivity of a spin liquid*

    Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

    *Czajka et al., Nature Physics 17, 915 (2021).

    Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

  • Quantum Matter
    11:49 am-1:49 pm
    12/01/2024

    Title: Line defects in CFTs: Renormalization group flows and semiclassical limits

    Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

  • Seminars

    Seminars Colloquia & Seminar
    10/24/2019 Quantum Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/21/2019 Condensed Matter seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/5/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/12/2019 Quantum Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/7/2019 Quantum Matter Seminar

    11:50 am
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/31/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Condensed Matter Seminar

    11:50 am-1:00 pm
    12/01/2024
  • CMSA EVENT: Quantum Information Workshop
    11:52 am-11:53 am
    12/01/2024
    Asset-6-600x338

    Please note, this workshop has been postponed to a later date. Details will be posted to this page when they are available.

    The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

    The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

    More information to follow.

  • Quantum Matter
    11:54 am-1:54 pm
    12/01/2024

    Title: A tour of categorical symmetry

    Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-12-2017 Random Matrix & Probability Theory Seminar

    11:56 am
    12/01/2024

    No additional detail for this event.

  • Colloquium
    11:56 am
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-22-2017 Random Matrix & Probability Theory Seminar

    11:58 am
    12/01/2024

    No additional detail for this event.

  • Algebraic Geometry in String Theory Seminar
    11:58 am-12:58 pm
    12/01/2024

    Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.

  • Colloquium
    11:58 am
    12/01/2024

    No additional detail for this event.

  • Seminars
    11:59 am
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4/1/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Chuck Doran

    Title: Modularity of Landau-Ginzburg Models

    Abstract:  Fano varieties are the basic building blocks of algebraic varieties.  Smooth Fano varieties have been classified in dimensions one (the projective line), two (del Pezzo surfaces), and three (Mori-Mukai classification).  What does Mirror Symmetry have to say about such classifications?  By studying the Landau-Ginzburg models mirror to smooth Fano threefolds we can transform the Mori-Mukai classification into an effective uniruledness result for moduli spaces of certain K3 and abelian surfaces.  This is joint work with Andrew Harder, Ludmil Katzarkov, Mikhail Ovcharenko, and Victor Przjalkowski (arXiv:2307.15607).

     

     

  • Seminars

    Seminars Colloquia & Seminar
    3/02/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3/19/2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/9/2020 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Samy Jelassi

    Title: An introduction to mixture of experts in deep learning

    Abstract: Scale has opened new frontiers in natural language processing – but at a high cost. Mixture-of-Experts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By doing so, the parameter count is decoupled from the compute per example leading to very large, but efficient models. In this talk, I will review the concept of mixture of experts, provide a basic description of the Switch Transformers model, characterize some of their behaviors and conclude by highlighting some open problems in the field. This talk is mainly based on the following papers: https://arxiv.org/pdf/2101.03961.pdfhttps://arxiv.org/pdf/2209.01667.pdf .

  • Seminars

    Seminars Colloquia & Seminar
    1/28/2018 Mathematical Physics Seminar

    12:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/24/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/22/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Mike Douglas

    Title: AI and Theorem Proving

    Abstract: We survey interactive theorem proving and the Lean theorem prover, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.

  • Seminars

    Seminars Colloquia & Seminar
    3/23/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/4/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Zi Yang Kang

    Title: Deformations of Landau-Ginzburg models and their fibers

    Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

  • Seminars

    Seminars Colloquia & Seminar
    4/25/2019 Fluid Dynamics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/25/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Kai Xu (CMSA)

    Title: Moduli of vector bundles on curve and semiorthogonal decomposition

    Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived Θ-stratification.

     

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    9/24/2020 Strongly Correlated Quantum Materials

    12:00 pm-1:30 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Juven Wang

    Title: Categorical Symmetry of the Standard Model from Gravitational Anomaly

    Abstract: In the Standard Model, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.147652204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ16 respectively. For this construction, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, or the 3d boundary topological order of 4d ℤTF4-time-reversal symmetric topological superconductor [2302.14862].

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Benjamin McKenna

    Title: Random matrices and large deviations

    Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson.

     

  • Seminars

    Seminars Colloquia & Seminar
    3/4/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Daniel Kapec (CMSA)

    Title: Black Holes as Quantum Systems

    Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles.

     

  • Seminars

    Seminars Colloquia & Seminar
    12/18/2019 Quantum Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/25/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/8/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/11/2019 Mathematical Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Max Wiesner

    Title: Quantum Gravity constraints beyond asymptotic regimes

    Abstract: Not every effective field theory that is consistent in the absence of gravity can be completed to a consistent theory of quantum gravity. The goal of the Swampland program is to find general criteria that distinguish effective field theories, that can be obtained as a low-energy approximation of quantum gravity, from those that are inconsistent in the presence of gravity. These criteria are oftentimes motivated by patterns observed in explicit compactifications of perturbative string theory and have passed many non-trivial tests in asymptotic regions of the field space such as, e.g., weak coupling limits. Still, the Swampland criteria should equally apply to effective theories that do not arise in asymptotic regions of the field space of string theory compactifications. In this talk I will summarize some of my recent works that studies the interior of regions of the field space of string theory in the context of the Swampland program.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/3/2020 Math-Physics

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/2/2019 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/3/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/4/2019 Math Physics Seminar

    12:00 pm-2:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/13/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024-04/22/2020
  • Seminars

    Seminars Colloquia & Seminar
    4/15/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2/10/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/29/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Sunghyuk Park

    Title: Quantum UV-IR map and curve counts in skeins

    Abstract: Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong.

    In this talk, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules, using skein-valued curve counts of Ekholm and Shende.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/29/2018 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Farzan Vafa

    Title: Dynamics of active nematic defects on cones

    Abstract: In the first part of the talk, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge, which in analogy to electrostatics, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle, which is determined by charged defects screening the effective apex charge: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk, we investigate the dynamics of an active nematic on a cone, and via simulations find long-time circular orbits of either one or two flank defects, with transitions between these states mediated by the apex via defect absorption, emission, or defect pair creation.

  • Probability Seminar
    12:00 pm-1:00 pm
    12/01/2024

    Probability Seminar

    Speaker: Jun Yin (UCLA)

    Title: A random matrix model towards the quantum chaos transition conjecture

    Abstract: The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE.

    This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of the same phenomenon, shedding light on the intricacies of this long-standing conjecture.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/5/2018 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Dan Kapec

    Title: Hints of Flat Space Holography

    Abstract: Despite our detailed understanding of holography in Anti-de Sitter space, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space, bulk gravitons produce a boundary stress tensor, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Changji Xu

    Title: Spectral gap and two-point functions in spin glasses

    Abstract: Many have worked on spin glass models over the past 50 years, including physicists, mathematicians, and computers. A question that arises is whether computers yield dependable simulation results. In this talk, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.

  • Algebraic Geometry in String Theory Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Algebraic Geometry in String Theory Seminar

    Speaker: Oliver Schlotterer (Uppsala University)

    Title: Modular graph forms and iterated integrals in string amplitudes

    Abstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful cross-talk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress in clarifying their connection with modular graph forms.

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Faidra Monachou

    Title: Optimal Dynamic Allocation: Simplicity through Information Design

    Abstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that, when the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the information disclosed about each object is an interval containing the object quality, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases, these intervals become coarser, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality, in terms of the Lorenz order.

  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Freid Tong

    Title: On complete Calabi-Yau metrics and some related Monge-Ampere equations

    Abstract: We will give a basic introduction to constructions for complete Calabi-Yau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of Tian-Yau in the 90s and have attracted a lot of attention in recent years. I will discuss some joint work with B. Guo and T. Collins on a singular version of such a construction, as well as some ongoing work with Prof. Yau on some related boundary value problems.

     

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Jue Liu

    Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds

    Abstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass, we define a new quasilocal mass using the Hamilton method. With this definition, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture, that is under what conditions there will be a static extension to the given Bartnik data.

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Barak Weiss  

    Title: New bounds on lattice covering volumes, and nearly uniform covers

    Abstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK, such that L+rK = R^n, normalized by the covolume of L. Pairs (L,K) with small covering volume correspond to efficient coverings of space by translates of K, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE, Hebrew University) and Oded Regev (CS, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.

  • Math Science Literature Lecture Series
    12:00 pm-1:30 pm
    12/01/2024

    Ralph Cohen (Stanford University)

    Title: Immersions of manifolds and homotopy theory

    Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest dimension Euclidean space into which every n-manifold embeds or immerses. The embedding question is still very much unsolved, and the immersion question was solved in the 1980’s. I will discuss the homotopy theoretic techniques involved in the solution of this problem, and contributions in the 60’s, 70’s and 80’s of Massey, Brown, Peterson, and myself. I will also discuss questions regarding the best embedding and immersion dimensions of specific manifolds, such has projective spaces. Finally, I will end by discussing more modern approaches to studying spaces of embeddings due to Goodwillie, Weiss, and others. This talk will be geared toward a general mathematical audience.

    Talk chair: Michael Hopkins

    Video

  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Quantum Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Condensed Matter Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/30/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars
    12:00 pm-1:30 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Puskar Mondal

    Title: Recent progress on coupled Einstein-Yang-Mills dynamics

    Abstract: I will discuss my recent work with prof. S.T. Yau on Einstein-Yang-Mills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gauge-gravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a double-null framework play an important role. I’ll sketch how the special structure of the Einstein and Yang-Mills nonlinearities play a crucial role in obtaining the stability result of non-expanding spacetimes in particular AF spacetimes.

  • Seminars

    Seminars Colloquia & Seminar
    9/16/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/20/2020 Math Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/6/2019 Math Physics

    12:00 pm-1:00 pm
    12/01/2024
  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    12/2/2020 Strongly Correlated Quantum Materials

    12:00 pm-1:30 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-5-2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/27/2020 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Puskar Mondal (CMSA)

    Title: On the Breakdown of Einstein’s Gravity

    Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-26-2018 Math Physics Seminar

    12:00 pm-1:30 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/3/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Aghil Alaee

    Title: A quasi-local mass in general relativity

    Abstract: One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime, which can include a star, black hole, or galaxy. We define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition.  Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau.

     

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Chuck Doran

    Title: Motivic Geometry of Two-Loop Feynman Integrals

    Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/19/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Gabriel Wong

    Title: Quantum information and extended topological quantum field theory

    Abstract: Recently, ideas from quantum information theory have played an important role in condensed matter and quantum gravity research. Most of these applications focus on the entanglement structure of quantum states, and the computation of entanglement measures such as entanglement entropy has been an essential part of the story. In this talk, we will address some subtleties that arise when trying to define entanglement entropy in quantum field theory and quantum gravity. In particular, we will explain why extended topological field theory provides a useful framework to define and compute entanglement entropy in a continuous system. Time permitting, we will explain some recent applications of these ideas in low dimensional quantum gravity and to topological string theory.

     

     

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-2-2018 Mathematical Physics Seminar

    12:00 pm-1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/28/2019 Math Physics

    12:00 pm-1:00 pm
    12/01/2024
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11/26/2018 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Aghil Alaee

    Title: Toroidal Positive Mass Theorem

    Abstract: In this talk, we review the positive mass conjecture in general relativity and prove a toroidal version of this conjecture in an asymptotically hyperbolic setting.

  • Seminars

    Seminars Colloquia & Seminar
    10/7/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Iacopo Brivio (CMSA)

    Title: Extension of pluricanonical forms in positive and mixed characteristics

    Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{times m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring.

     

  • Seminars

    Seminars Colloquia & Seminar
    9/9/2019 Math-Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Michael Simkin

    Title: Randomized algorithms in combinatorics

    Abstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples:

    1. Enumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other?
    2. Constructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In 1973 Erdos conjectured that there exist STSs with arbitrary large girth (informally, no small set of vertices spans many triples). I will discuss the use of randomized algorithms to prove this conjecture. Joint work with Kwan, Sah, and Sawhney.
    3. Thresholds in random graphs and hypergraphs: I will discuss how randomized algorithms can be combined with the recent resolution of the Kahn–Kalai conjecture to determine thresholds in random (hyper) graph theory. Joint work with Pham, Sah, and Sawhney.
  • Seminars

    Seminars Colloquia & Seminar
    3/25/2019 Mathematical Physics Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Quantum Matter
    12:00 pm-1:30 pm
    12/01/2024
  • Seminars
    12:00 pm-1:00 pm
    12/01/2024
    Raymarching and the Thurston Geometries

    On Wednesday, December 16 at 12:00 p.m. EST, WAM and CMSA will host a holiday seminar featuring Sabetta Matsumoto, Georgia Institute of Technology who will present The Inside View: Raymarching and the Thurston Geometries.

    The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon, Henry Segerman and Steve Trettel.

    Visit the event page

    Register to access this event here

     

  • Quantum Matter
    12:00 pm-1:00 pm
    12/01/2024

    Speaker: Eric Sharpe (Virginia Tech)

    Title: Anomaly resolution via decomposition

    Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

  • Quantum Matter
    12:00 pm-1:00 pm
    12/01/2024

    Speaker: Biao Lian (Princeton)

    Title: Integrability and chaos of 1+1d chiral edge states

    Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

  • General Relativity Seminar
    12:00 pm-1:00 pm
    12/01/2024

    The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
    04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
    04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
    04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
    05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
    05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
    05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
    05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Juven Wang

    Title: Open Problems in Physics and Novel Solutions from Math

     

    Abstract: (1) How do neutrinos obtain tiny mass and oscillate between e, \mu, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis?

    (2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions?

    (3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry?

    (4) Family/Generation problem: Why are there three families/generations of quarks and leptons?

    In my talk, I will sketch and propose novel solutions to these challenging open problems in physics based on my own work (available on arXiv, some jointly with my collaborators).

    I will show that the eclectic cross-disciplinary fertilization of ideas between the Math-Physics geometry and topology, Quantum Condensed Matter, and High-Energy Physics (theory, pheno, lattice) can help solving these big problems.

    The (1) answer relates to Ultra Unification: a Z_{16} class Atiyah-Patodi-Singer eta invariant (Baryon – Lepton)-protected topological superconductor and a symmetry-extended anomalous topological quantum field theory.

    The (2) and (3) answers relate to a trivial cobordism class and Symmetric Mass Generation, and disordering and removing the Pecci-Quinn axions.

    The (4) answer has to do with the Hirzebruch signature and Atiyah-Singer index theorem, gravitational Chern-Simons theory, and 3 E8 quantum Hall states.

     

  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Title: Duality in Einstein’s Gravity

    Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    4/8/2021 Interdisciplinary Science Seminar

    12:00 pm-1:00 pm
    12/01/2024
  • Member Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Alejandro Poveda

    Title: On compactness phenomena

    Abstract: In this presentation I shall be preoccupied with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behavior. This phenomenon is intrinsic to the very architecture of the mathematical universe and manifests to us in a cornucopia of forms. Over the past fifty years, the study of compactness phenomena has been a cornerstone of research in set theory. This talk will present recent discoveries regarding compactness principles, spanning classical themes like the tree property and stationary reflection, while also forging novel connections with other topics, such as Woodin’s HOD Conjecture.

  • Active Matter Seminar
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 10.20.22

    Active Matter Seminar
    Speaker: Sharad Ramanathan, Harvard
    Title: Attempts at understanding human axial elongation and patterning
    Abstract: Some of the most dramatic events during human development is the axial elongation of the embryo with concomitant changes in the geometry and composition of the underlying tissues. The posterior part of the embryo gives rise to the spinal cord, vertebral column, ribcage, back muscles, and dermis.  In this talk, I will present our attempts at coaxing human embryonic stem cells to form these structures of the early human embryo that closely recapitulate the geometry, relative arrangements, composition, and dynamics of development of the early spinal cord flanked progenitors of the musculoskeletal system. Our goal was to do so, such that we could build hundreds of these organoids at a time. I will also present preliminary results for the use of this system to understand key events during early human development through imaging and genetic perturbations.
  • Colloquium
    12:00 pm-1:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    colloquium

    Colloquium

    Speaker: Yannai Gonczarowski (Harvard)

    Title: Strategyproof-Exposing Mechanisms Descriptions

    Abstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.

    By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.

    Joint work with Ori Heffetz and Clayton Thomas.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-22-2017 Random Matrix & Probability Theory Seminar

    12:01 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:03 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Cosmic Road to New Physics
    12:04 pm
    12/01/2024
    The colourful star cluster NGC 3532

    The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

    The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

    The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

    Organizers:

    Scientific Advisory:

    Speakers: 

    CosmicRoad_Poster

  • Colloquium
    12:05 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:06 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:08 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:09 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar
    12:10 pm-1:10 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

     

    Speaker: Man-Wai Cheung

    Title: Compactification for cluster varieties without frozen variables of finite type

    Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

  • CMSA EVENT: 2019 Ding Shum Lecture
    12:11 pm
    12/01/2024
    DingShum-2019

    DSC_0468-e1568985499370

    On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

    Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

    Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

    Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

    This event is made possible by the generous funding of Ding Lei and Harry Shum.

    DingShum-2019

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-1-2017 Random Matrix & Probability Seminar

    12:11 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
    12:11 pm
    12/01/2024-04/19/2017

    From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

  • Colloquium
    12:12 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:13 pm-12:14 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-27-2017 Mathematical Physics Seminar

    12:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-7-2017 Social Science Applications Forum

    12:15 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:15 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/13/2019 Special Seminar

    12:15 pm-1:05 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3-8-2017 CMSA Special Lecture Series

    12:16 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
    12:19 pm
    12/01/2024-10/18/2019
    Noncommutative-Analysis-Poster-3

    On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

    This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

    The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

    Please register here

    Speakers:

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-8-2017 Random Matrix & Probability Theory Seminar

    12:21 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-6-2017 Mathematical Physics Seminar

    12:24 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    12:25 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-10-2017 Special Lecture Series

    12:27 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-21-2017 Social Science Applications Forum

    12:28 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
    12:28 pm
    12/01/2024-05/05/2019
    1 Oxford Street, Cambridge MA 02138
    Differential Geometry, Calabi-Yau theory and General Relativity

    Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

    On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

    Organizers:

    • Horng-Tzer Yau (Harvard)
    • Wilfried Schmid (Harvard)
    • Clifford Taubes (Harvard)
    • Cumrun Vafa (Harvard)

    Speakers:

    • Lydia Bieri, University of Michigan
    • Tristan Collins, MIT
    • Simon Donaldson, Imperial College
    • Fan Chung Graham, UC San Diego
    • Nigel Hitchin, Oxford University
    • Jun Li, Stanford University
    • Kefeng Liu, UCLA
    • Chiu-Chu Melissa Liu, Columbia University
    • Alina Marian, Northeastern University
    • Xenia de la Ossa, Oxford University
    • Duong H. Phong, Columbia University
    • Richard Schoen, UC Irvine
    • Andrew Strominger, Harvard University
    • Nike Sun, MIT
    • Clifford Taubes, Harvard University
    • Chuu-Lian Terng, UC Irvine
    • Valentino Tosatti, Northwestern University
    • Karen Uhlenbeck, University of Texas
    • Cumrun Vafa, Harvard University
    • Mu Tao Wang, Columbia University
    • Edward Witten, IAS
    • Stephen Yau, Tsinghua University, P.R. China
  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 03.22.2023

    Speaker: Mete Soner (Princeton University)

    Title: Synchronization in a Kuramoto Mean Field Game

    Abstract:  Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a  key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  We explore this system in the mean field formalism.  We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium.  The mean field game also exhibits a bifurcation from incoherence to self-organization.  This approach has found interesting applications including circadian rhythms and jet-lag recovery.  This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Tim Adamo, University of Edinburgh

    Title: An invitation to strong-field scattering

    Abstract: Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to all-multiplicity twistor and string methods.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Xi Yin (Harvard Physics) and Peter Kronheimer (Harvard Math)
    Topics:
    Xi Yin: What is string field theory?
    Peter Kronheimer: What is Seiberg-Witten theory?
  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Four-dimensional topology

    12:30 pm-1:30 pm
    12/01/2024
    Lecture_Manolescu-pdf

    Ciprian Manolescu (Stanford)

    Title: Four-dimensional topology

    Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to four-manifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience.

    Video

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 05.03.2023

    Speaker: Xin Guo, UC Berkeley

    Title: Generative Adversarial Networks (GANs): An Analytical Perspective

    Abstract: Generative models have attracted intense interests recently. In this talk, I will discuss one class of generative models, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis.

     

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)
    Topics:
    Dan Freed: What is framing anomaly? How is it different from other anomalies?
    Dan Berwick-Evans: What is Atiyah-Singer index theorem?
  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    Speakers: Dan Freed (Harvard Math and CMSA), Denis Auroux (Harvard Math)

  • Math Science Literature Lecture Series
    12:30 pm-2:00 pm
    12/01/2024
    Lecture_Freedman-1-pdf

    Michael Freedman (Microsoft – Station Q)

    Title: A personal story of the 4D Poincare conjecture

    Abstract:  The proof of PC4 involved the convergence of several historical streams.  To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.

    Talk Chair: Peter Kronheimer

    Video

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 03.08.2023

    Speaker: Ning Su, University of Pisa

    Title: Conformal symmetry, Optimization algorithms and the Critical Phenomena

    Abstract: In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid phase transition and Heisenberg magnet to very high precision.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 03.29.2023

    Speaker: Ruth Britto (Trinity College Dublin)

    Title: Scattering amplitudes in quantum field theory

    Abstract: Particle collider experiments require a detailed description of scattering events, traditionally computed through sums of Feynman diagrams. However, it is not practical to evaluate Feynman diagrams directly for all significant scattering processes. Moreover, adding all diagrams reveals many cancellations: scattering amplitudes in theories such as QCD take remarkably simple forms. This simplicity is a clue that the perturbative theory is perhaps best understood without reference to Feynman diagrams. In fact, it has recently become possible to explain some of this simplicity. I will show how to derive many amplitudes efficiently and elegantly, and propose taming the remaining complexity with ideas drawn from combinatorics and geometry.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 04.26.2023.rev2

    Speaker: Max Metlitski (MIT)

    Title: Boundary behavior at classical and quantum phase transitions

    Abstract: There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter, where exotic protected boundary states are ubiquitous. In this talk, I’ll ask: what happens at a boundary of a system, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field, as well as some extensions to quantum phase transitions.

     

  • Colloquium
    12:30 pm
    12/01/2024

    No additional detail for this event.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University)

    Topics:

    Michael Douglas: “What is non-commutative field theory?”
    Mayuko Yamashita: “What is differential cohomology?”
  • Topological Quantum Matter Seminar
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Hart Goldman, University of Chicago

    Title: Composite fermions and the fractional quantum anomalous Hall effect

    Abstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk, I will argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new zero-field context. In particular, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end, I will present exact diagonalization evidence for such composite Fermi liquid states at zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs), I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 04.12.2023

    Speaker: James Halverson (Northeastern University)
     
    Title: Unexpected Uses of Neural Networks: Field Theory and Metric Flows

    Abstract:  We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics, sometimes leading to rigorous results. In this talk, however, I will argue that breakthroughs in deep learning theory are also useful for making progress, focusing on applications to field theory and metric flows. Specifically, I will introduce a neural network approach to field theory with a different statistical origin, that exhibits generalized free field behavior at infinite width and interactions at finite width, and that allows for the study of symmetries via the study of correlation functions in a different duality frame. Then, I will review recent progress in approximating Calabi-Yau metrics as neural networks and cast that story into the language of neural tangent kernel theory, yielding a theoretical understanding of neural network metric flows induced by gradient descent and recovering famous metric flows, such as Perelman’s formulation of Ricci flow, in particular limits.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 11.16.22 - 2

    Colloquium

    Speaker: Hidenori Tanaka (NTT Research at Harvard)

    Title: Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks

    Abstract: In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle, but the role of symmetry breaking is not well understood. Here, we develop a Lagrangian formulation to study the geometry of learning dynamics in neural networks and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. Then, we generalize Noether’s theorem known in physics to describe a unique symmetry breaking mechanism in learning and derive the resulting motion of the Noether charge: Noether’s Learning Dynamics (NLD). Finally, we apply NLD to neural networks with normalization layers and discuss practical insights. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    A tale of two balloons

    12:30 pm-1:30 pm
    12/01/2024
    CMSA-Combinatorics-Physics-and-Probability-Seminar-11.16.21

    Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
    Joint work with Omer Angel and Gourab Ray.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-20-2017 Mathematical Physics Seminar

    12:30 pm
    12/01/2024

    No additional detail for this event.

  • Math Science Literature Lecture Series
    12:30 pm-1:30 pm
    12/01/2024
    Lecture_Lian-pdf

    Bong Lian (Brandeis)

    Title: From string theory and Moonshine to vertex algebras

    Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed at a general audience.

    Slides | Video

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium

    Colloquium
    Speaker: Melody Chan
    Title: Moduli spaces of graphs
    Abstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.
  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.13.2023

    Title: Complete Calabi-Yau metrics: Recent progress and open problems

    Abstract: Complete Calabi-Yau metrics are fundamental objects in Kahler geometry arising as singularity models or “bubbles” in degenerations of compact Calabi-Yau manifolds.  The existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to Yau and Tian-Yau. I will describe some recent progress towards the question of existence, and explain some future directions, highlighting connections with notions of algebro-geometric stability.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Mike Douglas (Harvard CMSA) and Anurag Anshu (Harvard Computer Science)

    Topics:

    Mike Douglas: What are scaling laws in deep learning?

    Anurag Anshu: What’s the difference between classical information theory and quantum information theory (or classical computation vs quantum computation)?

     

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.02.2023

    Speaker: Max Reppen (Boston University)

    Title: Neural Optimal Stopping Boundary

    Abstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.12.22 (1)

    Colloquium

    Title: Complete disorder is impossible: Some topics in Ramsey theory

    Speaker: James Cummings, Carnegie Mellon University

    Abstract: The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory, which touches on many areas of mathematics including graph theory, set theory and dynamics. I will give an overview of Ramsey theory, emphasizing the diverse ideas which are at play in this area.

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA)

    Topics:

    Dan Freed: What is Dijkgraaf-Witten theory?

    Sunghyuk Park: What happened at the Clay Math Institute Workshop?

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.19.22

    Colloquium

    Speaker: Patrick Lopatto (Brown)

    Title: The Mobility Edge of Lévy Matrices

    Abstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness, these models have been broadly applied in physics, finance, and statistics. When the entries have infinite mean, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.

  • Strongly Correlated Quantum Materials and High-Temperature Superconductors

    Strongly Correlated Quantum Materials and High-Temperature Superconductors
    11/6/2020 Strongly Correlated Quantum Materials Lecture

    12:30 pm-3:00 pm
    12/01/2024
  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.08.2023

    Speaker: David Gamarnik (MIT)

    Title: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property

    Abstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph, the problem of finding a near ground state in a spin glass model, the problem of finding a satisfying assignment in a random constraint satisfaction problem, and many many more. Unfortunately, at the same time no formal computational hardness results exist which  explains this persistent algorithmic gap.

    In the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms which exhibit a form of stability/noise insensitivity.

    We will specifically show how to use this property to obtain stronger (stretched exponential) than the state of the art (quasi-polynomial) lower bounds on the size of constant depth Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph, and the problem of finding a near ground state of a p-spin model.

    Joint work with Aukosh Jagannath and Alex Wein

  • CMSA Q&A Seminar
    12:30 pm-1:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    CMSA Q and A Seminar

    Speakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math)

    Topics:

    Mike Hopkins: What are topological modular forms?

    Mihnea Popa: What is the abundance conjecture and why should it to be true?

     

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 09.28.22

    Colloquium

    Speaker: Dima Sinapova (Rutgers University)

    Title: The Tree Property and uncountable cardinals

    Abstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes.

    We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.

     

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.26.22

    Speaker: Virginia Vassilevska Williams (MIT)

    Title: Clique listing algorithms

    Abstract: A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history.

    A fundamental question, with many applications, is “How fast can one list all k-cliques in a given graph?”.

    Even just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant, such as 3 or 4 (independent of n), even the brute-force algorithm runs in polynomial time, O(n^k), and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k), the brute-force algorithm is in some sense optimal, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques, with running times depending on the number of vertices n, the number of edges m, the number of k-cliques T and more. We will focus on the case when k=3, but we will note some extensions.

    (Based on joint work with Andreas Bjorklund, Rasmus Pagh, Uri Zwick, Mina Dalirrooyfard, Surya Mathialagan and Yinzhan Xu)

  • Colloquium
    12:30 pm-1:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 02.22.2023

    Speaker: Netta Engelhardt (MIT)

    Title: The Black Hole Information Paradox: A Resolution on the Horizon?

    Abstract: The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary, and in particular its application to entanglement and complexity, however, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-5-2017 Random Matrix & Probability Theory Seminar

    12:31 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:32 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
    12:33 pm
    12/01/2024-05/01/2019

    From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Videos

    Speakers: 

     

    Monday, April 29

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

    Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

    10:00 – 10:30amBreak
    10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

    Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

    11:30 – 1:30pmLunch
    1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

    Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

    2:30 – 3:00pmBreak
    3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

    Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

    4:00 – 4:30pmBreak
    4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

    Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

     

    Tuesday, April 30

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

    Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

    10:00 – 10:30amBreak
    10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

    Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

    11:30 – 1:00pmLunch
    1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

    Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

    2:00 – 2:15pmBreak
    2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

    Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

    Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

    We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

    This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

    3:15 – 3:30pmBreak
    3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

    Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

    4:30 – 4:45pmBreak
    4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

    Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

     

    Wednesday, May 1

    TimeSpeakerTitle/Abstract
    8:30 – 9:00amBreakfast
    9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

    Abstract: PDF

    This is joint work with Eric Rains and Douglas Stryker.

    10:00 – 10:30amBreak
    10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

    Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
    and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
    to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

    11:30 – 11:45amBreak
    11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

    Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

    In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

    This is a joint work with Felix Janda and Yongbin Ruan.

    12:45 – 2:30pmLunch
    2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

    Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

    3:30 – 4:00pmBreak
    4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

    Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-29-2017 Random Matrix & Probability Theory Seminar

    12:35 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3-24-2017 Random Matrix & Probability Theory Seminar

    12:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3-30-2017 CMSA Special Seminar

    12:38 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-27-2017 Mathematical Physics Seminar

    12:40 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:41 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-5-2017 Special Lecture Series

    12:42 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-7-2017 Special Lecture Series

    12:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Special Lecture Series

    12:44 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:45 pm-1:45 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 11.02.22

    Speaker: Liang Fu (MIT)

    Title: Doping and inverting Mott insulators on semiconductor moire superlattices

    Abstract: Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First, in an intermediate range of magnetic fields, doping this Mott insulator gives rise to a dilute gas of spin polarons, which form a pseudogap metal. Second, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.

  • Colloquium
    12:45 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-14-2017 Special Lecture Series

    12:46 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-3-2017 Mathematical Physics Seminar

    12:50 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    12:51 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    4-12-2017 Social Science Applications Forum

    12:53 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Mirror Symmetry and Stability
    12:55 pm
    12/01/2024-03/20/2019
    HMS-2019-1

    This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

    Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

    Speakers:

    Dylan Allegretti (Sheffield)
    Tristan Collins (MIT)
    Naoki Koseki (Tokyo)
    Chunyi Li (Warwick)
    Jason Lo (CSU Northridge)
    Emanuele Macrì (NEU & IHES)
    Genki Ouchi (Riken iTHEMS)
    Pranav Pandit (ICTS)
    Laura Pertusi (Edinburgh)
    Jacopo Stoppa (SISSA)
    Alex Takeda (UC Berkeley)
    Xiaolei Zhao (UC Santa Barbara)

    More details will be added later.

    Visit the event page for more information. 

     

    HMS-2019-1

  • Colloquium
    12:55 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    12:57 pm
    12/01/2024

    No additional detail for this event.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Active crystals are highly ordered structures that emerge from the nonequilibrium self-organization of motile objects, and have been widely studied in synthetic and bacterial active matter. In this talk, I will describe how swimming sea star embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiment, hydrodynamic theory, and simulations, we demonstrate that the formation, dynamics, and dissolution of these living crystals are controlled by the natural development of the embryos. Remarkably, due to nonreciprocal force and torque exchange between the embryos, the living chiral crystals exhibit self-sustained oscillations with dynamic signatures recently predicted to emerge in materials with odd elasticity.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character \theta of G, and a G-invariant function w on V.  This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient.  GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM, very few computations of these invariants have been carried out.  In this talk I will describe a new method for computing generating functions of GLSM invariants.  I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.

  • Math Science Literature Lecture Series
    1:00 pm-2:00 pm
    12/01/2024
    Lecture_Harris_updated-pdf

    Joe Harris (Harvard)

    Title: Rationality questions in algebraic geometry

    Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension two) and Hodge theory (dimension 3). But there remained much we didn’t understand about the condition of rationality, such as how it behaves in families. However, there has been recent progress: work of Hassett, Tschinkel, Pirutka and others, working with examples in dimension 4, showed that it is in general neither an open condition nor a closed one, but does behave well with respect to specialization. In this talk I’ll try to give an overview of the history of rationality and the current state of our knowledge.

    Video

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack), there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk, we first show that these three definitions are equivalent. Second, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third, we apply these results to various moduli situations, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    No additional detail for this event.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-01.27.2022

    Abstract: Fluids pervade complex systems, ranging from fish schools, to bacterial colonies and nanoparticles in drug delivery. Despite its importance, little is known about the role of fluid mechanics in such applications. Is schooling the result of vortex dynamics synthesized by individual fish wakes or the result of behavioral traits? Is fish schooling energetically favorable?  I will present multifidelity computational studies of collective swimming in 2D and 3D flows. Our studies demonstrate that classical models of collective swimming (like the Reynolds model) fail to maintain coherence in the presence of long-range hydrodynamic interactions. We demonstrate in turn that collective swimming can be achieved through reinforcement learning. We extend these studies to 2D and 3D viscous flows governed by the Navier Stokes equations. We examine various hydrodynamic benefits with a progressive increase of the school size and demonstrate the importance of controlling the vorticity field generated by up to 300 synchronized swimmers.

  • Seminars

    Seminars Colloquia & Seminar
    11/13/2019 General Relativity Seminar

    1:00 pm-2:00 pm
    12/01/2024
  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar
    Speaker: Herbert Levine (Northeastern)
    Title: Frustration-free states of cell fate networks: the case of the epithelial-mesenchymal transition

    Abstract: Cell fate decisions are made by allowing external signals to govern the steady-state pattern adopted by networks of interacting regulatory factors governing transcription and translation. One of these decisions, of importance for both developmental processes and for cancer metastasis, is the epithelial-mesenchymal transition (EMT). In this talk, we will argue that these biological networks have highly non-generic interaction structures such that they allow for phenotypic states with very low frustration, i.e. where most interactions are satisfied. This property has important consequences for the allowed dynamics of these systems.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA-GR-Seminar-03.10.22

    Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Gromov-Witten invariants count pseudo-holomorphic curves on a symplectic manifold passing through some fixed points and submanifolds. Similarly, open Gromov-Witten invariants are supposed to count disks with boundary on a Lagrangian, but in most cases such counts are not independent of some choices as we would wish. Motivated by Fukaya’11, J. Solomon and S. Tukachinsky constructed open Gromov-Witten invariants in their 2016 papers from an algebraic perspective of $A_{\infty}$-algebras of differential forms, utilizing the idea of bounding chains in Fukaya-Oh-Ohta-Ono’06. On the other hand, Welschinger defined open invariants on sixfolds in 2012 that count multi-disks weighted by the linking numbers between their boundaries. We present a geometric translation of Solomon-Tukachinsky’s construction. From this geometric perspective, their invariants readily reduce to Welschinger’s.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Max Lavrentovich, Worcester State University

    Title: Strongly driven mixtures and membranes: Out of equilibrium surprises

    Abstract: The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phase-separating colloidal mixture and a lipid membrane, which demonstrate counterintuitive properties when driven out of equilibrium. We will see that the phase separating mixture, when driven by a uniform force, develops (in simulations) an intriguing pattern with a characteristic length scale set by the magnitude of the drive. We will look at some theoretical approaches to understanding the pattern formation and possible experimental realizations. The membrane, when driven by an oscillatory electric field, develops (in experiments) a long-lived metastable state with a decreased capacitance and increased dissipation. This state may have implications for neuronal processing and memory formation.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.

    1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.

    2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-02.24.22

    Abstract: The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological
    disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes: (i) to explain the tortoise & hare story in bacterial competition: how motility of Pseudomonas aeruginosa bacteria leads to a slower invasion of bacteria colonies, which are individually faster, and
    (ii) how self-propelled defects lead to finding an unanticipated mechanism for cell death.

    I will then discuss various strategies to tame, otherwise chaotic, active flows, showing how hydrodynamic screening of active flows can act as a robust way of controlling and guiding active particles into dynamically ordered coherent structures. I will also explain how combining hydrodynamics with topological constraints can lead to further control of exotic morphologies of active shells.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    No additional detail for this event.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

  • Seminars

    Seminars Colloquia & Seminar
    12/6/2019 Special Seminar

    1:00 pm-2:00 pm
    12/01/2024
  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I will present a four-term exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations, the Hodge, weight, and perverse Leray filtrations, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the Clemens-Schmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran.

  • Combinatorics Physics and Probability

    Combinatorics Physics and Probability
    9/28/2021 Combinatorics, Physics and Probability Seminar

    1:00 pm
    12/01/2024

    Title: The hypersimplex and the m=2 amplituhedron

    Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.

  • Math Science Literature Lecture Series
    1:00 pm-2:00 pm
    12/01/2024

    Robert Griess (University of Michigan)

    Title: My life and times with the sporadic simple groups

    Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad school at University of Chicago,  I became fascinated with the unfolding story of sporadic simple groups. It involved theory, detective work and experiments. During this lecture, I will describe some of the people, important ideas and evolution of thinking about sporadic simple groups. Most should be accessible to a general mathematical audience.

    Video | Slides

  • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
    1:00 pm-6:00 pm
    12/01/2024-04/07/2018
    banner-image-1

    The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

    We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

    Confirmed Speakers:

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 11.17.22

    Active Matter Seminar

    Speaker: Max Prigozhin (Harvard)

    Title: Dynamic and multicolor electron microscopy

    Abstract: My lab is developing biophysical methods to achieve multicolor and dynamic biological imaging at the molecular scale. Our approach to capturing the dynamics of cellular processes involves cryo-vitrifying samples after known time delays following stimulation using custom cryo- plunging and high-pressure freezing instruments. To achieve multicolor electron imaging, we are exploring the property of cathodoluminescence—optical emission induced by the electron beam. We are developing nanoprobes (“cathodophores”) that will be used as luminescent protein tags in electron microscopy. We are applying these new methods to study G-protein- coupled receptor signaling and to visualize the formation of biomolecular condensates.

  • Algebraic Geometry in String Theory Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem, and new results in this direction, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-02.10.22

    Abstract: My lab is interested in the active and adaptive materials that underlie control of cell shape.  This has centered around understanding force transmission and sensing within the actin cytoskeleton.  I will first review our current understanding of the types of active matter that can be constructed by actin polymers.  I will then turn to our recent experiments to understand how Cell shape changes in epithelial tissue.  I will describe the two sources of active stresses within these tissues, one driven by the cell cycle and controlling cell-cell stresses and the other controlled by cell-matrix signaling controlling motility.  I will then briefly describe how we are using optogenetics to locally control active stresses to reveal adaptive and force-sensitive mechanics of the cytoskeletal machinery. Hopefully, I will convince you that recent experimental and theoretical advances make this a very promising time to study this quite complicated form of active matter.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: During development, organisms interact with their natural habitats while undergoing morphological changes, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria, a basal animal lineage that includes sea anemones, corals, hydras, and jellyfish, offers unique insight into the development and evolution of morphological complexity.  In my talk, I will introduce our research on “ethology of morphogenesis,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels, opening new perspectives about the design principle of soft-bodied animals. In addition, I will discuss a fascinating feature of cnidarian biology. For humans, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule.

    References
    Anniek Stokkermans, Aditi Chakrabarti, Ling Wang, Prachiti Moghe, Kaushikaram Subramanian, Petrus Steenbergen, Gregor Mönke, Takashi Hiiragi, Robert Prevedel, L. Mahadevan, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976

    Ikmi A, Steenbergen P, Anzo M, McMullen M, Stokkermans M, Ellington L, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensisNature communications, Sept 02; 11:4399

    He S, Del Viso F, Chen C, Ikmi A, Kroesen A, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensisScience, Vol. 361, Issue 6409, pp. 1377-1380.
    Ikmi A, McKinney SA, Delventhal KM, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensisNature communications. Nov 24; 5:5486.

  • Seminars

    Seminars Colloquia & Seminar
    Combinatorics & Complexity Seminar, Fridays

    1:00 pm-4:00 pm
    12/01/2024

    The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

    Additional information on CMSA’s Combinatorics and Complexity program can be found here.

     

    DateNameTitle/Abstract
    09-08-17TBA
    09-15-2017TBA
    09-22-17TBA
    09-29-17TBA
    10-06-17 TBA
    10-13-2017TBA
    10-20-2017TBA
    10-27-2017TBA
    11-03-2017TBA
    11-10-2017TBA
    11-17-2017TBA
    11-24-2017TBA
    12-01-2017TBA
    12-08-2017 TBA
  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 11.03.22

    Active Matter Seminar

    Speaker: Siavash Monfared, Niels Bohr Institute, Copenhagen

    Title: Force transmission informs the collective behavior of active cell layers

    Abstract: Collective cell migration drives numerous physiological processes such as tissue morphogenesis, wound healing, tumor progression and cancer invasion. However, how the interplay of mechanical interactions and the modes of collective self-organization among cells informs such processes is yet to be established. In this talk, I will focus on the role of three-dimensional force transmission, from a theoretical and computational perspective, on two phenomena: (1) cell extrusion from a cellular monolayer and (2) density-independent solid-like to fluid-like transition of active cell layers. For the first topic, I will focus on how increasing cell-cell adhesion relative to cell-substrate adhesion enables cells to collectively exploit distinct mechanical pathways – leveraging defects in nematic and hexatic phases associated with cellular arrangement – to eliminate an unwanted cell. For the second topic, I will show how solid-like to fluid-like transition in active cell layers is linked to the percolation of isotropic stresses. This is achieved via two distinct and independent paths to model this transition by increasing (a) cell-cell adhesion and (b) active traction forces. Additionally, using finite-size scaling analyses, the phase transition associated with each path is mapped onto the 2D site percolation universality class. Our results highlight the importance of force transmission in informing the collective behavior of living cells and opens the door to new sets of questions for those interested in connecting the physics of cellular self-organization to the dynamics of biological systems.

     

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will illustrate how this challenge can be overcome by elucidating the probabilistic connections between models of different levels of detail. These connections explain how stochastic partial differential equations (SPDE) arise naturally from particle models.

    I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.

  • Colloquium
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane. The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

     

     

    Speaker: Achilleas Porfyriadis, Harvard Black Hole Initiative

    Title: Extreme Black Holes: Anabasis and Accidental Symmetry

    Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of  AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Fred MacKintosh (Rice University)

    Title: Contractility, structure formation and fluctuations in active gels, with and without molecular motors

    Abstract: Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence, however, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified, reconstituted systems also point to contractility and structure formation in disordered, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this, as well as possible evidence for non-motor force generation.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Michael Shelley (Flatiron)

    Title: Active structures and flows in living cells

    Abstract: Flows in the fluidic interior of living cells can serve biological function or act as signatures of how intracellular forces are exerted. I’ll discuss examples of each. One is understanding the emergence of cell-spanning vortical flows in large developing egg cells, while the other arises in studying the nature of force transduction in single cell embryos moving towards their first cell division. Both involve the cytoskeleton, that set of polymers, cross-linkers, and molecular motors that underlie much of the active mechanics within cells, and has led to the development of new coarse-grained active matter models and novel instabilities.

  • Seminars

    Seminars Colloquia & Seminar
    4-11-2017 Social Science Applications Forum

    1:00 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

    In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

    This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

  • Active Matter Seminar
    1:00 pm-2:26 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-04.07.22

    Abstract: The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.

  • Math Science Literature Lecture Series
    1:00 pm-2:30 pm
    12/01/2024
    Lecture_Ma-1-pdf
    Yi Ma
    Photo Copyright Noah Berger / 2019

     

    Yi Ma (University of California, Berkeley)

    Title: Deep Networks from First Principles

    Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation, both for optimizing the same objective. This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.

    Talk chair: Harry Shum

    Slides | Video

  • Quantum Matter
    1:00 pm-2:30 pm
    12/01/2024
  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review  another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024

    Abstract: Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a self-organizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

  • Active Matter Seminar
    1:00 pm-2:20 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-03.24.22

    Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes and second layers within a base monolayer of M xanthus cells. We find that cells align with each other over the majority of the monolayer forming an active nematic liquid crystal with defect point where cell alignment is undefined. We find that new layers and holes form at positive and negative topological defects respectively. We model the cell layer using hydrodynamic modeling and find that this layer and hole formation process is driven by active nematic forces through cell motility and anisotropic substrate friction.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar
    Speaker: Alexander Grosberg (NYU)

    Title: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell

    Abstract: Nucleus of a living cell houses a cell genome – a polymer called chromatin, which is a functional form of DNA.  It is very long, e.g., 2 meters long for every human cell.  Nucleus is also an arena of incessant energy-driven activity.  Experiments show that chromatin undergoes large scale motions sustained over long times of order seconds.  In the talk, after reviewing the phenomenology, I will show how these flows may arise due to a phase transition in which chromatin-driving motors, such as RNA polymerase, form a polar (“ferromagnetic”) order controlled by hydrodynamic interactions.  The talk is based on the joint work with I.Eshghi and A.Zidovska.

  • Active Matter Seminar
    1:00 pm-2:30 pm
    12/01/2024
    CMSA-Active-Matter-Seminar-04.28.22

    Speaker: Guillaume Duclos (Brandeis)
    Title: Building active nematic and active polar liquids out of biological machines

    Abstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium, leading to emergent collective behaviors not found in passive materials. In this talk, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics, as well as shine light on the physical mechanisms that regulate self-organization in living matter.

     

    Video (Youtube)

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Active Matter Seminar

     

    Speaker:  Jonathan Bauermann, Max Planck Institute for the Physics of Complex Systems

    Title: Active chemical reactions in phase-separating systems

    Abstract: Motivated by the existence of membrane-less compartments in the chemically active environment of living cells, I will discuss the dynamics of droplets in the presence of active chemical reactions. Therefore, I will first introduce the underlying interplay between phase separation and active reactions, which can alter the droplet dynamics compared to equilibrium systems. A key feature of such systems is the emergence of concentration gradients even at steady states. In the second part of this talk, I will discuss how these gradients can trigger instabilities in the core of chemically active droplets, giving rise to a new non-equilibrium steady state of liquid spherical shells. Finally, I will present experimental and theoretical results discussing the existence and energetic cost of this non-equilibrium steady state in a coacervate system.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Shane McInally, Brandeis

    Title: Control of actin cable length by decelerated growth and network geometry

    Abstract: The sizes of many subcellular structures are coordinated with cell size to ensure that these structures meet the functional demands of the cell. In eukaryotic cells, these subcellular structures are often membrane-bound organelles, whose volume is the physiologically important aspect of their size. Scaling organelle volume with cell volume can be explained by limiting pool mechanisms, wherein a constant concentration of molecular building blocks enables subcellular structures to increase in size proportionally with cell volume. However, limiting pool mechanisms cannot explain how the size of linear subcellular structures, such as cytoskeletal filaments, scale with the linear dimensions of the cell. Recently, we discovered that the length of actin cables in budding yeast (used for intracellular transport) precisely matches the length of the cell in which they are assembled. Using mathematical modeling and quantitative imaging of actin cable growth dynamics, we found that as the actin cables grow longer, their extension rates slow (or decelerate), enabling cable length to match cell length. Importantly, this deceleration behavior is cell-length dependent, allowing cables in longer cells to grow faster, and therefore reach a longer length before growth stops at the back of the cell. In addition, we have unexpectedly found that cable length is specified by cable shape. Our imaging analysis reveals that cables progressively taper as they extend from the bud neck into the mother cell, and further, this tapering scales with cell length. Integrating observations made for tapering actin networks in other systems, we have developed a novel mathematical model for cable length control that recapitulates our quantitative experimental observations. Unlike other models of size control, this model does not require length-dependent rates of assembly or disassembly. Instead, feedback control over the length of the cable is an emergent property due to the cross-linked and bundled architecture of the actin filaments within the cable. This work reveals a new strategy that cells use to coordinate the size of their internal parts with their linear dimensions. Similar design principles may control the size and scaling of other subcellular structures whose physiologically important dimension is their length.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Open mic Swampland Discussion

    Topic: Cobordism

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Nicolas Romeo (UChicago)

    Title: Scaling behavior and control of nuclear wrinkling

    Abstract: The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. We characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behaviour. A spectral analysis of three-dimensional high-resolution live-imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing the mechanical properties of the nuclear envelope, highlighting in passing the importance of nonlinear response to biological robustness.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Mehran Kardar, MIT

    Title: Competition at the front of expanding populations

    Abstract: When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that  integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar

    Speaker: Josef Käs, Leipzig University

    Title: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

    Abstract: Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.

    Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.

    We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.

    Video (Youtube)

  • Quantum Matter
    1:00 pm-2:30 pm
    12/01/2024
  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Open Mic Discussion
    Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 02.02.23

    Active Matter Seminar

    Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen

    Title: Interacting Active Matter

    Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    Jefferson Hal Room 256, 17 Oxford Street, Cambridge MA 02138

    Active Matter Seminar
    Speaker: Sahand Hormoz, Harvard Medical School, Dana-Farber Cancer Institute
    Title: Insights from single cell lineage trees
    Abstract: In this talk, I will discuss two recent projects from my lab that involve lineage trees of cells (the branching diagram that represents the ancestry and division history of individual cells). In the first project, we reconstructed the lineage trees of individual cancer cells from the patterns of randomly occurring mutations in these cells. We then inferred the age at which the cancer mutation first occurred and the rate of expansion of the population of cancer cells within each patient. To our surprise, we discovered that the cancer mutation occurs decades before diagnosis. For the second project, we developed microfluidic ‘mother machines’ that allow us to observe mammalian cells dividing across tens of generations. Using our observations, we calculated the correlation between the duration of cell cycle phases in pairs of cells, as a function of their lineage distance. These correlations revealed many surprises that we are trying to understand using hidden Markov models on trees. For both projects, I will discuss the mathematical challenges that we have faced and open problems related to inference from lineage trees.
  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

  • Seminars

    Seminars Colloquia & Seminar
    5/15/2020 Math Physics Seminar

    1:00 pm-2:00 pm
    12/01/2024
  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Active Matter Seminar

    Speaker: Mark Bowick, Kavli Institute for Theoretical Physics, UCSB

    Title: The Role of Orientational Order in Development

    Abstract: Morphogenesis, the process through which genes generate form, establishes tissue scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fueled by cell proliferation, which, naively, should disrupt order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order remains an outstanding question in animal development. I will review the statistical mechanics of orientational order and discuss the observation of a fourfold orientationally ordered phase (tetratic) in the model organism Parhyale hawaiensis. I will also discuss theoretical mechanisms for the formation of orientational order that require both motility and cell division, with support from self-propelled vertex models of tissue. The aim is to uncover a robust, active mechanism for generating global orientational order in a non-equilibrium system that then sets the stage for the development of shape and form.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be “Swampland constraints, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.

  • Swampland Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

  • General Relativity Seminar
    1:00 pm-2:00 pm
    12/01/2024

    Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    Lyman Lab, 17 Oxford Street, Cambridge MA 02138
    CMSA Active Matter Seminar 12.08.22

    Active Matter Seminar

    Speaker: Julien Tailleur (MIT)

    Title: Self-organization of motile cells by quorum-sensing or chemotactic interactions

    Abstract: Equilibrium statistical mechanics tells us how to control the self-assembly of passive materials by tuning the competition between energy and entropy to achieve desired states of organization. Out of equilibrium, no such principles apply and self-organization principles are scarce. Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Dissipation and injection of energy are then disconnected at the microscopic scale, hence driving the system strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases in the absence of cohesive attractive forces, but it also leaves us without guiding principles to understand the self-organization of active matter. In this talk, I will review the progress which has been made over the past ten years to control the organization of self-propelled agents using motility control, either externally or through interactions. I will show that generic principles apply and illustrate the theoretical developments presented in the talk using recent experiments on the motility-induced self-organization of bacterial mixtures.

  • Active Matter Seminar
    1:00 pm-2:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Active Matter Seminar 02.16.23

    Active Matter Seminar

    Speaker: Jörn Dunkel, MIT

    Title: Towards programmable living materials and quantitative models of active matter

    Abstract: Over the last two decades, major progress has been made in understanding the self-organization principles of active matter.  A wide variety of experimental model systems, from self-driven colloids to active elastic materials, has been established, and an extensive theoretical framework has been developed to explain many of the experimentally observed non-equilibrium pattern formation phenomena. Two key challenges for the coming years will be to translate this foundational knowledge into functional active materials, and to identify quantitative mathematical models that can inform and guide the design and production of such materials. Here, I will describe joint efforts with our experimental collaborators to realize self-growing bacterial materials [1], and to implement computational model inference schemes for active and living systems dynamics [2,3].

    [1] Nature 608: 324, 2022
    [2] PNAS 120: e2206994120, 2023
    [3] eLife 10: e68679, 2021

  • CMSA EVENT: Second Annual STAR Lab Conference
    1:01 pm-1:02 pm
    12/01/2024

    The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

    For more information, please consult the event’s website.

  • Colloquium
    1:02 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-10-2017 Mathematical Physics Seminar

    1:07 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:07 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:09 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    1:10 pm-3:00 pm
    12/01/2024
  • Colloquium
    1:10 pm-3:10 pm
    12/01/2024

    Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

  • Colloquium
    1:10 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-31-2015 Mathematical Physics Seminar

    1:10 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:11 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Differential Geometry Seminar

    1:12 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-12-2017 Random Matrix & Probability Theory Seminar

    1:12 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-01-2015 Evolution Equation Seminar

    1:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-14-2015 Mathematical Physics Seminar

    1:14 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-17-2017 Mathematical Physics Seminar

    1:14 pm
    12/01/2024

    No additional detail for this event.

  • Active Matter Seminar
    1:15 pm-2:30 pm
    12/01/2024

    Abstract: In this talk I will review our ongoing theoretical and experimental efforts toward deciphering the hydrodynamic behavior of confluent epithelia. The ability of epithelial cells to collectively flow lies at the heart of a myriad of processes that are instrumental for life, such as embryonic morphogenesis and wound healing, but also of life-threatening conditions, such as metastatic cancer. Understanding the physical origin of these mechanisms requires going beyond the current hydrodynamic theories of complex fluids and introducing a new theoretical framework, able to account for biomechanical activity as well as for scale-dependent liquid crystalline order.

  • Quantum Matter
    1:15 pm-2:45 pm
    12/01/2024
    CMSA QMMP 1.24.23

    Quantum Matter Seminar

    Speakers: Jacob McNamara (Caltech) and Matthew Reece (Harvard)

    Title: Reflections on Parity Breaking

    Abstract: One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we will describe the formal meaning of parity as a gauge symmetry, and argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. We will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity, as well as their relationship with the Swampland Cobordism Conjecture.

     

    https://www.youtube.com/watch?v=hTeaVGRG3LA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=19

  • Seminars

    Seminars Colloquia & Seminar
    4-18-2017 Social Science Applications Forum

    1:15 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-08-2015 Geometric Analysis Seminar

    1:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-06-2015 Geometric Analysis Seminar

    1:17 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-08-2015 Evolution Equations Seminar

    1:18 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:18 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:20 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:21 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    1:21 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:22 pm-2:22 pm
    12/01/2024

    Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
    entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
    Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4-19-2017 Random Matrix & Probability Theory Seminar

    1:22 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-13-2015 Geometric Analysis Seminar

    1:22 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-10-2015 Evolution Equations Seminar

    1:23 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: 2016 Big Data Conference & Workshop
    1:24 pm
    12/01/2024-08/23/2016
    1 Oxford Street, Cambridge MA 02138

    ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

    The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

    Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

    The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

    The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

    Conference Speakers:

    1. Jörn Boehnke, Harvard CMSA
    2. Joan Bruna, UC Berkeley [Video]
    3. Tamara Broderick, MIT [Video]
    4. Justin Chen, MIT [Video]
    5. Yiling Chen, Harvard University [Video]
    6. Amir Farbin, UT Arlington [Video]
    7. Doug Finkbeiner, Harvard University [Video]
    8. Andrew Gelman, Columbia University [Video]
    9. Nina Holden, MIT [Video]
    10. Elchanan Mossel, MIT
    11. Alex Peysakhovich, Facebook
    12. Alexander Rakhlin, University of Pennsylvania [Video]
    13. Neal Wadhwa, MIT [Video]
    14. Jun Yin, University of Wisconsin
    15. Harry Zhou, Yale University [Video]

    Please click Conference Program for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Please click here for registration.

    Conference Schedule:

    August 22 – Day 1
    8:30amBreakfast
    8:55amOpening remarks
    9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
    9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
    2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
    4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
    August 23 – Day 2
    8:45amBreakfast
    9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
    9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
    10:40am – 11:10amBreak
    11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
    12:00pm – 1:30pmLunch
    1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
    2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
    3:10pm – 3:40pmBreak
    3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

    Workshop Participants:

    Richard Freeman’s Group:

    1. Sen Chai, ESSEC
    2. Brock Mendel, Harvard University
    3. Raviv Muriciano-Goroff, Stanford University
    4. Sifan Zhou, CMSA

    Scott Kominer’s Group:

    1. Bradly Stadie, UC Berkeley
    2. Neal Wadhwa, MIT [Video]
    3. Justin Chen

    Christopher Rogan’s Group:

    1. Amir Farbin, UT Arlington [Video]
    2. Paul Jackson, University of Adelaide

    For more information about the workshops, please reach out directly to the individual group leaders.

    This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

  • Seminars

    Seminars Colloquia & Seminar
    10-01-2015 Evolution Equations Seminar

    1:25 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-15-2015 Geometric Analysis Seminar

    1:26 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-16-2015 Random Matrix & Probability Theory Seminar

    1:27 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5-3-2017 Random Matrix & Probability Theory Seminar

    1:29 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-23-2015 Random Matrix & Probability Theory Seminar

    1:29 pm
    12/01/2024

    No additional detail for this event.

  • Computer Science for Mathematicians Seminar

    Computer Science for Mathematicians Seminar
    2/16/2021 Computer Science for Mathematicians

    1:30 pm-2:30 pm
    12/01/2024

    Speaker: Michael P. Kim (UC Berkeley)

    Title: Outcome Indistinguishability

    Abstract: Prediction algorithms assign numbers to individuals that are popularly understood as individual “probabilities” — e.g., what is the probability of 5-year survival after cancer diagnosis? — and which increasingly form the basis for life-altering decisions. The understanding of individual probabilities in the context of such unrepeatable events has been the focus of intense study for decades within probability theory, statistics, and philosophy. Building off of notions developed in complexity theory and cryptography, we introduce and study Outcome Indistinguishability (OI). OI predictors yield a model of probabilities that cannot be efficiently refuted on the basis of the real-life observations produced by Nature.

    We investigate a hierarchy of OI definitions, whose stringency increases with the degree to which distinguishers may access the predictor in question.  Our findings reveal that OI behaves qualitatively differently than previously studied notions of indistinguishability.  First, we provide constructions at all levels of the hierarchy.  Then, leveraging recently-developed machinery for proving average-case fine-grained hardness, we obtain lower bounds on the complexity of the more stringent forms of OI.  The hardness result provides scientific grounds for the political argument that, when inspecting algorithmic risk prediction instruments, auditors should be granted oracle access to the algorithm, not simply historical predictions.

    Joint work with Cynthia Dwork, Omer Reingold, Guy N. Rothblum, Gal Yona; to appear at STOC 2021.

  • Probability Seminar
    1:30 pm-2:30 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 05.11.23

    Probability Seminar

    Speaker: Giorgio Cipolloni (Princeton)

    Title: How do the eigenvalues of a large non-Hermitian random matrix behave?

    Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues. Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X.

    Location: Science Center Room 232

  • Seminars

    Seminars Colloquia & Seminar
    11/14/2018 Hodge Seminar

    1:30 pm
    12/01/2024
  • Probability Seminar
    1:30 pm-2:30 pm
    12/01/2024
    Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

    Probability Seminar

    Speaker: Arka Adhikari (Stanford)

    Title: Correlation decay for finite lattice gauge theories

    Abstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.

     

  • Seminars
    1:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5-2-2017 Social Sciences Application Forum

    1:30 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA GR Seminar 05.11.23

    General Relativity Seminar

    Speaker: Aghil Alaee, Clark University

    Title: Positivity of Static quasi-local Mass in general relativity

    Abstract: In this talk, we review results on the PMT of quasi-local masses and prove the positivity of static quasi-local masses with respect to the AdS and AdS Schwarzschild spacetimes.

  • Seminars
    1:30 pm-3:00 pm
    12/01/2024
  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 04.24.23 (1)

    General Relativity Seminar

    Speaker: Tin Yau Tsang, University of California Irvine

    Title: Recent advances in scalar curvature and positive mass theorems
    Abstract:  First, we have a review of classical tools for studying scalar curvature and positive mass theorem. Then we are going to discuss some advances and new perspectives on these tools which lead to a deeper understanding of geometry and initial data sets.
  • CMSA EVENT: Current Developments in Mathematics 2019
    1:30 pm-5:00 pm
    12/01/2024-11/23/2019
    CDM-POSTER-2019.email_-662x1024

     

    cdmFriday, Nov. 22, 2019 1:30 pm – 5:20 pm

    Saturday, Nov. 23, 2019  9:00 am – 5:00 pm

    Harvard University Science Center, Hall C

    Speakers:

    ·      Svetlana Jitomirskaya (UC Irvine)

    ·      Subash Khot (NYU)

    ·      Jun Li (Stanford)

    ·      André Neves (Chicago)

    ·      Geordie Williamson (U Sidney)

    Free and open to the public – registration is required.
    Please register in advance online at www.math.harvard.edu/cdm

    CDM_2019-agenda-791x1024

  • Special Seminar
    1:30 pm-2:30 pm
    12/01/2024
  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 02.09.23

    General Relativity Seminar

    Speaker: Maciej Zworski, UC Berkeley

    Title: Quasinormal modes and Ruelle resonances: mathematician’s perspective

    Abstract: Quasinormal modes of gravitational waves and Ruelle resonances in hyperbolic classical dynamics share many general properties and can be considered “scattering resonances”: they appear in expansions of correlations, as poles of Green functions and are associated to trapping of trajectories (and are both notoriously hard to observe in nature, unlike, say, quantum resonances in chemistry or scattering poles in acoustical scattering). I will present a mathematical perspective that also includes zeros of the Riemann zeta function (scattering resonances for the Hamiltonian given by the Laplacian on the modular surface) and stresses the importance of different kinds of trapping phenomena, resulting, for instance, in fractal counting laws for resonances.

  • Seminars

    Seminars Colloquia & Seminar
    11/21/2018 Hodge Seminar

    1:30 pm
    12/01/2024
  • Special Seminar
    1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/23/2019 Hodge Seminar

    1:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    12/5/2018 Hodge Seminar

    1:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/28/2018 Hodge Lecture

    1:30 pm
    12/01/2024
  • Special Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Random Matrix & Probability Theory Seminar
    Speaker: Minh-Binh TRAN (SMU & MIT)

    Location: CMSA, Room G02

    Title: On the wave turbulence theory for a stochastic KdV type equation

    Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic  Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave  kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is  $d\ge 2$, the smallness of the nonlinearity $\lambda$ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation.  Unlike the cubic nonlinear Schrodinger equation, for which such a general result is commonly expected without the noise, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen  as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.

  • Seminars

    Seminars Colloquia & Seminar
    5/27/2020 Quantum Matter Seminar

    1:30 pm-3:00 pm
    12/01/2024
  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 02.16.23

    General Relativity Seminar

    Speaker: Kwinten Fransen (UC Santa Barbara)

    Title: Quasinormal Modes from Penrose Limits

    Abstract: In this talk, I will explain how to describe quasinormal modes with large real frequencies using Penrose limits. To do so, I first recall relevant aspects of the Penrose limit, and its resulting plane wave spacetimes, as well as quasinormal modes to subsequently tie these together. Having established the main principle, I will illustrate the usefulness of this point of view with the geometric realization of the emergent symmetry algebra underlying the quasinormal modes in the large real frequency limit and present its application to the astrophysically important example of Kerr black holes. Based on arXiv:2301.06999.

  • Colloquium
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 04.20.2023

    Speaker: Julio Parra Martinez, Caltech

    Title: Black hole collider physics

    Abstract: Despite more than a century since the development of Einstein’s theory, the general relativistic two-body problem remains unsolved. A precise description of its solution is now essential, as it is necessary for understanding the strong-gravity dynamics of compact binaries observed at LIGO/VIRGO/KAGRA and in future gravitational wave observatories. In this talk, I will describe how considering the scattering of black holes and gravitons can shed new light on this problem. I will explain how using modern ideas from collider and particle physics we can calculate scattering observables in classical gravity, and extract the basic ingredients that describe the bound binary dynamics. Such calculations have produced state-of-art predictions for current and future gravitational wave observatories, which open the door for further discovery as we enter this new era of precision gravitational physics.

  • General Relativity Seminar
    1:30 pm-2:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA GR Seminar 03.23.23

    General Relativity Seminar

    Speaker: Prahar Mitra (University of Cambridge)

    Title: New Phases of N=4 SYM

    Abstract: We construct new static solutions to gauged supergravity that, via the AdS/CFT correspondence, are dual to thermal phases in N=4 SYM at finite chemical potential. These solutions dominate the micro-canonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. These are constructed in two distinct truncations of gauged supergravity and can be uplifted to solutions of type IIB supergravity. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials. We will also discuss the status of hairy supersymmetric black hole solutions in this theory.

    Based on: https://arxiv.org/pdf/2207.07134.pdf [hep-th]

  • Seminars

    Seminars Colloquia & Seminar
    09-28-2015 Mathematical Physics Seminar

    1:31 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-24-2017 Mathematical Physics Seminar

    1:31 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:31 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    1:32 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:33 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
    1:34 pm
    12/01/2024-04/10/2016

    The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

    Speakers:

    1. Lydia Bieri (University of Michigan)
    2. Luis Caffarelli (University of Texas at Austin)
    3. Mihalis Dafermos (Princeton University)
    4. Camillo De Lellis (Universität Zürich)
    5. Pengfei Guan (McGill University)
    6. Slawomir Kolodziej (Jagiellonian University)
    7. Melissa Liu (Columbia University)
    8. Duong H. Phong (Columbia University)
    9. Richard Schoen (UC Irvine)
    10. Cliff Taubes (Harvard University)
    11. Blake Temple (UC Davis)
    12. Valentino Tosatti (Northwestern University)
    13. Tai-Peng Tsai (University of British Columbia)
    14. Mu-Tao Wang (Columbia University)
    15. Xu-jia Wang (Australian National University)

    Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

    Schedule:

    April 8 – Day 1
    8:30amBreakfast
    8:45amOpening remarks
    9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
    10:00am – 10:15amBreak
    10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
    11:15am – 11:30amBreak
    11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
    April 9 – Day 2
    8:45amBreakfast
    9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
    10:00am – 10:15amBreak
    10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
    11:15am – 11:30amBreak
    11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
    12:30pm – 2:00pmLunch
    2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
    3:00pm – 3:15pmBreak
    3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
    4:15pm – 4:30pmBreak
    4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
    April 10 – Day 3
    8:45amBreakfast
    9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
    10:00am – 10:15amBreak
    10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
    11:15am – 11:30amBreak
    11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

    * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    10-22-2015 Evolution Equations Seminar

    1:37 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/11/2017 Mathematical Physics Seminar

    1:38 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-18-17 Mathematical Physics Seminar

    1:39 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-17-2015 Evolution Equations Seminar

    1:39 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    9-27-17 RM&PT Seminar

    1:41 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9-27-17 Mathematical Physics Seminar

    1:42 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-23-17 Mathematical Physics Seminar

    1:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/11/2019 Random Matrix

    1:45 pm-2:45 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-25-17 RMPT Seminars

    1:45 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:47 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-10-2017 RM & PT Seminar

    1:48 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:51 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-22-2015 Geometric Analysis Seminar

    1:52 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:52 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-30-2015 Random Matrix & Probability Theory Seminar

    1:53 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-13-2017 Mathematical Physics Seminar

    1:53 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-21-2015 Mathematical Physics Seminar

    1:54 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:54 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-15-17 RM & PT Seminar

    1:55 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    1:56 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    1:58 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    9/9/2020 RMPT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/18/2020 RMPT

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02/26/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
    2:00 pm-7:00 pm
    12/01/2024-09/17/2014

    The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    12.07.2022

    New Technologies in Mathematics Seminar

    Speaker: Cyril Zhang, Microsoft Research

    Title: How do Transformers reason? First principles via automata, semigroups, and circuits

    Abstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models, leading to dramatic advances in natural language understanding, program synthesis, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses, given that they resist interpretation? In this work, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure.

    Specifically, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory, we characterize shortcut solutions, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore, in synthetic experiments, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness, and discuss mitigations.

    Joint work with Bingbin Liu, Jordan Ash, Surbhi Goel, and Akshay Krishnamurthy.

  • Seminars
    2:00 pm-4:00 pm
    12/01/2024

    References: 

    • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
    • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
    • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
    • Nick Sheridan’s IAS and Jussieu lectures. 
    • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA NTM Seminar 10.26.2022

    New Technologies in Mathematics Seminar

    Speakers: João Araújo, Mathematics Department, Universidade Nova de Lisboa and Michael Kinyon, Department of Mathematics, University of Denver

    Title: From Engine to Auto

    Abstract: Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type, etc.
    In this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups, loops, semigroups, logic algebras, lattices and generalizations, quandles, and many more.
  • Seminars

    Seminars Colloquia & Seminar
    Homological Mirror Symmetry Seminar

    2:00 pm-4:00 pm
    12/01/2024-09/15/2017

    The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

    The list of speakers is below and will be updated as details are confirmed.

    DateNameTitle
    09-15-16
    09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

    Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

    Lecture Slides

    09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

    Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

    Lecture Slides

    10-06-16

    Hansol Hong, CMSAhong

    Title: Homological mirror symmetry for elliptic curves

    Abstract:
    We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
    which use homological algebra techniques and formal deformation theory of Lagrangians etc.

    Notes

    Notes (Baris)

    10-13-16

    Yu-Wei Fan, Harvard

    s_yuwei_fan

    Title: Semi-flat mirror symmetry and Fourier-Mukai transform

    Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

     10-20-16

    Tim Large, MIT

    Title: “Symplectic cohomology and wrapped Fukaya categories”

    Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

    Notes

     10-27-16

    Philip Engel, Columbia

    picture

    Title: Mirror symmetry in the complement of an anticanonical divisor”

    According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

    Notes

    11-03-16

    Yusuf Baris Kartal, MIT

    HMS for Del Pezzo surfaces

    I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

    11-10-16No seminar this week
     12-08-16

    Lino Amorim, Boston University

    Title: The Fukaya category of a compact toric manifold

    Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

    Video

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    12/2/2020 Random Matrix and Probability Theory

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024

    New Technologies in Mathematics Seminar

    Speaker: Timo Schick, Meta AI

    Title: Toolformer: Language Models Can Teach Themselves to Use Tools

    Abstract: Language models exhibit remarkable abilities to solve new tasks from just a few examples or textual instructions, especially at scale. They also, paradoxically, struggle with basic functionality, such as arithmetic or factual lookup, where much simpler and smaller models excel. In this talk, we show how these limitations can be overcome by letting language models teach themselves to use external tools via simple APIs. We discuss Toolformer, a model trained to independently decide which APIs to call, when to call them, what arguments to pass, and how to best incorporate the results into future token prediction. Through this, it achieves substantially improved zero-shot performance across a variety of downstream tasks without sacrificing its core language modeling abilities.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5/20/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024

    New Technologies in Mathematics Seminar

    Speaker: Dmitry Krotov, IBM Research – Cambridge

    Title: Modern Hopfield Networks for Novel Transformer Architectures

    Abstract: Modern Hopfield Networks or Dense Associative Memories are recurrent neural networks with fixed point attractor states that are described by an energy function. In contrast to conventional Hopfield Networks, which were popular in the 1980s, their modern versions have a very large memory storage capacity, which makes them appealing tools for many problems in machine learning and cognitive and neurosciences. In this talk, I will introduce an intuition and a mathematical formulation of this class of models and will give examples of problems in AI that can be tackled using these new ideas. Particularly, I will introduce an architecture called Energy Transformer, which replaces the conventional attention mechanism with a recurrent Dense Associative Memory model. I will explain the theoretical principles behind this architectural choice and show promising empirical results on challenging computer vision and graph network tasks.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speakers: Katherine Collins and Albert Jiang, Department of Computer Science and Technology, University of Cambridge

    Title: Evaluating Language Models for Mathematics through Interactions

    Abstract: There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs based on static pairs of inputs and outputs is insufficient to be able to make an informed decision about which LLMs, and under what assistive settings they can be sensibly utilised. Static assessment fails to take into account the essential interactive element in their deployment, and therefore limits how we understand language model capabilities. In this talk, we present our recent work introducing CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We discuss our study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we identify useful scenarios and existing issues of GPT-4 in mathematical reasoning through a series of case studies contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models which communicate uncertainty, respond well to user corrections, and are more interpretable and concise may constitute better assistants; interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models’ algebraic fallibility and discern where they are appropriate to use.

     

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Jimmy Ba, University of Toronto

    Title: How to steer foundation models?

    Abstract: By conditioning on natural language instructions, foundation models and large language models (LLMs) have displayed impressive capabilities as general-purpose computers. However, task performance depends significantly on the quality of the prompt used to steer the model. Due to the lack of knowledge of how foundation models work, most effective prompts have been handcrafted by humans through a demanding trial-and-error process. To reduce the human effort in this alignment process, I will discuss a few approaches to steer these powerful models to excel in various downstream language and image tasks.

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/21/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/04/2020 RMPT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/16/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/14/2020 RM&PT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/8/2019 Topology Seminar

    2:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/7/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/22/2019 Social Science Applications Forum

    2:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Johan Commelin, Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

    Title: Breaking the one-mind-barrier in mathematics using formal verification

    Abstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.

    I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.

    Video
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Random Matrix & Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024

    Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

    In the 2020-2021 AY, the Random Matrix and Probability Theory Seminar will take place on select Wednesdays from 2:00 – 3:00pm virtually. This seminar is organized by Christian Brennecke (brennecke@math.harvard.edu ).

    To learn how to attend this seminar, please fill out this form.

    The schedule below will be updated as the details are confirmed.

    Spring 2021:

    DateSpeakerTitle/Abstract
    3/31/2021Philippe Sosoe, Cornell UniversityTitle:  Fluctuation bounds for O’Connell-Yor type systems

    Abstract: The O’Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about this model thanks to remarkable algebraic structure uncovered by O’Connell, Yor and others, basic estimates for the behavior of the tails of the centered partition function for finite N that are available for zero temperature models are missing. I will present an iterative estimate to obtain strong concentration and localization bounds  for the O’Connell-Yor polymer on an almost optimal scale N^{1/3+\epsilon}.

    In the second part of the talk, I will introduce a system of interacting diffusions describing the successive increments of partition functions of different sizes. For this system, the N^{2/3} variance upper bound known for the OY polymer can be proved for a general class of interactions which are not expected to correspond to integrable models.

    Joint work with Christian Noack and Benjamin Landon.

    4/7/2021Yue M. Lu, HarvardTitleHouseholder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Random Matrices

    Abstract: In many problems in statistical learning, random matrix theory, and statistical physics, one needs to simulate dynamics on random matrix ensembles. A classical example is to use iterative methods to compute the extremal eigenvalues/eigenvectors of a (spiked) random matrix. Other examples include approximate message passing on dense random graphs, and gradient descent algorithms for solving learning and estimation problems with random initialization. We will show that all such dynamics can be simulated by an efficient matrix-free scheme, if the random matrix is drawn from an ensemble with translation-invariant properties. Examples of such ensembles include the i.i.d. Gaussian (i.e. the rectangular Ginibre) ensemble, the Haar-distributed random orthogonal ensemble, the Gaussian orthogonal ensemble, and their complex-valued counterparts.A “direct” approach to the simulation, where one first generates a dense n × n matrix from the ensemble, requires at least O(n^2) resource in space and time. The new algorithm, named Householder Dice (HD), overcomes this O(n^2) bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are O(nT) and O(n T^2), respectively, with T being the number of iterations. When T ≪ n, which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint.Finally, the HD algorithm is not just a computational trick. I will show how its construction can serve as a simple proof technique for several problems in high-dimensional estimation
    4/14/2021Canceled
    4/16/2021
    Friday
    Patrick Lopatto (IAS)Title: Fluctuations in local quantum unique ergodicity for generalized Wigner matrices

    Abstract: In a disordered quantum system, delocalization can be understood in many ways. One of these is quantum unique ergodicity, which was proven in the random matrix context by Bourgade and Yau. It states that for a given eigenvector and set of coordinates J, the mass placed on J by the eigenvector tends to N^{-1}|J|, the mass placed on those coordinates by the uniform distribution. Notably, this convergence holds for any size of J, showing that the eigenvectors distribute evenly on all scales.

    I will present a result which establishes that the fluctuations of these averages are Gaussian on scales where |J| is asymptotically less than N, for generalized Wigner matrices with smooth entries. The proof uses new eigenvector observables, which are analyzed dynamically using the eigenvector moment flow and the maximum principle.

    This is joint work with Lucas Benigni.

    4/21/2021Jean-Christophe Mourrat, Courant Institute, NYUTitleMean-field spin glasses: beyond Parisi’s formula?

    Abstract: Spin glasses are models of statistical mechanics encoding disordered interactions between many simple units. One of the fundamental quantities of interest is the free energy of the model, in the limit when the number of units tends to infinity. For a restricted class of models, this limit was predicted by Parisi, and later rigorously proved by Guerra and Talagrand. I will first show how to rephrase this result using an infinite-dimensional Hamilton-Jacobi equation. I will then present partial results suggesting that this new point of view may allow to understand limit free energies for a larger class of models, focusing in particular on the case in which the units are organized over two layers, and only interact across layers.

    Fall 2020:

    DateSpeakerTitle/Abstract
    9/9/2020Yukun He (Zurich)Title: Single eigenvalue fluctuations of sparse Erdős–Rényi graphs

    Abstract: I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdös-Rényi graph $G(N,p)$. I show that if $N^{-1}\ll p \ll N^{-2/3}, then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. The main technical tool of the proof is a rigidity bound of accuracy $N^{-1-\varepsilon}p^{-1/2}$ for the extreme eigenvalues, which avoids the $(Np)^{-1}$-expansions from previous works. Joint work with Antti Knowles.

    10/14/2020David Belius (University of Basel)TitleThe TAP approach to mean field spin glasses

    Abstract: The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated methods  in theoretical physics and mathematics, such as the replica method, which are largely orthogonal to the TAP approach. The TAP approach has the advantage of being interpretable as a variational principle optimizing an energy/entropy trade-off, as commonly encountered in statistical physics and large deviations theory, and potentially allowing for a more direct characterization of the Gibbs measure and its “pure states”. In this talk I will recall the TAP approach, and present preliminary steps towards a solution of mean field spin glass models entirely within a TAP framework.

    10/28/2020Giuseppe Genovese (University of Basel)TitleNon-convex variational principles for the RS free energy of restricted Boltzmann machines

    Abstract: From the viewpoint of spin glass theory, restricted Boltzmann machines represent a veritable challenge, as to the lack of convexity prevents us to use Guerra’s bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will present old and new results around the topic along with some open problems.

    11/4/2020Benjamin Landon (MIT)Title:  Fluctuations of the spherical Sherrington-Kirkpatrick model

    Abstract:  The SSK model was introduced by Kosterlitz, Thouless and Jones as a simplification of the usual SK model with Ising spins. Fluctuations of its observables may be related to quantities from random matrix theory using integral representations.  In this informal talk we discuss some results on fluctuations of this model at critical temperature and with a magnetic field

    11/11/2020
    3:00 – 4:00pm
    Lucas Benigni (University of Chicago)Title:  Optimal delocalization for generalized Wigner matrices

    Abstract: We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result, known as delocalization, to more general entry distributions. After giving a brief overview of the previous results going in this direction, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.

    11/18/2020Simone Warzel (Technical University of Munich)Title:  Hierarchical quantum spin glasses

    Abstract: Hierarchical spin glasses such as the generalised random energy model are known to faithfully model typical energy landscapes in the classical theory of mean-field spin glasses. Their built-in hierarchical structure is known to emerge spontaneously in the spin-glass phase of, e.g., the Sherrington-Kirkpatrick model. In this talk, I will review recent results on the effects of a transversal magnetic field on such hierarchical quantum spin glasses.
    In particular, I will present a formula of Parisi-type for their free energy which allows to make predictions about the phase diagram.
    12/2/2020Sabine Jansen (LMU Munich)TitleThermodynamics of a hierarchical mixture of cubes

    Abstract: The talk discusses a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes of side-lengths 2^j, j\in \N_0. Cubes belong to an admissible set such that if two cubes overlap, then one cube is contained in the other, a picture reminiscent of Mandelbrot’s fractal percolation model. I will present exact formulas for the entropy and pressure, discuss phase transitions from a fluid phase with small cubes towards a condensed phase with a macroscopic cube, and briefly sketch some broader questions on renormalization and cluster expansions that motivate the model. Based on arXiv:1909.09546 (J. Stat. Phys. 179 (2020), 309-340).

    For information on previous seminars, click here

    The schedule will be updated as details are confirmed.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Gabriel Poesia, Dept. of Computer Science, Stanford University

    Title: Peano: Learning Formal Mathematical Reasoning Without Human Data

    Abstract: Peano is a theorem proving environment in which a computational agent can start tabula rasa in a new domain, learn to solve problems through curiosity-driven exploration, and create its own higher level actions. Gabriel will describe the system, present case studies on learning to solve simple algebra problems from the Khan Academy platform, and describe work on progress on learning the Natural Number Game, a popular introduction to theorem proving in Lean for mathematicians.

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    10.19.2022

    New Technologies in Mathematics Seminar

    Speaker: Antonia Creswell, DeepMind

    Title: Towards Faithful Reasoning Using Language Models

    Abstract: Language models are showing impressive performance on many natural language tasks, including question-answering. However, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this, we will introduce Selection-Inference, a faithful reasoning model, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy.

     

     

  • New Technologies in Mathematics Seminar
    2:00 pm-4:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    10.05.2022

    New Technologies in Mathematics Seminar

    Speaker: Guy Gur-Ari, Google Research

    Title: Minerva: Solving Quantitative Reasoning Problems with Language Models

    Abstract: Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA NTM Seminar 09.28.2022

    New Technologies in Mathematics

    Speaker: Surya Ganguli, Stanford University

    Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
    Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size, sometimes achieving exponential scaling, by collecting small carefully curated datasets rather than large random ones.
    References: Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
    Sorscher, Ben, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/31/2021 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/28/2020 RM&PT seminar

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Sean Welleck, CMU, Language Technologies Institute

    Title: Llemma: an open language model for mathematics

    Abstract: We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of mathematical web data, code, and scientific papers. The resulting models show improved mathematical capabilities, and can be adapted to various tasks. For instance, Llemma outperforms the unreleased Minerva model suite on an equi-parameter basis, and is capable of tool use and formal theorem proving without any further fine-tuning. We openly release all artifacts, including the Llemma models, the Proof-Pile II, and code to replicate our experiments. We hope that Llemma serves as a platform for new research and tools at the intersection of generative models and mathematics.

     

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/29/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5/13/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Quantum Matter
    2:00 pm-3:30 pm
    12/01/2024

    Speaker: Clay Cordova (U Chicago)

    Title: Non-Invertible Duality Defects in 3+1 Dimensions

    Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

  • Topological Quantum Matter Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Ceren Dag, Harvard

    Title: Breaking ergodicity: quantum scars and regular eigenstates

    Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411, in peer review.

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo

    2:00 pm-5:00 pm
    12/01/2024-04/03/2018
    1 Oxford Street, Cambridge MA 02138
    Math Science Lectures in Honor of Raoul Bott

    DSC_0170-e1525711590120

    On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

    The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

     

    Cachazo-e1519325938458

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-20-2017 RM & PT Seminar

    2:00 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Special Seminar

    Speaker: Mayuko Yamashita, Kyoto University

    Title: Topological modular forms and heretoric string theory

    Abstract: In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF.

    Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

     

  • Topological Quantum Matter Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker:  Ken K. W. Ma (Northeastern University)

    Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future

    Abstract: The discovery of fractional quantum Hall (FQH) states started a new chapter in modern physics. Nowadays, more than 70 FQH states at different filling factors have been observed. Among them, the FQH state at the filling factor ν=5/2 in GaAs (or the 5/2 state) remains one of the most special and attractive states. Since its discovery in 1987, different possible topological orders have been proposed to describe the 5/2 state. Some of them can host an exotic type of particles, known as non-Abelian anyons. Recent experiments have provided more insights into the understanding of the 5/2 state, but its underlying nature is still under debate.

    In this talk, I will review the basics of the 5/2 state [1] and a more unified theoretical description of different possible topological orders of the 5/2 state that we have recently proposed [2]. I will also review the groundbreaking thermal Hall conductance experiment [3] and the follow-up quantum Hall interface experiments by the Weizmann Institute group [4, 5], and discuss what possible lessons that we can learn from the experimental results. Lastly, I will talk about some possible directions and related topics for future investigations.

    References:

    [1] K. K. W. Ma, M. R. Peterson, V. W. Scarola, and K. Yang, “Fractional quantum Hall effect at the filling factor ν = 5/2” in Encyclopedia of Condensed Matter Physics (Second Edition), edited by T. Chakraborty, Academic Press (2024).
    [2] K. K. W. Ma and D. E. Feldman, “The sixteenfold way and the quantum Hall effect at half-integer filling factors”, Phys. Rev. B 100, 035302 (2019).
    [3] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern, “Observation of half-integer thermal Hall conductance”, Nature (London) 559, 205 (2018).
    [4] B. Dutta, W. Yang, R. Melcer, H. K. Kundu, M. Heiblum, V. Umansky, Y. Oreg, A. Stern, D. Mross, “Distinguishing between non-Abelian topological orders in a quantum Hall system”, Science 375, 193 (2021).
    [5] B. Dutta, V. Umansky, M. Banerjee, and M. Heiblum, “Isolated ballistic non-Abelian interface channel”, Science 377, 1198 (2022).

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Yuanzhi Li, CMU Dept. of Machine Learning and Microsoft Research

    Title: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation

    Abstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking results about this question. Using a synthetic biography dataset, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence, can mitigate this issue. Using linear probing, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations.

    We then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset, so that it could answer “What is the birthday of XXX” with 100% accuracy.  Even so, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly.  Even using Chain of Thought training data only helps the model answer such questions in a CoT manner, not directly.

    We will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example, is a 1B parameter language model enough to store all the knowledge of a middle school student?

     

     

  • Topological Quantum Matter Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Prashant Kumar, University of Chicago

    Title: Emergent composite-fermion Luttinger liquid at the half-filled Landau level

    Abstract: The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, I will present our numerical calculations of the excitation spectrum of this state on infinite cylinders. By comparing our results with a quasi-1D theory of CFs, we show compelling quantitative evidence for the emergence of a Luttinger liquid of composite-fermions at low energies, distinct from that of electrons. I will comment on some future directions.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    5/6/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Abhishek Panigrahi, Dept. of Computer Science, Princeton University

    Title: On the Power of Forward pass through Transformer Architectures

    Abstract: Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of study. This talk studies two interesting phenomena.

    In the first half, we explore how and why pre-trained language models, specifically BERT of moderate sizes, can effectively learn linguistic structures like parse trees during pre-training. Specifically, using synthetic data through PCFGs, we show how moderate-sized transformers can perform forward-backward parsing, also known as the inside-outside algorithm, during inference. We further understand the role of the pre-training loss for the model to learn to parse during pre-training.

    In the second half, we consider in-context learning of large language models, where they learn to reason on the fly. An ongoing hypothesis is that transformers simulate gradient descent at inference to perform in-context learning. We propose the Transformer in Transformer (TinT) framework, which creates explicit transformer architectures that can simulate and fine-tune a small pre-trained transformer model during inference. E.g. a 1.3B parameter TINT model can simulate and fine-tune a 125 million parameter model in a single forward pass. This framework suggests that large transformers might execute intricate sub-routines during inference, and provides insights for enhancing their capabilities through intelligent design considerations.

     

  • Math Science Literature Lecture Series
    2:00 pm-3:00 pm
    12/01/2024

    Shing-Tung Yau (Harvard)

    Title: Shiing-Shen Chern as a Great Geometer of 20th Century

    Video | Slides | Article

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024

    New Technologies in Mathematics Seminar

    Speaker: Ronen Eldan, Microsoft Research

    Title: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent

    Abstract: While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity?

    In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4-year-olds typically understand, generated by GPT-3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the state-of-the-art models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for low-resource or specialized domains, and shed light on the emergence of language capabilities in LMs.

     

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: François Charton, Meta AI

    Title:  Transformers for maths, and maths for transformers

    Abstract: Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics.

    Problems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic, I show that model predictions can be explained, that trained models do not confabulate, and that carefully choosing the training distributions can help achieve better, and more robust, performance.

     

     

     

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/1/2020 Random Matrix and Probability Theory Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • General Relativity Seminar
    2:00 pm-3:00 pm
    12/01/2024
    17 Oxford St, Cambridge, MA 02138

    General Relativity Seminar

    Speaker: Suman Kundu (Weizmann Institute)

    Title: ‘Grey Galaxy’ as the endpoint of the Kerr-AdS super radiant blackhole

    Abstract: Kerr AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses near extremality. We conjecture that these instabilities settle down into Grey Galaxies (GG)s – a new class of solutions to Einstein’s equations which we construct for $d=3$. Grey Galaxies consist of an $mega=1$ black hole in the `centre’ of $AdS$, surrounded by a uniformly thick and very large disk of thermal bulk matter that revolves around the centre of AdS at the speed of light. The parametrically low energy density and parametrically large radius of the gas disk are inversely related; as a consequence, the gas carries a finite fraction of the total energy. Grey Galaxy saddles exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr AdS black holes and the gas. In addition to a smooth piece, the boundary stress tensor of these solutions includes a contribution from a delta function localized at the `equator’ of the boundary sphere, a term which may be used as an order parameter that sharply distinguishes GG solutions from ordinary Kerr-Black hole saddles. We also construct `Revolving Black Hole (RBH) saddles’,  macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, that describe black holes revolving around the centre of $AdS$, at the fixed radial location but in a quantum wave function in the angular directions. RBH saddles turn out to be (marginally) entropically subdominant to GG saddles. We argue that supersymmetric versions of RBH saddles exist and have interesting consequences for the spectrum of SUSY states in, e.g.  ${\cal N}=4$ Yang-Mills theory.

  • New Technologies in Mathematics Seminar
    2:00 pm-3:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    New Technologies in Mathematics Seminar

    Speaker: Alex Gu, MIT Dept. of EE&CS

    Title: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models

    Abstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

     

  • Seminars

    Seminars Colloquia & Seminar
    4/22/2020 RM&PT Seminar

    2:00 pm-3:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-29-17 RM & PT Seminar

    2:03 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    09-24-2015 Evolution Equations Seminar

    2:03 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2015 Special Random Matrix & Probability Theory Seminar

    2:05 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-18-2015 Random Matrix & Probability Theory Seminar

    2:07 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:08 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 RM&PT Seminar

    2:08 pm
    12/01/2024
  • Colloquium
    2:10 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    11-29-2017 Mathematical Physics Seminar

    2:11 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    2:11 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    09-29-2015 Geometric Analysis Seminar

    2:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-28-2015 CMSA Special Seminar

    2:15 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:15 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12-6-2017 RM & PT Seminar

    2:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-05-2015 Mathematical Physics Seminar

    2:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-15-2015 Evolution Equations Seminar

    2:17 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12-6-2017 Mathematical Physics Seminar

    2:17 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-07-2015 Random Matrix & Probability Theory Seminar

    2:19 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:20 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-29-2015 Evolution Equations Seminar

    2:20 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-14-2015 Random Matrix & Probability Theory Seminar

    2:21 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:21 pm
    12/01/2024-03/06/2018

    During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

    You can watch Prof. Sheshmani describe the series here.

    The Syllabus is as follows:

    Date………..TopicVideo/Audio
    1-25-2018Gromov-Witten invariants 

    Definition, examples via algebraic geometry I

    Video / Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture.

     2-01-2018Gromov-Witten invariants 

    Virtual Fundamental Class I (definition)

    Video Audio / Combined 


    *due to technical difficulties the audio and video are split for this lecture

    2-13-2018Gromov-Witten invariants 

    Virtual Fundamental Class II (computation in some cases)

     2-15-2018Computing GW invariants 

    Three level GW classes

    Genus zero invariants of the projective plane

     2-20-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) I

    2-22-2018Quantum Cohomology 

    Small Quantum Cohomology (Definition and Properties) II

    2-27-2018Quantum Cohomology 

    Big Quantum Cohomology I

     3-1-2018Quantum Cohomology 

    Big Quantum Cohomology II

    GW potential

    WDVV equation

    3-6-2018GW invariants via Quantum Cohomology 

    The Quintic threefold case

    The P^2 case

    GW invariants via Quantum Cohomology 

    Dubrovin (quantum) connection

    Nakajima varieties 

    -Algebraic and symplectic reduction

    Nakajima varieties 

    Quasi maps to Nakajima varieties

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) I

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Small Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) I

     
    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) II

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) III

    Quantum cohomology of Nakajima varieties 

    Big Quantum Cohomology of Hilb^n (C2) IV

     
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    11/11/21 Interdisciplinary Science Seminar

    2:22 pm-3:22 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-11.11.21

    Title: The Kervaire conjecture and the minimal complexity of surfaces

    Abstract: We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture.
    The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/<<w>> is still nontrivial. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of surfaces in HNN extensions. This gives a conceptually simple proof of Klyachko’s theorem that confirms the Kervaire conjecture for any G torsion-free. I will also explain new results obtained using this approach.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-21-2015 Random Matrix & Probability Theory Seminar

    2:22 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Existence of Canonical Metrics on Non-Kähler Geometry
    2:23 pm-2:24 pm
    12/01/2024

    On Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on “Existence of Canonical Metrics on Non-Kähler Geometry.

    In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses works by Jun Li of Fudan University in Shanghai, Ji-Xiang Fu of Fudan University, Ivan Smith of the University of Cambridge, Richard P. Thomas of Imperial College London, Tristan C. Collins of the Massachusetts Institute of Technology, French mathematician Émile Picard, Teng Fei of Rutgers University in Newark, New Jersey, Adam Jacob of the University of California, Davis, and Duong H. Phong of Columbia University.

    More information about this talk can be found on the Simons Foundation website.

  • Colloquium
    2:23 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:24 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    11/18/2021 Interdisciplinary Science Seminar

    2:25 pm-3:25 pm
    12/01/2024

    Title: Amplituhedra, Scattering Amplitudes and Triangulations

    Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    12/2/2021 Interdisciplinary Science Seminar

    2:28 pm-3:28 pm
    12/01/2024

    Title: Polyhomogeneous expansions and Z/2-harmonic spinors branching along graphs

    Abstract: In this talk, we will first reformulate the linearization of the moduli space of Z/2-harmonic spinorsv branching along a knot. This formula tells us that the kernel and cokernel of the linearization are isomorphic to the kernel and cokernel of the Dirac equation with a polyhomogeneous boundary condition. In the second part of this talk, I will describe the polyhomogenous expansions for the Z/2-harmonic spinors branching along graphs and formulate the Dirac equation with a suitable boundary condition that can describe the perturbation of graphs with some restrictions. This is joint work with Andriy Haydys and Rafe Mazzeo.

  • Colloquium
    2:29 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    12/9/21 Interdisciplinary Science Seminar

    2:29 pm-3:29 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-12.09.21-1583x2048

    Title: Numerical Higher Dimensional Geometry

    Abstract: In 1977, Yau proved that a Kahler manifold with zero first Chern class admits a Ricci flat metric, which is uniquely determined by certain “moduli” data. These metrics have been very important in mathematics and in theoretical physics, but despite much subsequent work we have no analytical expressions for them. But significant progress has been made on computing numerical approximations. We give an introduction (not assuming knowledge of complex geometry) to these problems and describe these methods.

  • Seminars

    Seminars Colloquia & Seminar
    9/26/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-Quantum-Matter-in-Mathematics-and-Physics-11.18.21-1583x2048

    Speaker: B. Andrei Bernevig (Princeton University)

    Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

    Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

  • Seminars

    Seminars Colloquia & Seminar
    9/19/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/12/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-28-2015 Random Matrix & Probability Theory Seminar

    2:30 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    2:30 pm-3:30 pm
    12/01/2024-04/26/2020
  • Seminars

    Seminars Colloquia & Seminar
    12/10/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-QMMP-1.18.22-1544x2048-1

    Speaker: Aavishkar Patel (UC Berkeley)

    Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

    Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

  • Seminars

    Seminars Colloquia & Seminar
    11/26/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024

    Speaker: Jeongwan Haah (Microsoft)

    Title: A degeneracy bound for homogeneous topological order

  • Seminars

    Seminars Colloquia & Seminar
    11/21/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    2/27/2019 Colloquium

    2:30 pm-4:00 pm
    12/01/2024
  • Quantum Matter
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-QMMP-1.28.2022-1544x2048-1

    Speaker: Maria Tikhanovskaya (Harvard)

    Title: Maximal quantum chaos of the critical Fermi surface

    Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

  • Seminars

    Seminars Colloquia & Seminar
    11/14/2019 Spacetime Seminar

    2:30 pm
    12/01/2024
  • Colloquium
    2:30 pm-3:00 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    4/10/2019 Colloquium

    2:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/3/2019 Colloquium

    2:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/31/2019 Spacetime Seminar

    2:30 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Social Science Applications Forum

    2:30 pm-4:00 pm
    12/01/2024
  • Quantum Matter
    2:30 pm-4:00 pm
    12/01/2024
    CMSA-QMMP-12.10.21-1544x2048

    Speaker: Lukasz Fidkowski (U Washington)

    Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

    Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

  • Seminars

    Seminars Colloquia & Seminar
    3/7/2019 Social Science Applications Forum

    2:30 pm-3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/18/2019 Spacetime Seminar

    2:30 pm-3:00 pm
    12/01/2024
  • Colloquium
    2:32 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-19-2015 Mathematical Physics Seminar

    2:33 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-20-2015 Geometric Analysis Seminar

    2:35 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10-26-2015 Mathematical Physics Seminar

    2:36 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-02-2015 Mathematical Physics Seminar

    2:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    01-26-2018 Mirror Symmetry Seminar

    2:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-03-2015 Geometric Analysis Seminar

    2:39 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-04-2015 Random Matrix & Probability Theory Seminar

    2:40 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    1-29-2018 Mathematical Physics Seminar

    2:42 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    2:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2-2-2018 Mirror Symmetry Seminar

    2:44 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:44 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:45 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    12/16/2021 Interdisciplinary Science Seminar

    2:46 pm-3:46 pm
    12/01/2024

    Title: Quadratic reciprocity from a family of adelic conformal field theories

    Abstract: We consider a deformation of the 2d free scalar field action by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it’s no longer invariant under the local conformal symmetry algebra. Furthermore, there is an adelic version of this family of global conformal field theories, parametrized by the choice of a number field, together with a Hecke character. Tate’s thesis plays an important role here in calculating Green’s functions of these theories, and in ensuring the adelic compatibility of these theories. In particular, the local L-factors contribute to prefactors of these Green’s functions. We shall try to see quadratic reciprocity from this context, as a consequence of an adelic version of holomorphic factorization of these theories. This is work in progress with B. Stoica and X. Zhong.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/6/2022 Interdisciplinary Science Seminar

    2:47 pm-3:47 pm
    12/01/2024

    Title: The smooth closing lemma for area-preserving surface diffeomorphisms

    Abstract: In this talk, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing result of twisted Seiberg- Witten Floer homology. This is joint work with Dan Cristofaro-Gardiner and Rohil Prasad.

  • Colloquium
    2:47 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:48 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/13/2022 Interdisciplinary Science Seminar

    2:48 pm-3:48 pm
    12/01/2024

    Title: A universal triangulation for flat tori

    Abstract: A celebrated theorem of Nash completed by Kuiper implies that every smooth Riemannian surface has a C¹ isometric embedding in the Euclidean 3-space E³. An analogous result, due to Burago and Zalgaller, states that every polyhedral surface, obtained by gluing Euclidean triangles, has an isometric PL embedding in E³. In particular, this provides PL isometric embeddings for every flat torus (a quotient of E² by a rank 2 lattice). However, the proof of Burago and Zalgaller is partially constructive, relying on the Nash-Kuiper theorem. In practice, it produces PL embeddings with a huge number of vertices, moreover distinct for every flat torus. Based on a construction of Zalgaller and on recent works by Arnoux et al. we exhibit a universal triangulation with less than 10.000 vertices, admitting for any flat torus an isometric embedding that is linear on each triangle. Based on joint work with Florent Tallerie.

  • Seminars

    Seminars Colloquia & Seminar
    11-19-2015 Evolution Equations Seminar

    2:50 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 CMSA Special Lecture

    2:51 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/20/2022 – Interdisciplinary Science Seminar

    2:52 pm-4:52 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-01.20.22-1577x2048

    Title: Markov chains, optimal control, and reinforcement learning

    Abstract: Markov decision processes are a model for several artificial intelligence problems, such as games (chess, Go…) or robotics. At each timestep, an agent has to choose an action, then receives a reward, and then the agent’s environment changes (deterministically or stochastically) in response to the agent’s action. The agent’s goal is to adjust its actions to maximize its total reward. In principle, the optimal behavior can be obtained by dynamic programming or optimal control techniques, although practice is another story.

    Here we consider a more complex problem: learn all optimal behaviors for all possible reward functions in a given environment. Ideally, such a “controllable agent” could be given a description of a task (reward function, such as “you get +10 for reaching here but -1 for going through there”) and immediately perform the optimal behavior for that task. This requires a good understanding of the mapping from a reward function to the associated optimal behavior.

    We prove that there exists a particular “map” of a Markov decision process, on which near-optimal behaviors for all reward functions can be read directly by an algebraic formula. Moreover, this “map” is learnable by standard deep learning techniques from random interactions with the environment. We will present our recent theoretical and empirical results in this direction.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    1/27/2022 – Interdisciplinary Science Seminar

    2:54 pm-4:54 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-1.27.2022-1583x2048

    Title: Polynomials vanishing at lattice points in convex sets

    Abstract: Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number, which we compute for many (but maybe not all) triangles P.

  • Seminars

    Seminars Colloquia & Seminar
    11-09-2015 Mathematical Physics Seminar

    2:54 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:54 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    2:55 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:56 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-19-2015 Random Matrix and Probability Theory Seminar

    2:57 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    2:57 pm
    12/01/2024

    Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    2/3/2022 – Interdisciplinary Science Seminar

    2:57 pm-4:57 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.03.2022-1583x2048-1

    Title:Quasiperiodic prints from triply periodic blocks

    Abstract: Slice a triply periodic wooden sculpture along an irrational plane. If you ink the cut surface and press it against a page, the pattern you print will be quasiperiodic. Patterns like these help physicists see how metals conduct electricity in strong magnetic fields. I’ll show you some block prints that imitate the printing process described above, and I’ll point out the visual features that reveal conductivity properties.

    Interactive slides:https://www.ihes.fr/~fenyes/seeing/slices/

  • Colloquium
    2:59 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    11-16-2015 Mathematical Physics Seminar

    2:59 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/31/2020 Quantum Matter Seminar

    3:00 pm-4:30 pm
    12/01/2024
  • Special Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11-17-2015 Geometric Analysis Seminar

    3:00 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    2/25/2020 Fluid Dynamics

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2-27-2018 HMS Lecture

    3:00 pm-4:00 pm
    12/01/2024-03/01/2018
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024

    Speaker: Jason Rute, CIBO Technologies

    Title: Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models

    Abstract: Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.

  • New Technologies in Mathematics Seminar
  • Seminars

    Seminars Colloquia & Seminar
    Algebraic Geometry Seminar, Thursdays

    3:00 pm-4:00 pm
    12/01/2024

    This seminar will not be held in the Spring 2018 Semester.

    The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated as details are confirmed.

     

     

    DateNameTitle/Abstract
    09-14-17 Yu-Wei Fan (Harvard Math)

    Entropy of an autoequivalence on Calami-Yau manifolds

    Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

    11-1-17

    *5:00pm, G10*

     Shamil Shakirov, Harvard Math

    Undulation invariants of plane curves

    Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

    11-2-17

     

    Alexander Moll, IHES

    Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

    ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

    11-9-17  TBD  TBD
    11-16-17 TBD TBD
    11-23-17  TBD  TBD
    11-30-17  TBD  TBD
    12-7-17  TBD  TBD
    12-15-17  TBD  TBD
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/4/2019 Special Seminar

    3:00 pm
    12/01/2024
  • Math Science Literature Lecture Series
    3:00 pm-4:00 pm
    12/01/2024
    Lecture_Donaldson-pdf

    Simon Donaldson (Stony Brook)

    Title: The ADHM construction of Yang-Mills instantons

    Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the Yang-Mills instanton equations over the 4-sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics,  and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof,  using Penrose’s twistor theory and results on algebraic vector bundles over projective 3-space. As time permits, we will also discuss some further developments, for example, the work of Nahm on monopoles and connections to Mukai duality for bundles over complex tori.

    Video | Slides

  • Math Science Literature Lecture Series

    Math Science Literature Lecture Series Event
    CMSA Math-Science Literature Lecture: Quantum Groups

    3:00 pm-4:00 pm
    12/01/2024-05/05/2020
    Lecture_Etingof-pdf

    Pavel Etingof (MIT)

    Title: Quantum Groups

    Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum Yang-Baxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as representation theory, the Langlands program, low-dimensional topology, category theory, enumerative geometry, quantum computation, algebraic combinatorics, conformal field theory, integrable systems, integrable probability, and others. I will review some of the main ideas and examples of quantum groups and try to briefly describe some of the applications.

    Video | Slides

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    10/9/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Probability Seminar
    3:00 pm-4:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 04.10.23

    Probability Seminar

    *Please note room change: Science Center 232*

    Speaker: Ron Peled (Tel Aviv University)

    Title: Localization for random band matrices

    Abstract: I will explain an approach via “an adaptive Mermin-Wagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}.

    Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/03/2018 RMPT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Dmytro Shklyrov HMS Focused Lecture Series

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/25/2019 Math Physics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Fluid Dynamics Seminar

    3:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • CMSA EVENT: 2018 Ding Shum Lecture
    3:00 pm-4:00 pm
    12/01/2024
    ding-shum-2018

     

    Screen-Shot-2018-06-14-at-1.41.25-PM

    On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

    This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

    Pictures of the event can be found here.

  • Seminars

    Seminars Colloquia & Seminar
    2/14/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Fluid Dynamics Seminar

    3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/31/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Special Seminar
    3:00 pm-4:30 pm
    12/01/2024-05/09/2019

    In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

    Click here for reference material

    Click here for a syllabus

    Schedule:

    Section 1: Basic setting of derived geometry

    The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

    2/05/2019Lecture 1: Model and с-categoriesVideo
    2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
    2/12/2019Lecture 3: Derived Artin stacksVideo 
    2/14/2019Lecture 4: Cotangent complexes

    Section 2: Loop spaces and differential forms

    The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

    2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
    2/21/2019Lecture 6: Chern characterVideo
    2/26/2019

    Room G02

    Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
    2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
    3/05/2019Lecture 9: Cyclic homologyVideo

    Section 3: Shifted symplectic structures
    Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

    3/07/2019Lecture 10: Definition and existence resultsVideo
    3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
    3/14/2019

    Room G02

    Lecture 12: Lagrangians and Lagrangian fibrationsVideo
    3/26/2019Lecture 13: Intersections of LagrangiansVideo
    3/28/2019

    Room G02

    Lecture 14: Examples and applications 2 (Part I)Video
    4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

    Section 4: Uhlenbeck–Yau construction and correspondence

    4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
    4/09/2019

    Room G02

    Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    2/7/2019 General Relativity Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/11/2020 RM&PT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars
    3:00 pm-4:00 pm
    12/01/2024
  • Quantum Matter
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/24/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Quantum Matter
    3:00 pm-4:30 pm
    12/01/2024

    Speaker: Jie Wang (Simons Foundation)

    Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

    Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

    [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
    [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
    [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

  • Seminars

    Seminars Colloquia & Seminar
    2/20/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Probability Seminar
    3:00 pm-4:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 11.30.22

    Probability Seminar

    Title: Lipschitz properties of transport maps under a log-Lipschitz condition

    Abstract: Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting, for applications, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition.

    I will present a construction of a transport map, constructed infinitesimally along the Langevin flow, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds, and which, at the moment, seem to be out of reach of the classically studied optimal transport theory.

    Joint work with Max Fathi and Yair Shenfeld.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/6/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/8/2019 Special Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024

    Speaker: Josef Urban, Czech Technical University

    Title: AI and Theorem Proving

    Abstract: The talk will discuss the main approaches that combine machine learning with automated theorem proving and automated formalization. This includes learning to choose relevant facts for “hammer” systems, guiding the proof search of tableaux and superposition automated provers by interleaving learning and proving (reinforcement learning) over large ITP libraries, guiding the application of tactics in interactive tactical systems, and various forms of lemmatization and conjecturing. I will also show some demos of the systems, and discuss autoformalization approaches such as learning probabilistic grammars from aligned informal/formal corpora, combining them with semantic pruning, and using neural methods to learn direct translation from Latex to formal mathematics.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/28/2018 Random Matrix and Probability Theory Seminar

    3:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/7/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024

    Speaker: Thomas Hales, Univ. of Pittsburgh Dept. of Mathematics

    Title: A Mathematical Language

    Abstract: A controlled natural language for mathematics is an artificial language that is designed in an explicit way with precise computer-readable syntax and semantics.  It is based on a single natural language (which for us is English) and can be broadly understood by mathematically literate English speakers.  This talk will describe the design of a controlled natural language for mathematics that has been influenced by the Lean theorem prover, by TeX, and by earlier controlled natural languages. The semantics are provided by dependent type theory.

  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/14/2018 RM & PT Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/22/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    12/5/2018 Random Matrix and Probability Theory Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/15/2019 Fluid Dynamics

    3:00 pm-4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    5/1/2019 Fluid Dynamics Seminar

    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
    3:00 pm-4:00 pm
    12/01/2024
  • New Technologies in Mathematics Seminar
  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    2/10/2022 – Interdisciplinary Science Seminar

    3:00 pm-4:00 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.10.2022-1

    Title: Metric Algebraic Geometry

    Abstract: A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a distance metric. In this talk, we introduce metric algebraic geometry through a discussion of Voronoi cells, bottlenecks, and the reach of an algebraic variety. We also show applications to the computational study of the geometry of data with nonlinear models.

  • Seminars

    Seminars Colloquia & Seminar
    11-23-2015 Mathematical Physics Seminar

    3:01 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    Random Matrix & Probability Theory Seminar (2016-2017)

    3:01 pm
    12/01/2024-12/14/2017
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    DSC_0025-768x512

    The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

  • Member Seminar
    3:02 pm
    12/01/2024-01/01/2021

    The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below.

    Previous seminars can be found here.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/29/2021Cancelled
    2/5/2021Itamar ShamirTitle: Boundary CFT and conformal anomalies

    Abstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.

    2/12/2021Louis FanTitle:  Joint distribution of Busemann functions in corner growth models

    Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.

    2/19/2021Daniel JunghansTitle: Control issues of the KKLT scenario in string theory

    Abstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular, we show that, generically, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.

    2/26/2021Tsung-Ju LeeTitle: SYZ fibrations and complex affine structures

    Abstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.

    3/5/2021Cancelled
    3/11/2021

    9:00pm ET

    Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification

    Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

    3/18/2021

    9:00pm ET

    Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification
    Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.
    3/26/2021

    8:30am ET

    Aghil AlaeeTitle:  Rich extra dimensions are hidden inside black holes

    Abstract: In this talk, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.

    4/2/2021
    8:30am ET
    Enno KeßlerTitle: Super Stable Maps of Genus Zero

    Abstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.

    4/9/2021Juven Wang

    Video

    Title: Ultra Unification

    Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate more on the nonperturbative global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.

    4/16/2021Sergiy VerstyukTitle: Deep learning methods for economics

    Abstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way, interpretability of neural networks features prominently.

    4/23/2021Yifan WangTitle: Virtues of Defects in Quantum Field Theories

    Abstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra, precision studies of defect observables, and the implications thereof for strongly coupled dynamics. In this talk, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics, and that open new windows to nonperturbative effects in quantum gravity.

    4/30/2021Yun ShiTitle: D-critical locus structure for local toric Calabi-Yau 3-fold

    Abstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.

    5/7/2021Thérèse Yingying WuTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2

    Abstract: In this talk, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.

    5/14/2021Du PeiTitle: Three applications of TQFTs

    Abstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds, and 3) smooth structures on 4-manifolds.

    5/21/2021Farzan VafaTitle: Active nematic defects and epithelial morphogenesis

    Abstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/11/2020Moran KorenTitle:  Observational Learning and Inefficiencies in Waitlists

    Abstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents, upon receiving an offer, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.

    9/18/2020Michael DouglasTitle: A talk in two parts, on strings and on computers and math

    Abstract: I am dividing my time between two broad topics. The first is string theory, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert,GPT) which have led to breakthroughs on natural language processing, describe their potential for helping us do math, and sketch some related theoretical problems.

    9/25/2020Cancelled – Math Science Lecture
    10/2/2020Cancelled – Math Science Lecture
    10/9/2020Wai Tong (Louis) FanTitle: Stochastic PDE as scaling limits of interacting particle systems

    Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
    In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.

    10/16/2020Tianqi WuTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

    Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.

    10/23/2020Changji XuTitle: Random Walk Among Bernoulli Obstacles

    Abstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk, we will discuss some recent results about the behaviors of the conditional random walk, in quenched, annealed, and biased settings.

    10/30/2020Michael SimkinTitle: The differential equation method in Banach spaces and the $n$-queens problem

    Abstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
    We apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.

    11/6/2020Kenji KawaguchiTitle: Deep learning: theoretical results on optimization and mixup

    Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization, robustness, and generalization, during the optimization process of a neural network. In this talk, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.

    11/13/2020Omri Ben-EliezerTitle: Sampling in an adversarial environment

    Abstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations, the existing statistical literature does not apply.

    We propose a new sequential adversarial model capturing these situations, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results, techniques, and applications reveal close connections to various areas in mathematics and computer science, including VC theory, discrepancy theory, online learning, streaming algorithms, and computational geometry.

    Based on joint works with Noga Alon, Yuval Dagan, Shay Moran, Moni Naor, and Eylon Yogev.

    11/20/2020Charles DoranTitle: The Calabi-Yau Geometry of Feynman Integrals

    Abstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.

    Colloquia & Seminars,Seminars

  • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
    3:02 pm-3:03 pm
    12/01/2024-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Participants:

    Gerard Ben Arous, Courant Institute of Mathematical Sciences

    Alex Bloemendal, Broad Institute

    Arup Chakraburty, MIT

    Zhou Fan, Stanford University

    Alpha Lee, Harvard University

    Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

    David R. Nelson, Harvard University

    Nick Patterson, Broad Institute

    Marc Potters, Capital Fund management

    Yasser Roudi, IAS

    Tom Trogdon, UC Irvine

    Organizers:

    Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

    Please click Program for a downloadable schedule with talk abstracts.

    Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

    Schedule:

    January 9 – Day 1
    9:30am – 10:00amBreakfast & Opening remarks
    10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
    11:00am – 12:00pmYasser Roudi
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 10 – Day 2
    8:30am – 9:00amBreakfast
    9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
    10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
    11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 11 – Day 3
    8:30am – 9:00amBreakfast
    9:00am – 10:00amNick Patterson
    10:00am – 11:00amLucy Colwell
    11:00am – 12:00pmAlpha Lee
    12:00pm – 2:00pmLunch
    2:00pm-4:00pmAfternoon Discussion
    4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
    January 12 – Day 4
    8:30am – 9:00amBreakfast
    9:00am – 10:00amGovind Menon
    10:00am – 11:00amAlex Bloemendal
    11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
    12:00pm – 2:00pmLunch
    2:00pmAfternoon Discussion
    January 13 – Day 5
    8:30am – 9:00amBreakfast
    9:00am – 12:00pmFree for Working
    12:00pm – 2:00pmLunch
    2:00pmFree for Working

    * This event is sponsored by CMSA Harvard University.

  • Colloquium
    3:03 pm-4:00 pm
    12/01/2024

    Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

  • Colloquium
    3:03 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    3:03 pm-4:03 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.11.22-1583x2048

    Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.

  • Seminars

    Seminars Colloquia & Seminar
    11-24-2015 Geometric Analysis Seminar

    3:03 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-04-2016 Evolution Equations Seminar

    3:04 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    3:05 pm-4:05 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.12.22-1583x2048-1

    Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Sparse Markov Models for High-dimensional Inference

    3:05 pm-4:05 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.17.2022-1-1583x2048-1

    Abstract: Finite order Markov models are theoretically well-studied models for dependent data.  Despite their generality, application in empirical work when the order is larger than one is quite rare.  Practitioners avoid using higher order Markov models because (1) the number of parameters grow exponentially with the order, (2) the interpretation is often difficult. Mixture of transition distribution models (MTD)  were introduced to overcome both limitations. MTD represent higher order Markov models as a convex mixture of single step Markov chains, reducing the number of parameters and increasing the interpretability. Nevertheless, in practice, estimation of MTD models with large orders are still limited because of curse of dimensionality and high algorithm complexity. Here, we prove that if only few lags are relevant we can consistently and efficiently recover the lags and estimate the transition probabilities of high order MTD models. Furthermore, we show that using the selected lags we can construct non-asymptotic confidence intervals for the transition probabilities of the model. The key innovation is a recursive procedure for the selection of the relevant lags of the model.  Our results are  based on (1) a new structural result of the MTD and (2) an improved martingale concentration inequality. Our theoretical results are illustrated through simulations.

  • Colloquium
    3:06 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-02-2016 Geometric Analysis Seminar

    3:06 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Hodge and Noether-Lefschetz Loci Seminar

    3:06 pm
    12/01/2024

    In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

    The schedule below will be updated as talks are confirmed.

    DateTitle/Abstract
    11/7/2018

    Video

    Title: Hodge and Noether-Lefschetz loci

    Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

    In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

    11/14/2018

    Video

    Title:  Integral Hodge conjecture for Fermat varieties

    Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

    11/21/2018

    Video

    Title:  Periods of algebraic cycles

    Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

    11/28/2018

    Video

    Title: Periods of Complete Intersection Algebraic Cycles

    Speaker: Roberto Villaflor

    Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

    12/05/2018

    Room G02

    Title: Some explicit Hodge cycles

    Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

    12/12/2018

    Video

    Title: A conjectural Hodge locus for cubic tenfold

    Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

    1/16/2019Title: Algebraic BCOV anomaly equation

    Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

    1/23/2019

    Video

    Title: A new model for modular curves

    Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

    The talk is based on the article arXiv:1808.01689.

    1/30/2019

    Video

    Title: Constant Yukawa couplings

    Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

    2/6/2019

    Video

    Title: Integrality properties of CY modular forms

    Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

    We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

    2/13/2019Title: Foliations and Hodge loci

    Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

     

    References:

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Singular Set in Obstacle Problems

    3:08 pm-4:08 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-2.24.2022-1583x2048

    Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.

  • Colloquium
    3:09 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
    3:09 pm-3:10 pm
    12/01/2024-04/08/2016

    The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

    Workshop Locations:

    April 4 – 7 (Monday ~ Thursday)

    Room G10,
    20 Garden Street, Cambridge, MA 02138 

    April 8 (Friday)

    EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
    20 Oxford Street, Cambridge, MA 02138

     Participants:

    • Peter Hubyers (Harvard University)
    • Eli Tziperman (Harvard University)
    • Andrew Rhines (University of Washington)
    • Karen McKinnon (UCAR)
    • Douglas MacMartin (Caltech)
    • Thomas Laepple (Alfred Wegener Institute)
    • Yossi Ashkenazy (Ben-Gurion University)
    • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
    • Natesh Pillai (Harvard University)
    • Judah Cohen (Atmospheric and Environmental Research)
    • Cristian Proistosescu (Harvard University)

    Please click Workshop Agenda for a downloadable agenda.

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    02-11-2016 Evolution Equations Seminar

    3:09 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-16-2018 RM & PT Seminar

    3:09 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Colloquium
    3:11 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-03-2016 Random Matrix & Probability Theory Seminar

    3:11 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:11 pm-4:11 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.03.2022-1583x2048-1

    Abstract: While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573.

    Bio: Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research, New England. In 2019, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text, images, and other forms of data, using techniques such as non-convex optimization and tensor decompositions.

  • Colloquium
    3:12 pm-4:12 pm
    12/01/2024

    Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
    In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

    I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

  • Interdisciplinary Science Seminar
    3:13 pm-4:13 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.10.2022-1583x2048-1

    Abstract: The gig economy provides workers with the benefits of autonomy and flexibility, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms, an unexplored aspect is the organization identity. In a series of studies, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach, combining methodologies from randomized field experiments, recommender systems, and counterfactual machine learning. Together, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy.

    Bio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning, causal inference, and field experiments in his research, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences, including PNAS, ACM TOIS, WWW, and ICWSM.

  • Colloquium
    3:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 RM & PT Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 RM & PT Seminar

    3:15 pm
    12/01/2024
  • Colloquium
    3:15 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2019 Random Matrix and Probability Theory Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Interdisciplinary Science Seminar
    3:15 pm-4:15 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048

    Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization, during the optimization process. In this talk, I will discuss some mathematical properties of optimization and generalization for deep neural networks.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11/6/2019 Random Matrix and Probability Theory Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/23/2019 RMPT Seminar

    3:15 pm-4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02-16-2016 Geometric Analysis Seminar

    3:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    02-15-2016 Mathematical Physics Seminar

    3:17 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    An operadic structure on supermoduli spaces

    3:17 pm-5:17 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048 (1)

    Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin. Based joint work with Yu. I. Manin and Y. Wu. https://arxiv.org/abs/2202.10321

  • Seminars

    Seminars Colloquia & Seminar
    02-18-2016 Evolution Equations Seminar

    3:19 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:20 pm-5:20 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-03.231.2022-1583x2048-1

    Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space.  Many fundamental questions have been open for these classical objects.  We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry.  Key objects involve compactifications of embedded vector spaces, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector bundles and the cohomology ring of stellahedral varieties.

  • Seminars

    Seminars Colloquia & Seminar
    02-22-2016 Mathematical Physics Seminar

    3:20 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:22 pm-5:22 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.07.2022-1583x2048-1

    Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson, as well as joint work with (separately) Larson and Jim Bryan.

  • Seminars

    Seminars Colloquia & Seminar
    02-23-2016 Geometric Analysis Seminar

    3:22 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    02-24-2016 Random Matrix & Probability Theory

    3:23 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
    3:23 pm
    12/01/2024-12/02/2016

    The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

    Organizers:

    Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

    Speakers:

    1. Conan Leung, Chinese University of Hong Kong
    2. Junwu Tu, University of Missouri
    3. Jingyu Zhao, Columbia University
    4. David Treumann, Boston College
    5. Hiro Lee Tanaka, Harvard University
    6. Fabian Haiden, Harvard University
    7. Hansol Hong, Harvard CMSA/Brandeis University
    8. Netanel Blaier, Harvard CMSA/Brandeis University
    9. Garret Alston, The University of Oklahoma

    Please click Workshop Program for a downloadable schedule with talk abstracts.

    Conference Schedule:

    Monday, November 28 – Day 1
    10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
    Lunch
    1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
    4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
    Tuesday, November 29 – Day 2
    10:30am –11:30amConan Leung, “Remarks on SYZ”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30pm-2:45pm Break
    2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
    4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
    Wednesday, November 30 – Day 3
    10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
    Lunch
    1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
     2:30-2:45pm Break
    2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
    Thursday, December 1 – Day 4
    10:30am –11:30amDavid Treumann“Some examples in three dimensions”
    Lunch
    1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
     2:30-2:45pm Break
    2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

    * This event is sponsored by the Simons Foundation and CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    02-25-2016 Evolution Equations Seminar

    3:25 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    3:25 pm
    12/01/2024

    During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

    The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

    To learn how to attend, please fill out this form.

    Information on previous colloquia can be found here.

    Spring 2021:

    DateSpeakerTitle/Abstract
    1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

    Slides

    Video

    Title: Topology protects chiral edge currents in stochastic systems

    Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

    2/3/2021André Luiz de Gouvêa (Northwestern)

    Video

    Title: The Brave Nu World

    Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

    2/10/2021Mykhaylo Shkolnikov (Princeton)

    Video

    Title: Probabilistic approach to free boundary problems and applications

    Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

    2/17/2021
    9:00 – 10:00PM ET
    C. Seshadhri (UC Santa Cruz)

    Video

    Title: Studying the (in)effectiveness of low dimensional graph embeddings

    Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

    2/24/2021David Ben-Zvi (U Texas)

    Video

    Title: Electric-Magnetic Duality for Periods and L-functions

    Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
    A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
    We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

    3/3/2021

    9:00pm ET

    Omer Tamuz (Caltech)Title: Monotone Additive Statistics

    Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

    (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

    3/10/2021

    9:00pm ET

    Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

    Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

    3/17/2021
    9:00pm ET
    Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

    Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

    3/24/2021Weinan E (Princeton)

    Video

    Title: Machine Learning and PDEs

    Abstract: I will discuss two topics:
    (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
    (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

    3/31/2021Thore Graepel (DeepMind/UCL)

    Video

    Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

    Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

    4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

    Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

    4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

    Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

    4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
    Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
    4/28/2021

    9:00 – 10:00pm ET

    Shamit Kachru (Stanford)

    Slides

    Title: K3 Metrics from String Theory

    Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


    Fall 2020:

    DateSpeakerTitle/Abstract
    9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

    Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

    10/7/2020

    10:00am

    Mariangela Lisanti (Princeton University)

    Video

    Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

    Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

    10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

    Video

    Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

    Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
    a) My general argument “against” quantum computers,
    b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
    Relevant papers:
    Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
    wordpress.com/2019/11/stat-quantum2.pdf

    Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
    wordpress.com/2020/08/laws-blog2.pdf

    Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
    wordpress.com/2019/09/main-pr.pdf

    10/21/2020Marta Lewicka (University of Pittsburgh)

    Video

    Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

    Abstract: We propose results that relate the following two contexts:
    (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
    (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
    For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
    geometry and mechanics of materials in the prediction of patterns and shape formation.

    10/28/2020Jonathan Heckman (University of Pennsylvania)

    Video

    Title: Top Down Approach to Quantum Fields

    Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

    11/4/2020
    9:00pm ET
    Surya Ganguli (Stanford)

    Video

    Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

    Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
    Selected References:
    M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
    M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
    A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
    H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
    S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
    B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
    Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
    S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

    11/11/2020Kevin Buzzard (Imperial College London)

    Video

    Title: Teaching proofs to computers

    Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
    I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

    11/18/2020Jose A. Scheinkman (Columbia)

    Video

    Title: Re-pricing avalanches

    Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

    11/25/2020

    10:45am

    Eric J. Heller (Harvard)

    Video

    Title: Branched Flow

    Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

    12/2/2020Douglas Arnold (U of Minnesota)

    Video

    Title: Preserving geometry in numerical discretization

    Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

    12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

    Video

    Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

    Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
    After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

  • Seminars

    Seminars Colloquia & Seminar
    03-03-2016 Evolution Equations Seminar

    3:26 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    3-5-2018 Mathematical Physics Seminar

    3:27 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Seminars

    Seminars Colloquia & Seminar
    03-29-2016 Geometric Analysis Seminar

    3:27 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    3:28 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
    3:29 pm
    12/01/2024-05/02/2017

    In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

    Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

    Confirmed Speakers

    * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Tomas Berggren (MIT)

    Title: Geometry of the doubly periodic Aztec dimer model

    Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions — known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.

     

     

  • Colloquium
    3:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 05.03.23

    Probability Seminar

    Speaker: Boris Hanin (Princeton)

    Title: Random Neural Networks

    Abstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially L) are large. The first set of results are for deep linear networks, which are simply products of L random matrices of size N x N. I’ll explain how the setting where the ratio L / N is fixed with both N and L large reveals a number of phenomena not present when only one of them is large. I will then state several results about non-linear networks in which this depth-to-width ratio L / N again plays a crucial role and gives an effective notion of depth for a random neural network.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 04.26.23

    Probability Seminar

    Speaker: Jimmy He (MIT)

    Title: Boundary current fluctuations for the half space ASEP

    Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

  • Seminars

    Seminars Colloquia & Seminar
    11/12/2019 Spacetime Seminar

    3:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/10/2019 Spacetime Seminar

    3:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    Harvard Science Center, 1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 04.19.23

    Probability Seminar

    Speaker: Evita Nestoridi (Stonybrook)

    Title: Diagonalizing Transition Matrices of Card Shuffles

    Abstract: In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 04.12.23

    Probability Seminar

    Speaker: Emma Bailey (CUNY)

    Title: Large deviations of Selberg’s central limit theorem

    Abstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance.  It is natural to investigate how far into the tails this Gaussianity persists, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials.  It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations, as well as certain maxima and moments. In this talk I will focus more on the techniques we apply to approach this problem and I will assume no number theoretic knowledge. This is joint work with Louis-Pierre Arguin.

  • Seminars

    Seminars Colloquia & Seminar
    7/29/2020 Quantum Matter Seminar

    3:30 pm-5:00 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 04.05.23

    Probability Seminar

    Speaker: Ahmed El Alaoui (Cornell)

    Title: Sampling from the SK and mixed p-spin measures with stochastic localization

    Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model. This is based on a joint work with Andrea Montanari and Mark Sellke.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/17/2018 RM & PT Seminar

    3:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA Probability Seminar 03.22.23

    Probability Seminar

    Speaker: Wei-Kuo Chen (Minnesota)

    Title: Some rigorous results on the Lévy spin glass model

    Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024

    Probability Seminar

    Speaker: Benjamin Landon (University of Toronto)

    Title: Tail estimates for stationary KPZ models

    Abstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size, including the stochastic six vertex model, the ASEP and a class of non-integrable interacting diffusions.

    Joint work with Christian Noack and Phil Sosoe.

     

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main)

    Title: Solving spin systems, the Babylonian way

    Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues, but quite astonishingly, evidence is mounting that Parisi’s ultrametricity assumption, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024

    Probability Seminar

    Speaker: Vishesh Jain (University of Illinois Chicago)
    Title: Thresholds for edge colorings
    Abstract: We show that if each edge of the complete bipartite graph K_{n,n} is given a random list of C(\log n) colors from [n], then with high probability, there is a proper edge coloring where the color of each edge comes from the corresponding list. We also prove analogous results for Latin squares and Steiner triple systems. This resolves several related conjectures of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-Osthus. I will discuss some of the main ingredients which go into the proof: the Kahn-Kalai conjecture, absorption, and the Lovasz Local Lemma distribution. Based on joint work with Huy Tuan Pham.
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 02.15.23

    Probability Seminar

    Speaker: Zhigang Yao (Harvard CMSA/National University of Singapore)

    Title: Manifold Fitting: An Invitation to Statistics

    Abstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference: https://arxiv.org/abs/1909.10228

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Youngtak Sohn (MIT)

    Title: Universality of max-margin classifiers

    Abstract: Many modern learning methods, such as deep neural networks, are so complex that they perfectly fit the training data. Despite this, they generalize well to the unseen data. Motivated by this phenomenon, we consider high-dimensional binary classification with linearly separable data. First, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule, namely the max-margin classification, has near-optimal prediction accuracy. Then, we discuss universality of max-margin classification. In particular, we characterize the prediction accuracy of the non-linear random features model, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally, we consider the wide-network limit, where the number of neurons tends to infinity, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective.

    Joint work with Andrea Montanari, Feng Ruan, Jun Yan, and Basil Saeed.

  • Quantum Matter
    3:30 pm-5:00 pm
    12/01/2024

    Title: Electric-magnetic duality and the Geometric Langlands duality

    Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    Virtual and in 20 Garden Street, Room G10
    CMSA Probability Seminar 02.08.23

    Probability Seminar

    Speaker: Roland Bauerschmidt (Cambridge)

    Title: Bakry-Emery theory and renormalisation

    Abstract: I will discuss an approach to log-Sobolev inequalities that
    combines the Bakry-Emery theory with renormalisation and present several
    applications. These include log-Sobolev inequalities with polynomial
    dependence for critical Ising models on Z^d when d>4 and singular SPDEs
    with uniform dependence of the log-Sobolev constant on both the
    regularisation and the volume. The talk is based on joint works with
    Thierry Bodineau and Benoit Dagallier.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024

    Probability Seminar

    Speaker: Antoine Maillard (ETH Zürich)

    Title: Fitting ellipsoids to random points

    Abstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science, and is conjectured to undergo a sharp transition: with high probability, it has a solution if n < d^2/4, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture, and highlight some recent progress, in three different directions:

    • A proof that the problem is feasible for n < d^2 / C, for some (large) constant C, significantly improving over previously-known bounds.
    • A non-rigorous characterization of the conjecture, as well as significant generalizations, using analytical methods of statistical physics.
    • A rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.

    This talk is based on the three manuscripts: arXiv:2307.01181, arXiv:2310.01169, arXiv:2310.05787, which are joint works with A. Bandeira, Tim Kunisky, Shahar Mendelson and Elliot Paquette.

  • Seminars

    Seminars Colloquia & Seminar
    4/4/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    12/01/2024
  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    CMSA Probability Seminar 12.07.22

    Probability Seminar

    Note location change: Science Center Room 300H

    Speaker: Lior Alon (MIT)

    Title: Fourier quasicrystals and stable polynomials

    Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A, such that the sum of exp(iat), over a in A, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial, and the measures associated with each irreducible factor is either supported on an arithmetic progression, or its support has a bounded intersection with any arithmetic progression. Finally, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix.

    Based on joint work with Pravesh Kothari.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 11.16.22

    Probability Seminar

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Probability Seminar 11.09.22 (1)

    Probability Seminar

    Speaker: Hugo Falconet (Courant Institute, NYU)

    Title: Liouville quantum gravity from random matrix dynamics

    Abstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary group at equilibrium, then the measures $|det(U_t – e^{i theta}|^gamma dt dtheta$ converge to the 2d LQG measure with parameter $gamma$, in the limit of large dimension. This extends results from Webb, Nikula and Saksman for fixed time. The proof relies on a new method for Fisher-Hartwig asymptotics of Toeplitz determinants with real symbols, which extends to multi-time settings. I will explain this method and how to obtain multi-time loop equations by stochastic analysis on Lie groups.

    Based on a joint work with Paul Bourgade.

     

  • Seminars

    Seminars Colloquia & Seminar
    3/14/2019 General Relativity Seminar

    3:30 pm-4:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Social Science Application Forum

    3:30 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2-23-2018 RM & PT Seminar

    3:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Quantum Matter
    3:30 pm-5:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-04.22.22-1583x2048-1

    Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Jinyoung Park (NYU)

    Title: Thresholds

    Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a “threshold.” Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

  • Probability Seminar
    3:30 pm-4:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Catherine Wolfram (MIT)

    Title: Large deviations for the 3D dimer model

    Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is different from two, explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.

     

  • Seminars

    Seminars Colloquia & Seminar
    10/15/2019 Spacetime Seminar

    3:30 pm-5:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02-29-2016 Mathematical Physics Seminar

    3:31 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-01-2016 Geometric Analysis Seminar

    3:32 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    3:33 pm-5:33 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-04.28.22-1583x2048-1

    Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole,  length of the shortest closed geodesic on X.

  • Seminars

    Seminars Colloquia & Seminar
    03-10-2016 Evolution Equations Seminar

    3:34 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
    3:34 pm
    12/01/2024-03/30/2017

    The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Photos of the event can be found on CMSA’s Blog.

     Participants:

    Organizers:

    * This event is sponsored by CMSA Harvard University.

    Schedule:

    Monday, March 27

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
    10:00am – 11:00amKieron Burke, University of California, Irvine

    The density functionals machines can learn

    11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

    Tuesday, March 28

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amRyan Adams, HarvardTBA
    10:00am – 11:00amGábor Csányi, University of Cambridge

    Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

     Wednesday, March 29 

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
    10:00am – 11:00amJörg Behler, University of GöttingenTBA
    11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
    4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

    CMSA Colloquium

    Thursday, March 30

    TimeSpeakerTitle
    8:30am – 9:00amBreakfast
    9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
    10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
    11:00am – 1:00pmLunch Break
    1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-09-2016 Random Matrix & Probability Theory

    3:35 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    3:35 pm-4:35 pm
    12/01/2024

    Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Fluid Dynamics Seminar

    3:35 pm
    12/01/2024
  • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
    3:35 pm-3:36 pm
    12/01/2024-01/13/2017

    The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    Titles, abstracts and schedule will be provided nearer to the event.

    Participants:

    Dan Freed, UT Austin

    Anton Kapustin, California Institute of Technology

    Alexei Y. Kitaev, California Institute of Technology

    Greg Moore, Rutgers University

    Constantin Teleman, University of Oxford

    Organizers:

    Mike Hopkins, Shing-Tung Yau

    * This event is sponsored by CMSA Harvard University.

  • Interdisciplinary Science Seminar
    3:36 pm-5:36 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.05.2022-1583x2048

    Abstract: Although everyone talks about AI + healthcare, many people were unaware of the fact that there are two possible outcomes of the collaboration, due to the inherent dissimilarity between the two giant subjects. The first possibility is healthcare-leads, and AI is for building new tools to make steps in healthcare easier, better, more effective or more accurate. The other possibility is AI-leads, and therefore the protocols of healthcare can be redesigned or redefined to make sure that the whole infrastructure and pipelines are ideal for running AI algorithms.

    Our system Qianfang belongs to the second category. We have designed a new kind of clinic for the doctors and patients, so that it will be able to collect high quality data for AI algorithms. Interestingly, the clinic is based on Traditional Chinese Medicine (TCM) instead of modern medicine, because we believe that TCM is more suitable for AI algorithms as the starting point.

    In this talk, I will elaborate on how we convert TCM knowledge into a modern type-safe large-scale system, the mini-language that we have designed for the doctors and patients, the interpretability of AI decisions, and our feedback loop for collecting data.

    Our project is still on-going, not finished yet.Bio: Yang Yuan is now an assistant professor at IIIS, Tsinghua. He finished his undergraduate study at Peking University in 2012. Afterwards, he received his PhD at Cornell University in 2018, advised by Professor Robert Kleinberg. During his PhD, he was a visiting student at MIT/Microsoft New England (2014-2015) and Princeton University (2016 Fall). Before joining Tsinghua, he spent one year at MIT Institute for Foundations of Data Science (MIFODS) as a postdoc researcher. He now works on AI+Healthcare, AI Interpretability and AI system.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-23-2016 Random Matrix & Probability Theory

    3:37 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Geometric Models for Sets of Probability Measures

    3:38 pm-5:38 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-05.12.22-1583x2048

    Abstract: Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models.  In this setting, we often are unable to match individual data points but rather need to deduce relationships between entire weighted and unweighted point sets. In this talk, I will summarize our team’s recent efforts to apply geometric techniques to problems in this space, using tools from optimal transport and spectral geometry. Motivated by applications in dataset comparison, time series analysis, and robust learning, our work reveals how to apply geometric reasoning to data expressed as probability measures without sacrificing computational efficiency.

  • Seminars
    3:38 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
    3:40 pm-3:41 pm
    12/01/2024-05/02/2017

    The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

    This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Speakers:

    Orr Ashenberg, Fred Hutchinson Cancer Research Center

    John Barton, Massachusetts Institute of Technology

    Simona Cocco, Laboratoire de Physique Statistique de l’ENS

    Sean Eddy, Harvard University

    Efthimios Kaxiras, Harvard University

    Michael Laub, Massachusetts Institute of Technology

    Debora S. Marks, Harvard University

    Govind Menon, Brown University

    Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

    Andrew Murray, Harvard University

    Ilya Nemenman, Emory College

    Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

    Dave Thirumalai, University of Texas at Austin

    Martin Weigt, IBPS, Université Pierre et Marie Curie

    Matthieu Wyart, EPFL

    More speakers will be confirmed soon.

     

    Schedule:

    (Please click here for a downloadable version of the schedule.)

    Please note that the schedule for both days is currently tentative and is subject to change.

    May 1, Monday

    TimeSpeakerTopic
    9:00-10:00amSean EddyTBA
    10:00-11:00amMike LaubTBA
    11:00am-12:00pmIlya NemenmanTBA
    May 2, Tuesday
    TimeSpeakerTopic
    9:00-10:00amOrr AshenbergTBA
    10:00-11:00amDebora MarksTBA
    11:00am-12:00pmMartin WeigtTBA
    4:30pm-5:30pmSimona CoccoCMSA Colloquia

     

    May 3, Wednesday
    TimeSpeakerTopic
    9:00-10:00amAndrew MurrayTBA
    10:00-11:00amMatthieu WyartTBA
    11:00am-12:00pmRémi MonassonTBA

     

    May 4, Thursday
    TimeSpeakerTopic
    9:00-10:00amDavid ThirumalaiTBA
    10:00-11:00amChris SanderTBA
    11:00am-12:00pmJohn BartonTBA

     

    Organizers:

    Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

    * This event is sponsored by CMSA Harvard University.

  • Seminars

    Seminars Colloquia & Seminar
    03-07-2016 Mathematical Physics Seminar

    3:41 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    2-26-2018 Mathematical Physics Seminar

    3:42 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-11-2016 Random Matrix & Probability Theory

    3:42 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-08-2016 Geometric Analysis Seminar

    3:44 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
    3:44 pm
    12/01/2024-05/04/2017

    In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

    To register for this event, please click here.

    Confirmed speakers:

    The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

    For a list of lodging options convenient to the Center, please see our recommended lodgings page.

    Schedule:

    The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

    June 5, Monday (Full day)

    TimeSpeakerTopic
    8:30am – 9:0amBreakfast
    9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
    10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

    Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

    Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

    Video

    3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

    Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

    4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
    Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

    June 6, Tuesday (Full day)

    TimeSpeakerTopic
    8:30am – 9:00amBreakfast
    9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

    Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

    Video

    10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

    Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

    Video

    11:30am – 1:30pmBreak
    1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

    Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

    Video

    3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

    Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

    Video


  • Seminars

    Seminars Colloquia & Seminar
    03-21-2016 Mathematical Physics Seminar

    3:46 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-24-2016 Evolution Equations Seminar

    3:47 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: 2017 Big Data Conference
    3:47 pm
    12/01/2024-08/19/2017
    1 Oxford Street, Cambridge MA 02138

    The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

    The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

    Confirmed Speakers:

     

    Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

    • Jörn Boehnke, Harvard University
    • Nikhil Naik, Harvard University
    • Bradly Stadie, Open AI, University of California, Berkeley

     

    Conference Schedule

    A PDF version of the schedule below can also be downloaded here.

    August 18, Friday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amMohammad Akbarpour

    Video

    Title: Information aggregation in overlapping generations and the emergence of experts

    Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

    9:40 am – 10:20 amLucas Janson

    Video

    Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

    Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

    Slides

    10:20 am – 10:50 amBreak
    10:50 pm – 11:30 pmNoureddine El Karoui

    Video

    Title: Random matrices and high-dimensional statistics: beyond covariance matrices

    Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

    11:30 am – 12:10 pmNikhil Naik

    Video

    Title: Understanding Urban Change with Computer Vision and Street-level Imagery

    Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

    (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

    12:10 pm – 12:25 pmVideo #1

    Video #2

    Data Science Lightning Talks
    12:25 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmTracy Ke

    Video

    Title: A new SVD approach to optimal topic estimation

    Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

    We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

    For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

    2:10 pm – 2:50 pmAlbert-László Barabási

    Video

    Title: Taming Complexity: From Network Science to Controlling Networks

    Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

     

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmMarena Lin

    Video

    Title: Optimizing climate variables for human impact studies

    Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

    4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

    Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

    4:40 pm – 5:20 pmTze Leung Lai

    Video

    Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

    Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

    August 19, Saturday (Full day)

    TimeSpeakerTopic
    8:30 am – 9:00 amBreakfast
    9:00 am – 9:40 amNatesh Pillai

    Video

    Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

    Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

    9:40 am – 10:20 amRavi Jagadeesan

    Video

    Title: Designs for estimating the treatment effect in networks with interference

    Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

    10:20 am – 10:50 amBreak
    10:50 am – 11:30 amAnnie Liang

    Video

    Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

    Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

    11:30 am – 12:10 pmZak Stone

    Video

    Title: TensorFlow: Machine Learning for Everyone

    Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

    12:10 pm – 1:30 pmLunch
    1:30 pm – 2:10 pmJann Spiess

    Video

    Title: (Machine) Learning to Control in Experiments

    Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

    2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

    Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
    We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

    2:50 pm – 3:20 pmBreak
    3:20 pm – 4:00 pmHau-Tieng Wu

    Video

    Title: When Medical Challenges Meet Modern Data Science

    Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

    4:00 pm – 4:40 pmSifan Zhou

    Video

    Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

    Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

     

    To view photos and video interviews from the conference, please visit the CMSA blog.

     

  • Seminars

    Seminars Colloquia & Seminar
    12-07-2015 Mathematical Physics Seminar

    3:49 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    03-22-2016 Geometric Analysis Seminar

    3:51 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: CMSA/Math Fall Gathering
    4:00 pm-6:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA
    Friday, Sep 22, 2022
    4:00 pm
    All CMSA and Math affiliates are invited.
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Quantum cohomology as a deformation of symplectic cohomology

    4:00 pm-5:00 pm
    12/01/2024
    20211124_Nick-Sheridan_RESCHEDULED_poster

    Abstract: Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.

  • Math Science Lectures in Honor of Raoul Bott

    Math Science Lectures in Honor of Raoul Bott Event
    Math Science Lectures in Honor of Raoul Bott: Mina Aganagic

    4:00 pm
    12/01/2024-04/10/2019
    1 Oxford Street, Cambridge MA 02138

    On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

    The lectures took place in Science Center, Hall C

    “Two math lessons from string theory”

    Lecture 1:

     

     

     

     

     

    April 9, 2019

    Title: “Lesson on Integrability”

     

    Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

    Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

    Lecture 2:

     

     

     

     

     

    April 10, 2019

    Title: “Lesson on Knot Categorification”

     

    Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

    The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

    This talk is mostly based on joint work with Andrei Okounkov.

     

    Information about last year’s Math Science Bott lecture can be found here. 

    Aganagic

  • Seminars
    4:00 pm-5:00 pm
    12/01/2024

  • Topological Quantum Matter Seminar
    4:00 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Yizhuang You, UC San Diego

    Title: Symmetric Mass Generation
    Abstract: Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Higher rank DT theory from rank 1

    4:00 pm-5:00 pm
    12/01/2024
    20211110_Richard-Thomas_poster

    Abstract: Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

  • Yip Lecture Series

    Yip Lecture Series Event
    Yip Annual Lecture

    4:00 pm-5:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

    The lecture was held from 4:00-5:00pm in Science Center, Hall A.

    Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
  • Math Science Lectures in Honor of Raoul Bott
    4:00 pm-5:30 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    Fibered ribbon knots vs. major 4D conjectures

    Location: Harvard University Science Center Hall A & via Zoom webinar

    Dates: Feb 20 & 22, 2024

    Time: 4:00-5:30 pm

    Directions and Recommended Lodging

    Registration is required.

    Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin and a Clay Research Fellow.

    This will be the fourth annual Math Science Lecture Series held in Honor of Raoul Bott.

    Talk topic:  Fibered ribbon knots vs. major 4D conjectures

    Feb. 20, 2024

    Title: Fibered ribbon knots and the Poincaré conjecture

    Abstract: A knot is “fibered” if its complement in S^3 is the total space of a bundle over the circle, and ribbon if it bounds a smooth disk into B^4 with no local maxima with respect to radial height. A theorem of Casson-Gordon from 1983 implies that if a fibered ribbon knot does not bound any fibered disk in B^4, then the smooth 4D Poincaré conjecture is false. I’ll show that unfortunately (?) many ribbon disks bounded by fibered knots are fibered, giving some criteria for extending fibrations and discuss how one might search for non-fibered examples.

    Feb. 22, 2024

    Title: Fibered knots and the slice-ribbon conjecture

    Abstract: The slice-ribbon conjecture (Fox, 1962) posits that if a knot bounds any smooth disk into B^4, it also bounds a ribbon disk. The previously discussed work of Casson-Gordon yields an obstruction to many fibered knots being ribbon, yielding many interesting potential counterexamples to this conjecture — if any happy to bound a non-ribbon disk. In 2022, Dai-Kong-Mallick-Park-Stoffregen showed that unfortunately( ?) many of these knots don’t bound a smooth disk into B^4 and thus can’t disprove the conjecture. I’ll show a simple alternate proof that a certain interesting knot (the (2,1)-cable of the figure eight) isn’t slice and discuss remaining open questions. This talk is joint with Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.

     

    Talk Chair: Cliff Taubes (Harvard Mathematics)

    Moderator: Freid Tong (Harvard CMSA)


    Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.

  • Probability Seminar
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Probability Seminar

    Speaker: Wei-Kuo Chen (University of Minnesota)

    Title: A Gaussian convexity for logarithmic moment generating function

    Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy.

     

  • Quantum Matter
    4:00 pm-5:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.18.22-1583x2048-1

    Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045

  • Seminars

    Seminars Colloquia & Seminar
    10/16/2019 Colloquium

    4:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    3/12/2020 Colloquium

    4:00 pm-5:00 pm
    12/01/2024
  • Colloquium
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    02CMSA Colloquium 03.02.2023

    Speaker: Erez Urbach, Weizmann Institute of Science

    Title: The string/black hole transition in anti de Sitter space

    Abstract: String stars, or Horowitz-Polchinski solutions, are string theory saddles with normalizable condensates of thermal-winding strings. In the past, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux), their possible connection to small black holes in AdS, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model, and their relation to the deconfined phase of 3+1 pure Yang-Mills.

  • Colloquium
    4:00 pm
    12/01/2024
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Lagrangians and mirror symmetry in the Higgs bundle moduli space

    4:00 pm-5:00 pm
    12/01/2024

    Abstract: The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed, but  also to open up new features involving finite-dimensional algebras which are deformations of cohomology algebras. Answering some of the questions raised  requires revisiting basic constructions of stable bundles on curves.

  • Probability Seminar
    4:00 pm-5:00 pm
    12/01/2024
    Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

    Probability Seminar

    Speaker: Marius Lemm, University of Tuebingen

    Title: Light cones for open quantum systems
    Abstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely, if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound on the slope of this light cone (i.e., on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang.

     

  • Topological Quantum Matter Seminar
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Roman Geiko, UCLA

    Title: Homotopy classes of loops of Clifford unitaries

    Abstract: We study Clifford locality-preserving unitaries and stabilizer Hamiltonians by means of Hermitian K-theory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two short-range entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu.  https://arxiv.org/abs/2306.09903.

  • Joint Harvard-CUHK-YMSC Differential Geometry
    4:00 pm-5:00 pm
    12/01/2024

    Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class S[A1]. I will describe the resulting geometric structures using a kind of complexified Hitchin system parameterising bundles on curves equipped with pencils of flat connections.

  • Topological Quantum Matter Seminar
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Daniele Guerci, Flatiron Institute

    Title: Chern Mosaic and ideal bands in helical trilayer graphene

    Abstract: In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat bands features the superposition of a Chern -1 and a Chern 2 bands described by the superposition of two lowest Landau level [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [3]. Building on this knowledge, I will discuss the properties of the zero-modes at higher magic angles.

    [1] Y.Mao,D.Guerci,C.Mora, PRB 107, 125423 (2023) [Editors’ Suggestion]

    [2] D.Guerci,Y.Mao,C.Mora, arXiv:2305.03702 (2023)

    [3] D.Guerci,Y.Mao,C.Mora, arXiv:2308.02638 (2023)

  • Colloquium
    4:00 pm-5:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    CMSA Colloquium 10.05.22 (1)

    Colloquium

    Please note this colloquium will be held at a special time:  4:00-5:00 pm.

    Speaker: Subir Sachdev (Harvard)

    Title: Quantum statistical mechanics of charged black holes and strange metals
    Abstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.
    Slides: cmsa22
  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    03-28-2016 Mathematical Physics Seminar

    4:08 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-06-2016 Random Matrix & Probability Theory

    4:10 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    03-30-2016 Random Matrix & Probability Theory Seminar

    4:11 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:12 pm-5:12 pm
    12/01/2024

    Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    Fast Point Transformer

    4:13 pm-5:13 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-06.02.2022-1583x2048-1

    Abstract: The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine the local predictions together. However, this scheme inevitably involves additional stages for pre- and post-processing and may also degrade the final output due to predictions in a local perspective. This talk introduces Fast Point Transformer that consists of a new lightweight self-attention layer. Our approach encodes continuous 3D coordinates, and the voxel hashing-based architecture boosts computational efficiency. The proposed method is demonstrated with 3D semantic segmentation and 3D detection. The accuracy of our approach is competitive to the best voxel-based method, and our network achieves 129 times faster inference time than the state-of-the-art, Point Transformer, with a reasonable accuracy trade-off in 3D semantic segmentation on S3DIS dataset.

    Bio: Jaesik Park is an Assistant Professor at POSTECH. He received his Bachelor’s degree from Hanyang University in 2009, and he received his Master’s degree and Ph.D. degree from KAIST in 2011 and 2015, respectively. Before joining POSTECH, He worked at Intel as a research scientist, where he co-created the Open3D library. His research interests include image synthesis, scene understanding, and 3D reconstruction. He serves as a program committee at prestigious computer vision conferences, such as Area Chair for ICCV, CVPR, and ECCV.

  • Seminars

    Seminars Colloquia & Seminar
    04-14-2016 Evolution Equations Seminar

    4:13 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-12-2016 Geometric Analysis Seminar

    4:14 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/11/2019 Special Seminar

    4:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Duality String Seminar, Thursdays

    4:15 pm-6:00 pm
    12/01/2024-10/12/2016

    The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

    For details, please visit the website.

    * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

  • Seminars

    Seminars Colloquia & Seminar
    03-31-2016 Evolution Equations Seminar

    4:15 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    4:15 pm-5:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    04-04-2016 Mathematical Physics Seminar

    4:20 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-05-2016 Geometric Analysis Seminar

    4:21 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-11-2016 Mathematical Physics Seminar

    4:22 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar
    4:23 pm-5:23 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-06.30.22-1583x2048-1

    Abstract: Entanglement is a type of correlation found in composite quantum systems, connected with various non-classical phenomena. Currently, entanglement plays a key role in quantum information applications such as quantum computing, quantum communication, and quantum sensing. In this talk the concept of entanglement will be introduced along with various methods that have been proposed to detect and quantify it. The fundamental role of entanglement in both quantum theory and quantum technology will also be discussed.

    Bio: Spyros Tserkis is a postdoctoral researcher at Harvard University, working on quantum information theory. Before joining Harvard in Fall 2021, he was a postdoctoral researcher at MIT and the Australian National University. He received his PhD from the University of Queensland.

  • Seminars

    Seminars Colloquia & Seminar
    04-07-2016 Evolution Equations Seminar

    4:24 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-06-2016 Seminar on General Relativity

    4:25 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-11-2016 Random Matrix & Probability Theory Seminar

    4:28 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-13-2016 General Relativity Seminar

    4:29 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Colloquium

    Speaker: Justin Moore (Cornell University)

    Title: Homology, higher derived limits, and set theory

    Abstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the “shape” of the space and can give counterintuitive information about its dimension. One remedy of this is to develop a homology theory based on approximating spaces by polyhedra, computing their homologies, and then taking a limit. This is the approach taken by Steenrod-Sitnikov homology and Lisica and Mardesic’s strong homology. Even within the class of locally compact second countable spaces though, the properties of these homology theories — and the higher derived limits which underly them — are dependent on axioms of set theory beyond ZFC. Recently it was shown that it is consistent with (and therefore independent of) ZFC that strong homology and Steenrod Sitnikov homology coincide in the class of locally compact second countable spaces — and therefore each of these homology theories enjoys the desirable properties of the other. These results also point to how we might develop variants of these homology theories which enjoy their desirable properties, but which are less sensitive to set theory. This is joint work with Nathaniel Bannister, Jeff Bergfalk, and Stevo Todorcevic.

  • Seminars

    Seminars Colloquia & Seminar
    04-20-2016 General Relativity Seminar

    4:30 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: CMSA/MATH Fall Gathering
    4:30 pm-6:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    CMSA/MATH Fall Gathering

    Friday, Sep 23, 2022
    4:30–6:00 pm
    All CMSA and Math affiliates are invited.
  • Seminars

    Seminars Colloquia & Seminar
    3/20/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/13/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Joel D. Hamkins (Notre Dame and Oxford)

    Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers

    Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually, and in the talk I shall begin slowly with some easy elementary observations. By the end, however, we shall engage with sophisticated ideas in descriptive set theory, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses, for example, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.

  • Colloquium
    4:30 pm
    12/01/2024
  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Cenke Xu (UCSB)

    Title: Quantum field theory approach to quantum information

    Abstract: We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement and decoherence. The Euclidean space-time path integral allows us to map this problem to a quantum field theory with (temporal) boundary or defects. We therefore investigate two types of quantum many-body systems with nontrivial boundary physics: quantum critical points, and states with nontrivial topology, such as Chern insulator and symmetry protected topological states. For example, we demonstrate that a Wilson-Fisher quantum critical point can be driven into an “extraordinary-log” phase after weak-measurement. Another example is that, we argue that a system with higher form symmetry may be driven to a self-dual phase transition under weak measurement.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Seth Koren (Notre Dame)

    Title: Non-invertible symmetries, leptons, quarks, and why multiple generations

    Abstract: Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof.  After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this theory works by virtue of the SM having the same numbers of colors and generations.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    2/20/2019 Colloquium

    4:30 pm-5:00 pm
    12/01/2024
  • Topological Quantum Matter Seminar
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Kaifeng Bu (Harvard University)

    Title: Quantum information: the interplay of mathematics and physics

    Abstract: I will provide an introduction to quantum information, which points to a new connection with experiment on the one hand, and a potential new area of mathematical analysis on the other. I will introduce two recent results about the application of this new area in quantum information: (1) a novel Quantum Central Limit Theorem (QCLT), and (2) a physically realizable protocol for testing and measuring quantum advantage. This talk is based on a collaboration with Arthur Jaffe, and Weichen Gu (PNAS120(25)2023, arXiv: 2302.08423, arXiv:2306.09292).

     

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Yu-Shen Lin (Boston University)

    Title: Gravitational Instantons

    Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk, we will discuss the Torelli theorem of gravitational instantons, how the cohomological invariants of a gravitational instanton determine them. As a consequence, this leads to a description of the moduli space of gravitational instantons.

  • Colloquium
    4:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    02/21/2020 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/20/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    11/25/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    Colloquium 12/4/2019

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    4:30 pm-5:00 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4/17/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Seminars
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Dana Bartosova (University of Florida)

    Title: What do topological dynamics, combinatorics, and model theory have in common?

    Abstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory.  Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front, however, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts, which is an AIMSQuaRE project with Džamonja, Patel, and Scow.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Jeff W. Lichtman (Harvard University)

    Title: The analytical challenges of connectomics

    Abstract: Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    2/14/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    1/30/2019 Colloquium

    4:30 pm
    12/01/2024
  • Topological Quantum Matter Seminar
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar

    Speaker: Liujun Zou (Perimeter Institute)

    Title: Landscape of quantum phases in quantum materials

    Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.

  • CMSA EVENT: CMSA/MATH Bi-Annual Gathering
    4:30 pm-6:00 pm
    12/01/2024
    20 Garden Street, Cambridge, MA 02138 USA

    On Friday, March 24th, 4:30PM – 6PM, the CMSA will host the CMSA/MATH Bi-Annual Gathering for Harvard CMSA and Math affiliates in the Common Room at 20 Garden Street, Cambridge MA 02138.

  • Seminars

    Seminars Colloquia & Seminar
    4/24/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Topological Quantum Matter Seminar
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Topological Quantum Matter Seminar

    Speaker: Bruno Mera, Instituto Superior Tecnico

    Title: Uniqueness of Landau levels and their analogs with higher Chern numbers

    Abstract: Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged par- ticle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this talk, using the Stone-von Neumann the- orem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions.

    Ref: Bruno Mera and Tomoki Ozawa. Uniqueness of Landau levels and their analogs with higher Chern numbers. arXiv:2304.00866, 2023. arXiv:2304.00866.

     

  • Colloquium
    4:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Matthew Foreman (UC Irvine)

    Title: Impossibility results in classical dynamical systems

    Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.

     

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Manuel Cortés-Izurdiaga (University of Malaga)

    Title:  Homotopy categories of rings: some properties and consequences in module categories

    Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the first step in studying other (algebraic) homotopy categories, such as those associated to a scheme. To study these categories, one can use results from the category of modules or the category of complexes. In the first part of the talk, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes, for a natural number N greater than or equal to 2, using some techniques from module categories, such us the deconstruction of a class of modules.

    Another approximation is to use other methods for studying homotopy categories, like those coming from triangulated categories. In some cases, the results obtained in homotopy categories imply some consequences in the category of modules. In the second part of the talk, we will see how to prove the existence of Gorenstein-projective precovers for some specific rings using this approach.

  • Seminars

    Seminars Colloquia & Seminar
    9/18/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/28/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    9/25/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Cameron Krulewski (MIT) and Leon Liu (Harvard)

    Title: A Long Exact Sequence in Symmetry Breaking

    Abstract: We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES).

    The mathematical backbone of the SBLES is the Smith homomorphism, which gives a family of maps between twisted bordism groups. Though many examples have been studied, we give the first completely general account of the Smith homomorphism. We lift it to a map of Thom

    spectra and identify the cofiber, producing a long exact sequence of twisted bordism groups; the SBLES is the Anderson dual of that long exact sequence. Our work develops further the theory of higher Berry phase and its bulk-boundary correspondence and serves as a new computational tool for classifying symmetry protected topological phases.

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Boaz Barak (Harvard)

    Title: On Provable Copyright Protection for Generative Model

    Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set.

    Roughly speaking, a generative model p is k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content.

    Joint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870

  • Quantum Matter
    4:30 pm-6:00 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Quantum Matter Seminar

    Speaker: Clay Córdova (U Chicago)

    Title: Anomalies of Non-Invertible Symmetries

  • Seminars

    Seminars Colloquia & Seminar
    10/3/2019 RM & PT Seminar

    4:30 pm-5:00 pm
    12/01/2024
  • Seminars
    4:30 pm-5:30 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    4/4/2019 Random Matrix and Probability Theory Seminar

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/9/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    10/2/2019 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars
    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Brian Williams (Boston University)

    Title: Koszul duality in QFT

    Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello, Gaiotto, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory.

     

  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Sean Cox, Virginia Commonwealth University

    Title: Predicting non-continuous functions

    Abstract: One of the strangest consequences of the Axiom of Choice is the following Hardin-Taylor 2008 result: there is a “predictor” such that for every function $f$ from the reals to the reals—even nowhere continuous $f$—the predictor applied to $f \restriction (-\infty,t)$ correctly predicts $f(t)$ for *almost every* $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$-invariant predictors? Bajpai-Velleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular, do there exist analytic-invariant predictors? We have partially answered that question: assuming the Continuum Hypothesis (CH), the answer is “no”. Regarding other subgroups of Homeo^+(R), we have affirmative answers that rely solely on topological group-theoretic properties of the subgroup. But these properties are very restrictive; e.g., all known positive examples are metabelian. So there remain many open questions. This is joint work with Aldi, Buffkin, Cline, Cody, Elpers, and Lee.

  • Seminars

    Seminars Colloquia & Seminar
    3/11/2020 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Colloquium
    4:30 pm-5:30 pm
    12/01/2024
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Speaker: Xuwen Zhu (Northeastern)

    Title: Analysis of ALH* gravitational instantons

    Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.

  • Seminars

    Seminars Colloquia & Seminar
    4/15/2020 Colloquium

    4:30 pm-5:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Social Science Application Forum

    4:31 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:33 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-19-2016 Geometric Analysis Seminar

    4:33 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:34 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-18-2016 Mathematical Physics Seminar

    4:34 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-21-2016 Evolution Equations Seminar

    4:35 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:36 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-20-2016 Random Matrix & Probability Theory Seminar

    4:37 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-26-2016 Geometric Analysis Seminar

    4:38 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:39 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-25-2016 Mathematical Physics Seminar

    4:39 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    4:41 pm
    12/01/2024
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    04-27-2016 Random Matrix & Probability Theory Seminar

    4:42 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-27-2016 General Relativity Seminar

    4:44 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-28-2016 CMSA Special Seminar

    4:45 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    3/4/2020 Colloquium

    4:45 pm-5:45 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    04-28-2016 Evolution Equations Seminar

    4:46 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-04-2016 General Relativity Seminar

    4:48 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    04-29-2016 CMSA Special Seminar

    4:49 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    05-02-2016 Mathematical Physics Seminar

    4:50 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-05-2016 Evolution Equations Seminar

    4:51 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    05-25-2016 General Relativity Seminar

    4:52 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar
    4:54 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    4:56 pm-5:56 pm
    12/01/2024

    Abstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learning-based approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, data-hungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.

  • General Relativity Seminar
    4:58 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    4:59 pm-6:59 pm
    12/01/2024

    Abstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible, and after considerable work by many authors, it is generally conjectured by computer scientists that as the size of matrices becomes large, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk, no knowledge of algebraic geometry or representation theory will be needed.

  • CMSA EVENT: 2017 Ding Shum Lecture
    5:00 pm-6:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

    Learning as a Theory of Everything

    Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

     

  • Seminars

    Seminars Colloquia & Seminar
    2018 HMS Focused Lecture Series

    5:00 pm
    12/01/2024

    As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

    The schedule will be updated below.

    DateSpeakerTitle/Abstract
    January 23, 25, 30 and February 1 

    3-5pm

    *Room G10*

    Ivan Losev 

    (Northeastern)

    Title: BGG category O: towards symplectic duality 

    Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

    Approximate (optimistic) plan of the lectures:

    1) Preliminaries and BGG category O.

    2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

    3) Localization theorem continued. Soergel modules.

    4) Koszul algebras and Koszul duality for categories O.

    Time permitting: other instances of Symplectic duality.

    Prerequisites:

    Semi-simple Lie algebras and their finite dimensional representation theory.

    Some  Algebraic geometry. No prior knowledge of category O/ Geometric

    Representation theory is assumed.

    Scanned from a Xerox Multifunction Device

    February 27, 

    and March 1

    3-5pm

    Colin Diemer 

    (IHES)

    Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

    Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

    March 6 and 8 

    4-5pm

    Adam Jacob 

    (UC Davis)

    Title: The deformed Hermitian-Yang-Mills equation 

    Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

    March 6, 8, 13, 15 

    3-4pm

    Dmytro Shklyarov 

    (TU Chemnitz)

    Title: On categories of matrix factorizations and their homological invariants 

    Abstract: The talks will cover the following topics:

    1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

    2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

    3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

    April 10 & 12 

    3-4pm

    Mauricio Romo 

    (IAS)

    Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

    Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

    Lecture notes

    April 17, 19, 26 

    3-5pm

    Andrew  Harder 

    (University of Miami)

    Title: Perverse sheaves of categories on surfaces 

    Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

    I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

     

    May 15, 17 

    1-3pm

    Charles Doran 

    (University of Alberta)

    Lecture One:
    Title: Picard-Fuchs uniformization and Calabi-Yau geometry
    Abstract:
    Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
    Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

     

    Lecture Two:
    Title: Calabi-Yau fibrations: construction and classification
    Abstract:

    Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

    Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    05-11-2016 Random Matrix & Probability Theory Seminar

    5:00 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
    5:00 pm-6:00 pm
    12/01/2024

    Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Network Science: From the Online World to Cancer Genomics

    Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

     

  • Math Science Literature Lecture Series
    5:00 pm-6:30 pm
    12/01/2024
    Lecture_Sahai-pdf

    Amit Sahai  (UCLA)

    Title: Indistinguishability Obfuscation: How to Hide Secrets within Software

    Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way compiler” remained elusive for decades.

    In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running time) be indistinguishable to any efficient adversary. Leveraging the notion of punctured programming, introduced in our work with Waters in 2013, well over a hundred papers have explored the remarkable power of iO.

    We’ll then discuss the intense effort that recently culminated in our 2020 work with Jain and Lin, finally showing how to construct iO in such a way that, for the first time, we can prove the security of our iO scheme based on well-studied computational hardness conjectures in cryptography.

    Talk chair: Sergiy Verstyuk

    Video

  • Colloquium
    5:00 pm
    12/01/2024
  • CMSA EVENT: 2023 Ding Shum Lecture
    5:00 pm-6:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    Cynthia Dwork

    On March 21, 2023, the CMSA will host the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS and Microsoft Research).

    Time: 5:00-6:00 pm ET

    Location: Harvard University Science Center Hall D

    This event will be held in person and via Zoom webinar.

    Registration is required.

    In-person registration (link)

    Zoom Webinar registration (link)

    Title: Measuring Our Chances: Risk Prediction in This World and its Betters

    Abstract: Prediction algorithms score individuals, assigning a number between zero and one that is often interpreted as an individual probability: a 0.7 “chance” that this child is in danger in the home; an 80% “probability” that this woman will succeed if hired; a 1/3 “likelihood” that they will graduate within 4 years of admission. But what do words like “chance,” “probability,” and “likelihood” actually mean for a non-repeatable activity like going to college? This is a deep and unresolved problem in the philosophy of probability. Without a compelling mathematical definition we cannot specify what an (imagined) perfect risk prediction algorithm should produce, nor even how an existing algorithm should be evaluated. Undaunted, AI and machine learned algorithms churn these numbers out in droves, sometimes with life-altering consequences.

    An explosion of recent research deploys insights from the theory of pseudo-random numbers – sequences of 0’s and 1’s that “look random” but in fact have structure – to yield a tantalizing answer to the evaluation problem, together with a supporting algorithmic framework with roots in the theory of algorithmic fairness.

    We can aim even higher. Both (1) our qualifications, health, and skills, which form the inputs to a prediction algorithm, and (2) our chances of future success, which are the desired outputs from the ideal risk prediction algorithm, are products of our interactions with the real world. But the real world is systematically inequitable. How, and when, can we hope to approximate probabilities not in this world, but in a better world, one for which, unfortunately, we have no data at all? Surprisingly, this novel question is inextricably bound with the very existence of nondeterminism.

    Professor Cynthia Dwork is Gordon McKay Professor of Computer Science at the Harvard University John A. Paulson School of Engineering and Applied Sciences, Affiliated Faculty at Harvard Law School, and Distinguished Scientist at Microsoft. She uses theoretical computer science to place societal problems on a firm mathematical foundation.

    Her recent awards and honors include the 2020 ACM SIGACT and IEEE TCMF Knuth Prize, the 2020 IEEE Hamming Medal, and the 2017 Gödel Prize.

    Talk Chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)
    Moderator: Faidra Monachou (Harvard CMSA)

    The 2020-2022 Ding Shum lectures were postponed due to Covid-19.


    Watch the Lecture on Youtube:

    https://youtu.be/wGpZE8QrCKY

  • CMSA EVENT: Noga Alon Public Talk, 9-7-17
    5:00 pm-6:00 pm
    12/01/2024

    Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

    Title: Graph Coloring: Local and Global

    Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

  • General Relativity Seminar
    5:02 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:02 pm-6:02 pm
    12/01/2024

    Abstract: Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the ““game” of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.

  • New Technologies in Mathematics Seminar
    5:03 pm-6:03 pm
    12/01/2024

    Abstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions, has allowed major progress on other related questions about M theory, and briefly discuss other applications in field theory and beyond.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-01-2016 Random Matrix & Probability Theory Seminar

    5:03 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    06-08-2016 Random Matrix & Probability Theory Seminar

    5:04 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:04 pm-6:04 pm
    12/01/2024

    Abstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size.

    We demonstrate the effectiveness of the SAT approach by presenting some recent successes, including the solution of the Boolean Pythagorean Triples problem, computing the fifth Schur number, and resolving the remaining case of Keller’s conjecture. Moreover, we constructed and validated a proof for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular, we discuss our progress on applying SAT solving techniques to the chromatic number of the plane (Hadwiger-Nelson problem), optimal schemes for matrix multiplication, an

  • Seminars

    Seminars Colloquia & Seminar
    07-12-2016 Chinese Economy Seminar

    5:06 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:07 pm-6:07 pm
    12/01/2024

    Speaker: Patrick Massot, Laboratoire de Mathématiques d’Orsay and CNRS

    Title: Why explain mathematics to computers?

    Abstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics, and I won’t assume any prior knowledge about formalization.

  • Seminars

    Seminars Colloquia & Seminar
    07-19-2016 Chinese Economy Seminar

    5:07 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    08-02-2016 China Gazetteer Seminar

    5:08 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-12-2016 Mathematical Physics Seminar

    5:10 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-19-2016 Mathematical Physics Seminar

    5:11 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:12 pm-6:12 pm
    12/01/2024
    CMSA-NTM-Seminar-11.03.21

    Abstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms.  This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers.  This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-21-2016 Random Matrix & Probability Theory Seminar

    5:13 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium
    5:15 pm-6:15 pm
    12/01/2024

    Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    4-23-2018 Math Physics

    5:15 pm
    12/01/2024

    No additional detail for this event.

  • Colloquium

    Colloquium Colloquia & Seminar
    2/13/2019 Colloquium

    5:15 pm-6:15 pm
    12/01/2024
  • Colloquium

    Colloquium Colloquia & Seminar
    3/27/2019 Colloquium

    5:15 pm-6:15 pm
    12/01/2024
  • Colloquium
    5:15 pm-6:15 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    4-16-2018 Social Science Applications Forum

    5:16 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:17 pm-6:17 pm
    12/01/2024
    CMSA-NTM-Seminar-12.01.21

    Abstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data.

    In terms of their “microscopic” definition, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem, analogous to criticality, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting, we will explain how the interactions induce representation learning.

    This talk is based on a book, The Principles of Deep Learning Theory, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.

  • Seminars

    Seminars Colloquia & Seminar
    4-20-2018 Social Science Applications Forum

    5:18 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:32 pm-6:32 pm
    12/01/2024
    CMSA-NTM-Seminar-12.08.21

    Abstract: Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured images produced by DALL-E. These large language models are impressive but also very inefficient and costly, which limits their applications and accessibility. We postulate that having an explicit hierarchical architecture is the key to Transformers that efficiently handle long sequences. To verify this claim, we first study different ways to upsample and downsample activations in Transformers so as to make them hierarchical. We use the best performing upsampling and downsampling layers to create Hourglass – a hierarchical Transformer language model. Hourglass improves upon the Transformer baseline given the same amount of computation and can yield the same results as Transformers more efficiently. In particular, Hourglass sets new state-of-the-art for Transformer models on the ImageNet32 generation task and improves language modeling efficiency on the widely studied enwik8 benchmark.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    09-26-16 Mathematical Physics Seminar

    5:32 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    Fluid Dynamics Seminar

    5:33 pm
    12/01/2024

    Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. Links to connect can be found in the schedule below once they are created. 

    In the Spring 2019 Semester, the Center of Mathematical Sciences and Applications will be hosting a seminar on Fluid Dynamics. The seminar will take place on Wednesdays from 3:00-4:00pm in CMSA G10.

    Spring 2020:

    DateSpeakerTitle/Abstract
    2/25/2020Keaton Burns, MITTitle: Flexible spectral simulations of low-Mach-number astrophysical fluids

    Abstract: Fluid dynamical processes are key to understanding the formation and evolution of stars and planets. While the astrophysical community has made exceptional progress in simulating highly compressible flows, models of low-Mach-number stellar and planetary flows typically use simplified equations based on numerical techniques for incompressible fluids. In this talk, we will discuss improved numerical models of three low-Mach-number astrophysical phenomena: tidal instabilities in binary neutron stars, waves and convection in massive stars, and ice-ocean interactions in icy moons. We will cover the basic physics of these systems and how ongoing additions to the open-source Dedalus Project are enabling their efficient simulation in spherical domains with spectral accuracy, implicit timestepping, phase-field methods, and complex equations of state.

    3/4/2020

    G02

    3/11/2020
    3/18/2020
    3/25/2020
    4/1/2020
    4/8/2020 G02
    4/15/2020
    4/22/2020
    4/29/2020

    G02

    5/6/2020
    5/13/2020

    Fall 2019:

    DateSpeakerTitle/Abstract
    9/18/2019Jiawei Zhuang (Harvard)Title: Simulation of 2-D turbulent advection at extreme accuracy with machine learning and differentiable programming

     Abstract: The computational cost of fluid simulations grows rapidly with grid resolution. With the recent slow-down of Moore’s Law, it can take many decades for 10x higher resolution grids to become affordable. To break this major barrier in high-performance scientific computing, we used a data-driven approach to learn an optimal numerical solver that can retain high-accuracy at much coarser grids. We applied this method to 2-D turbulent advection and achieved 4x effective resolution than traditional high-order flux-limited advection solvers. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The model can achieve near-peak FLOPs on CPUs and accelerators via convolutional filters.

    9/25/2019Yantao Yang (Peking University)Title: Double diffusive convection and thermohaline staircases 

    Abstract: Double diffusive convection (DDC), i.e. the buoyancy-driven flow with fluid density depending on two scalar components, is omnipresent in many natural and engineering environments. In ocean this is especially true since the seawater density is mainly determined by temperature and salinity. In upper water of both (sub-) tropical and polar oceans, DDC causes the intriguing thermohaline staircases, which consist of alternatively stacked convection layers and sharp interfaces with high gradients of temperature and salinity. In this talk, we will focus on the fingering DDC usually found in (sub-)tropical ocean, where the mean temperature and salinity decrease with depth. We numerically investigate the formation and the transport properties of finger structures and thermohaline staircases. Moreover, we show that multiple states exit for the exactly same global condition, and individual finger layers and finger layers within staircases exhibit very different transport behaviors.

    10/2/2019No talk
    10/9/2019Samuel Rudy (MIT)Title: Data-driven methods for discovery of partial differential equations and forecasting

    Abstract: A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for partial differential equations with or without parametric dependencies and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will also be discussed.​

    10/16/2019No talk
    10/23/2019Kimee Moore (Harvard)Title: Using magnetic fields to investigate Jupiter’s fluid interior

    Abstract: The present-day interior structure of a planet is an important reflection of the formation and subsequent thermal evolution of that planet. However, despite decades of spacecraft missions to a variety of target bodies, the interiors of most planets in our Solar System remain poorly constrained. In this talk, I will discuss how actively generated planetary magnetic fields (dynamos) can provide important insights into the interior properties and evolution of fluid planets. Using Jupiter as a case study, I will present new results from the analysis of in situ spacecraft magnetometer data from the NASA Juno Mission (currently in orbit about Jupiter). The spatial morphology of Jupiter’s magnetic field shows surprising hemispheric asymmetry, which may be linked to the dissolution of Jupiter’s rocky core in liquid metallic hydrogen. I also report the first definitive detection of time-variation (secular variation) in a planetary dynamo beyond Earth. This time-variation can be explained by the advection of Jupiter’s magnetic field by the zonal winds, which places a lower bound on the velocity of Jupiter’s winds at depth. These results provide an important complement to other analysis techniques, as gravitational measurements are currently unable to uniquely distinguish between deep and shallow wind scenarios, and between solid and dilute core scenarios. Future analysis will continue to resolve Jupiter’s interior, providing broader insight into the physics of giant planets, with implications for the formation of our Solar System.

    10/30/2019No Talk
    11/6/2019Federico Toschi (Eindhoven University of Technology)Title: Deep learning and reinforcement learning for turbulence

    Abstract: This talk tells two stories.

    Chapter 1: We investigate the capability of a state-of-the-art deep neural model at learning features of turbulent velocity signals. Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected. We consider turbulent velocity signals, spanning decades in Reynolds numbers, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of the turbulent signals, we focus on the fundamental question of whether a deep neural network (DNN) is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. Can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning?

    Chapter 2: Thermally driven turbulent flows are common in nature and in industrial applications. The presence of a (turbulent) flow can greatly enhance the heat transfer with respect to its conductive value. It is therefore extremely important -in fundamental and applied perspective- to understand if and how it is possible to control the heat transfer in thermally driven flows. In this work, we aim at maintaining a Rayleigh–Bénard convection (RBC) cell in its conductive state beyond the critical Rayleigh number for the onset of convection. We specifically consider controls based on local modifications of the boundary temperature (fluctuations). We take advantage of recent developments in Artificial Intelligence and Reinforcement Learning (RL) to find -automatically- efficient non-linear control strategies. We train RL agents via parallel, GPU-based, 2D lattice Boltzmann simulations. Trained RL agents are capable of increasing the critical Rayleigh number of a factor 3 in comparison with state-of-the-art linear control approaches. Moreover, we observe that control agents are able to significantly reduce the convective flow also when the conductive state is unobtainable. This is achieved by finding and inducing complex flow fields.

    11/13/2019

     

    2:10pm

    G02

    Martin Lellep (Philipps University of Marburg, Germany)Title: Predictions of relaminarisation in turbulent shear flows using deep learning

     

    Abstract: Given the increasing performance of deep learning algorithms in tasks such as classification during the last years and the vast amount of data that can be generated in turbulence research, I present one application of deep learning to fluid dynamics in this talk. We train a deep learning machine learning model to classify if turbulent shear flow becomes laminar a certain amount of time steps ahead in the future. Prior to this, we use a 2D toy example to develop an understanding how the performance of the deep learning algorithm depends on hyper parameters and how to understand the errors. The performance of both algorithms is high and therefore opens up further steps towards the interpretation of the results in future work.

    11/19/2019

    Tuesday

    3-4 pm

    Pierce Hall 209, 29 Oxford Street 

    Detlef Lohse (University of Twente)Title: Rayleigh vs. Marangoni Abstract: In this talk I will show several examples of an interesting and surprising competition between buoyancy and Marangoni forces. First, I will introduce the audience to the jumping oil droplet – and its sudden death – in a density stratified liquid consisting of water in the bottom and ethanol in the top : After sinking for about a minute, before reaching the equilibrium the droplet suddenly jumps up thanks to the Marangoni forces. This phenomenon repeats about 30-50 times, before the droplet falls dead all the sudden. We explain this phenomenon and explore the phase space where it occurs.

    Next, I will focus on the evaporation of multicomponent droplets, for which the richness of phenomena keeps surprising us. I will show and explain several of such phenomena, namely evaporation-triggered segregation thanks to either weak solutal Marangoni flow or thanks to gravitational effects. The dominance of the latter implies that sessile droplets and pending droplets show very different evaporation behavior, even for Bond number << 1. I will also explain the full phase diagram in the Marangoni number vs Rayleigh number phase space, and show where Rayleigh convections rolls prevail, where Marangoni convection rolls prevail, and where they compete.

    The research work shown in this talks combines experiments, numerical simulations, and theory. It has been done by and in collaboration with Yanshen Li, Yaxing Li, and Christian Diddens, and many others.

    11/20/2019Time: 3:00-3:35 pm

    Speaker:  Haoran Liu

    Title: Applications of Phase Field method: drop impact and multiphase turbulence 

    Abstract: Will a mosquito survive raindrop collisions? How the bubbles under a ship reduce the drag force? In nature and industry, flows with drops and bubbles exist everywhere. To understand these flows, one of the powerful tools is the direct numerical simulation (DNS). Among all the DNS methods, we choose the Phase Field (PF) method and develop some models based on it to simulate the complicated flows, such as flows with moving contact lines, fluid-structure interaction, ternary fluids and turbulence. In this talk, I will firstly introduce the advantages and disadvantages of PF method. Then, I will show its applications: drop impact on an object, compound droplet dynamics, water entry of an object and multiphase turbulence.


    Time: 3:35-4:10 pm

    Speaker:  Steven Chong

    Title: Confined Rayleigh-Bénard, rotating Rayleigh-Bénard, double diffusive convection and quasi-static magnetoconvection: A unifying view on their scalar transport enhancement 

    Abstract: For Rayleigh-Bénard under geometrical confinement, under rotation or the double diffusive convection with the second scalar component stabilizing the convective flow, they seem to be the three different canonical models in turbulent flow. However, previous research coincidentally reported the scalar transport enhancement in these systems. The results are counter-intuitive because the higher efficiency of scalar transport is bought about by the slower flow. In this talk, I will show you a fundamental and unified perspective on such the global transport behavior observed in the seemingly different systems. We further show that the same view can be applied to the quasi-static magnetoconvection, and indeed the regime with heat transport enhancement has been found. The beauty of physics is to understand the seemingly unrelated phenomena by a simplified concept. Here we provide a simplified and generic view, and this concept could be potentially extended to other situations where the turbulent flow is subjected to an additional stabilization.

    11/27/2019
    12/4/2019
    12/11/2019

     

    See previous seminar information here.
  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    09-28-2016 Random Matrix & Probability Theory Seminar

    5:35 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    5:35 pm-6:35 pm
    12/01/2024
    CMSA-NTM-Seminar-12.15.21

    Abstract: A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular, we will consider the gapped ground states and Gibbs states on low dimensional lattices, which are believed to exhibit ‘low complexity’ due to the widely studied area law behaviour. Here, we will see the crucial role of complexity-theoretic methods in progress on the ‘area law conjecture’ and in the development of efficient algorithms to classically simulate quantum many-body systems.

  • Seminars
    5:36 pm
    12/01/2024

    As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    DateSpeakerTitle/Abstract
    8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

    Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

    9/10/2018Dominic Else, MIT

    Video

    Title: Phases and topology in periodically driven (Floquet) systems

    Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

    9/17/2018Adrian Po, MIT

    Video

    Title: A modern solution to the old problem of symmetries in band theory

    Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

    9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

    Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

    10/1/2018Cancelled
    10/9/2018

    Tuesday

    3:00-4:30pm

    Sagar VijayTitle: Fracton Phases of Matter

    Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

    10/15/2018Ethan LakeTitle: A primer on higher symmetries

    Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

    10/22/2018

    Room G02

    Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

    Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

    10/29/2018Dominic Williamson, Yale

    Video

    Title: Symmetry and topological order in tensor networks

    Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

    11/13/2018

    Tuesday

    3:00-4:30pm

    Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
    11/19/2018X. G. Wen, MIT

    Video

    Title: A classification of 3+1D topological orders

    Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

    12/3/2018

    *Room G02*

    Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

    Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

    12/10/2018

    Room G02

    Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

    Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

    1/8/2019Lukasz Fidkowski, Univ. of Washington

    Video

    Title: Non-trivial quantum cellular automata in 3 dimensions

    Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

    3/18/2019Ari Turner, Technion

    Video

    Title:  Trapping Excitations at Phantasmagoric Wave Vectors

    Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

    4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

    Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

    4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

    Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

    4/16/2019

    Lyman 425

    1:30pm

    Xie Chen (Calthech)Title: Foliated Fracton Order

    Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

    4/24/2019

    10:30am

    Michael Freedman (Microsoft Station Q)

    Video

    Title: Quantum cellular automata in higher dimensions

    Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

    4/26/2019

    10:30am

    Maissam Barkeshli (University of Maryland)

    Video

    Title: Relative anomalies in (2+1)D symmetry enriched topological states

    Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

    5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

    Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

    5/9/2019

    10:30am

    Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

    Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

    5/28/2019

    10:30am

    Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

     

    Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

    7/18/2019Eslam Khalaf (Harvard)

    Title: Dynamical correlations in anomalous disordered wires

    Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
    The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
    The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
  • Seminars

    Seminars Colloquia & Seminar
    Spacetime and Quantum Mechanics Seminar

    5:38 pm
    12/01/2024

    As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

    DateSpeakerTitle/Abstract
    9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
    19/18/2019

    2:00pm

    G02

    Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
    9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

    Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

    Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

    These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

    Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

    9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
    10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
    10/10/2019

    3:30pm

    Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
    10/15/2019

    Tuesday

    3:30pm

     

    Sergey Fomin (Univ. of Michigan)

     

    Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
    10/18/2019

    Friday 

    G02

    Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
    10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
    11/1/2019

    SC 232

    1:30pm

    George Lusztig (MIT)Title: Total positivity in Springer fibres
    11/12/2019

    Tuesday

    G02

    3:30pm

     

    Pierpaolo Mastrolia (University of Padova)

    Title: Feynman Integrals and Intersection Theory
    11/14/2019

    G02

    Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
    11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
    11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
    12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

    Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

     12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
    12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

    Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/10/2018 Math-Physics Seminar

    5:41 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-05-2016 Random Matrix & Probability Theory Seminar

    5:41 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    5:42 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    3/14/2019 Random Matrix and Probability Theory Seminar

    5:45 pm
    12/01/2024
  • Seminars
    5:48 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    5:52 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    5:52 pm-6:52 pm
    12/01/2024

    Abstract:  Online marketplaces are the main engines of legal and illegal e-commerce, yet the aggregate properties of buyer-seller networks behind them are poorly understood. We analyse two datasets containing 245M transactions (16B USD)  between 2010 and 2021 involving online marketplaces: 28 dark web marketplaces (DWM), unregulated markets whose main currency is Bitcoin, and 144 product markets of one regulated e-commerce platform. We show how transactions in online marketplaces exhibit strikingly similar patterns of aggregate behavior despite significant differences in language, products, time, regulation, oversight, and technology. We find remarkable regularities in the distributions of (i) transaction amounts, (ii) number of transactions, (iii) inter-event times, (iv) time between first and last transactions. We then show how buyer behavior is affected by the memory of past interactions, and draw on these observations to propose a model of network formation able to reproduce the main stylised facts of the data. Our findings have important implications for understanding market power on online marketplaces as well as inter-marketplace competition.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/17/2018 Math-Physics Seminar

    5:53 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    9/24/2018 Math-Physics Seminar

    5:55 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    5:56 pm
    12/01/2024

    No additional detail for this event.

  • General Relativity Seminar
    5:59 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
    6:00 pm-6:01 pm
    12/01/2024-10/06/2017

    The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

    • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
    • Linear patterns in the primes (Green, Tao, Ziegler);
    • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
    • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

    Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

    • Constructions of pseudorandom objects (eg. extractors and expanders);
    • Constructions of extremal objects (eg. BCH codes);
    • Property testing (eg. testing linearity);
    • Algebraic algorithms (eg. matrix multiplication).

    The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

    Monday, October 2

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

    Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

    The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    10:20-11:00amCoffee Break 
    11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

    Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

    12:00-1:30pmLunch 
    1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

    Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

    Joint work with Sivakanth Gopi

    2:20-3:00pmCoffee Break 
    3:00-3:50pmFernando Shao

    Large deviations for arithmetic progressions

    Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

    4:00-6:00pmWelcome Reception

    Tuesday, October 3

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amEmanuele ViolaInterleaved group products

    Authors: Timothy Gowers and Emanuele Viola

    Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

    These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

    10:20-11:00amCoffee Break
    11:00-11:50amVsevolod LevOn Isoperimetric Stability

    Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

    As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

    We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

    12:00-1:30pmLunch
    1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

    Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

    Joint work with Venkata Gandikota and Badih Ghazi.

    2:20-3:00pmCoffee Break
    3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

    Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

    Wednesday, October 4

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast 
    9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

    Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

    Joint work with Thomas Bloom.

    10:20-11:00amCoffee Break 
    11:00-11:50amThomas BloomBounds on capsets via properties of spectra

    This is a continuation of the previous talk by Olof Sisask.

    12:00-1:30pmLunch 
    1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

    Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

    2:20-3:00pmCoffee Break
    3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

    Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

    When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

    Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

    Thursday, October 5

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

     Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

    I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

    Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

    10:20-11:00amCoffee Break
    11:00-11:50amJulia WolfStable arithmetic regularity

    The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

    Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

    This is joint work with Caroline Terry.

    12:00-1:30pmLunch 
    1:30-2:20pmWill Sawin

    Constructions of Additive Matchings

    Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

    2:20-3:00pmCoffee Break
    3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

    Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

    Friday, October 6

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

    Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

    Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

    10:20-11:00amCoffee Break
    11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

    Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

    This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

    Joint work with Hamed Hatami and Shachar Lovett

    12:00-1:30pmLunch
    1:30-2:20pmGuy Kindler

    From the Grassmann graph to Two-to-Two games

    Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

    The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

    These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

    This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

  • CMSA EVENT: Current Developments In Mathematics 2018
    6:00 pm-5:00 pm
    12/01/2024-11/17/2018
    CDM2018

    Current Developments in Mathematics 2018 Conference.

    Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

    Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

    Harvard University Science Center, Hall B

    Visit the conference page here 

  • New Technologies in Mathematics Seminar
    6:00 pm-7:00 pm
    12/01/2024
    CMSA-New-Technologies-Seminar-01.26.2022-1553x2048-1

    Abstract: Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the four colour theorem are among the most notable. Up until now there hasn’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk we will discuss the results of our recent Nature paper, where we worked together with top mathematicians to use machine learning to achieve two new results – proving a new connection between the hyperbolic and geometric structure of knots, and conjecturing a resolution to a 50-year problem in representation theory, the combinatorial invariance conjecture. Through these examples we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/01/2018 Math-Physics Seminar

    6:01 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
    6:02 pm
    12/01/2024-03/15/2018
    Fluid turbulence

    The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

    For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    List of registrants

    Speakers: 

  • General Relativity Seminar
    6:03 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/08/2018 Math-Physics Seminar

    6:04 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:05 pm-7:05 pm
    12/01/2024
    CMSA-NTM-Seminar-02.02.2022-2-1583x2048

    Abstract: In this talk, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry, it is possible to provide a principled view on such GNN architectural choices as positional encoding and graph rewiring as well as explain and remedy the phenomena of oversquashing and bottlenecks.

  • CMSA EVENT: Blockchain Conference
    6:05 pm
    12/01/2024-01/25/2018
    Blockchain

    On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

    https://youtu.be/FyKCCutxMYo

    List of registrants

    Photos

    Speakers: 

  • Seminars
    6:05 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    6:06 pm
    12/01/2024

    No additional detail for this event.

  • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
    6:07 pm
    12/01/2024-11/17/2017

    The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

    The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

    Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

    A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

    Confirmed participants include:

    Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

    Click here for a list of registrants.

    Monday, Nov. 13

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Jozsef Solymosi

     

    On the unit distance problem

    Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

     

    Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

    Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Andrew Hoon Suk

    Ramsey numbers: combinatorial and geometric

    Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Josh Zahl

    Cutting curves into segments and incidence geometry

    4:00-6:00pmWelcome Reception

    Tuesday, Nov. 14

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Péter Pál Pach

    Polynomials, rank and cap sets

    AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

    10:30-11:00amCoffee Break
    11:00-12:00pmJordan Ellenberg

    The Degeneration Method

    Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Larry GuthThe polynomial method in Fourier analysis

    Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

     

    2:30-3:00pm

    Coffee Break
    3:00-4:00pmOpen Problem

    Wednesday, Nov. 15

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

     

    Avi Wigderson

    The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

    Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

    In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

    In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

    This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

    I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

    (despite the fact that a random such tensor has rank quadratic in n).

    No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Venkat Guruswami

    Subspace evasion, list decoding, and dimension expanders

     Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

    Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

    This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

    (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

    12:00-1:30pmLunch
    1:30-2:30pm

     

    David Conlon

    Finite reflection groups and graph norms

    Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

     

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Laszlo Miklós Lovasz

    Removal lemmas for triangles and k-cycles.

    Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

    In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

    The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

    Thursday, Nov. 16

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Janos PachLet’s talk about multiple crossings

    Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Misha Rudnev

    Few products, many sums

    Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

    $$

    |A|^{10} \ll |A-A|^4|AA|^4

    $$

    to

    $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

    The other is the bound 

    $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

    12:00-1:30pmLunch
    1:30-2:30pm

    Video

    Adam Sheffer

    Geometric Energies: Between Discrete Geometry and Additive Combinatorics

    Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

    2:30-3:00pmCoffee Break
    3:00-4:00pm

    Video

    Boris Bukh

    Ranks of matrices with few distinct entries

    Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

    Friday, Nov. 17

    TimeSpeakerTitle/Abstract
    9:00-9:30amBreakfast
    9:30-10:30am

    Video

    Benny Sudakov

    Submodular minimization and set-systems with restricted intersections

    AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

    We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

    Joint work with M. Nagele and R. Zenklusen

    10:30-11:00amCoffee Break
    11:00-12:00pm

    Video

    Robert Kleinberg 

    Explicit sum-of-squares lower bounds via the polynomial method

    AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

    Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

    Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

    This is joint work with Sam Hopkins.

    12:00-1:30pmLunch

     

  • New Technologies in Mathematics Seminar
    6:07 pm-7:07 pm
    12/01/2024
    CMSA-NTM-Seminar-02.09.2022-1553x2048

    Abstract: Over the past several years, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning, leading to advances in natural language processing, computer vision, code synthesis, protein structure prediction, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet, there is at present limited principled understanding of the reasons for its success. In this talk, I’ll explain how attention mechanisms and Transformers work, and then I’ll share the results of a preliminary investigation into why they work so well. In particular, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions, with statistical generalization guarantees akin to sparse regression.

  • New Technologies in Mathematics Seminar
    6:09 pm-7:09 pm
    12/01/2024
    CMSA-NTM-Seminar-02.16.2022-1553x2048

    Abstract: Hyperbolic manifolds are a class of Riemannian manifolds that are important in mathematics and physics, playing a prominent role in topology, number theory, and string theory. Associated with a given hyperbolic metric is a sequence of numbers corresponding to the discrete eigenvalues of the Laplace-Beltrami operator. While these eigenvalues usually cannot be calculated exactly, they can be found numerically and must also satisfy various bounds. In this talk, I will discuss a new approach for finding numerical bounds on the eigenvalues of closed hyperbolic manifolds using general consistency conditions and semidefinite programming, inspired by the approach of the conformal bootstrap from physics. Although these bootstrap bounds follow from seemingly trivial consistency conditions, they are surprisingly strong and are sometimes almost saturated by actual manifolds; for example, one such bound implies that the first nonzero eigenvalue of a closed hyperbolic surface must be less than 3.83890, and this is very close to being saturated by a particular genus-2 surface called the Bolza surface. I will show how to derive this and other bounds and will discuss some possible future directions for this approach.

  • Special Seminar
    6:10 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:11 pm-6:12 pm
    12/01/2024-10/25/2016

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/10/2018 RM & PT Seminar

    6:11 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:11 pm-7:11 pm
    12/01/2024
    03.2.2022-1553x2048-1

    Abstract:  Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes, and prospects for RL and other techniques.

  • General Relativity Seminar
    6:12 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:13 pm-7:13 pm
    12/01/2024
    CMSA-NTM-Seminar-03.09.2022

    Abstract: We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time.
    We curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics, Chemical Engineering, Chemistry, Computer Science, Economics, Electrical Engineering, Materials Science, Mathematics, Mechanical Engineering, Nuclear Science, Physics, and Statistics.
    We generate new questions and use them in a Columbia University course, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations, again for the first time.
    Our approach consists of five steps:
    (i) Given course questions, turn them into programming tasks;
    (ii) Automatically generate programs from the programming tasks using a Transformer model, OpenAI Codex, pre-trained on text and fine-tuned on code;
    (iii) Execute the programs to obtain and evaluate the answers;
    (iv) Automatically explain the correct solutions using Codex;
    (v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.
    This work is a significant step forward in applying machine learning for education, automating a considerable part of the work involved in teaching.
    Our approach allows personalization of questions based on difficulty level and student backgrounds, and scales up to a broad range of courses across the schools of engineering and science.

    This is joint work with students and colleagues at MIT, Harvard University, Columbia University, Worcester Polytechnic Institute, and the University of Waterloo.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-03-16 Mathematical Physics Seminar

    6:13 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:14 pm-7:14 pm
    12/01/2024
    CMSA-NTM-Seminar-03.23.2022-1553x2048-1

    Abstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems,  without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark,  automatically solving multiple challenging problems drawn from high school olympiads.

  • Seminars

    Seminars Colloquia & Seminar
    10/15/2018 Topology Seminar

    6:14 pm
    12/01/2024

    No additional detail for this event.

  • New Technologies in Mathematics Seminar
    6:15 pm-7:15 pm
    12/01/2024
    CMSA-NTM-Seminar-03.30.2022-1583x2048-1

    Abstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this talk, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.

    Video

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/15/2018 Math Physics Seminar

    6:15 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-12-2016 Random Matrix & Probability Theory Seminar

    6:16 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:17 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-24-2016 Random Matrix & Probability Theory Seminar

    6:18 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:19 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10/30/2018 RM & PT Seminar

    6:19 pm
    12/01/2024

    No additional detail for this event.

  • Seminars
    6:20 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:22 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10/22/2018 Mathematical Physics Seminar

    6:24 pm
    12/01/2024
  • Member Seminar
    6:24 pm
    12/01/2024

    No additional detail for this event.

  • Member Seminar
    6:26 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:27 pm
    12/01/2024

    No additional detail for this event.

  • Member Seminar
    6:29 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:30 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:31 pm-7:31 pm
    12/01/2024

    Title: Naturalness and muon anomalous magnetic moment

    Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:32 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    6:34 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:34 pm-7:34 pm
    12/01/2024

    Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

    Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

  • Seminars
    6:36 pm
    12/01/2024

    No additional detail for this event.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-19-2016 Random Matrix & Probability Theory Seminar

    6:37 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:37 pm-7:37 pm
    12/01/2024

    Title: Cornering the universal shape of fluctuations and entanglement

    Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

    Ref: arXiv:2102.06223

  • Quantum Matter
    6:38 pm-7:38 pm
    12/01/2024

    Title: Quantum gravity from quantum matter

    Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    9/23/2021 Interdisciplinary Science Seminar

    6:40 pm-8:40 pm
    12/01/2024

    Title: The number of n-queens configurations

    Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

    Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

  • Member Seminar
    6:40 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-17-16 Mathematical Physics Seminar

    6:41 pm
    12/01/2024

    No additional detail for this event.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    10/7/2021 Interdisciplinary Science Seminar

    6:41 pm
    12/01/2024

    Title: SiRNA Targeting TCRb: A Proposed Therapy for the Treatment of Autoimmunity

    Abstract: As of 2018, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent, treatment options remain relatively poor, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness over time. Given this, new forms of therapy are needed. To this end, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted, novel means of therapy for the treatment of autoimmune disorders.

    This talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    10/14/2021 Interdisciplinary Science Seminar

    6:42 pm-8:42 pm
    12/01/2024

    Title: D3C: Reducing the Price of Anarchy in Multi-Agent Learning

    Abstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.

  • Quantum Matter
    6:44 pm-7:44 pm
    12/01/2024

    Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

    Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
    Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    10/21/2021 Interdisciplinary Science Seminar

    6:44 pm-8:44 pm
    12/01/2024

    Title: Mathematical resolution of the Liouville conformal field theory.

    Abstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David, Kupiainen, Rhodes, Vargas.

    Many works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable », the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras, representations of Virasoro algebras, the theory of conformal blocks). However, for Liouville Theory this was not done at the mathematical level by algebraic methods.

    I’ll explain how to combine probabilistic, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure, which is viewed as the space of fields, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space.

    This is joint work with A. Kupiainen, R. Rhodes and V. Vargas.

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    ARCH: Know What Your Machine Doesn’t Know

    6:45 pm-8:45 pm
    12/01/2024

    Speaker: Jie Yang, Delft University of Technology

    Title: ARCH: Know What Your Machine Doesn’t Know

    Abstract: Despite their impressive performance, machine learning systems remain prohibitively unreliable in safety-, trust-, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk, I will present our ongoing work on ARCH, a knowledge-driven, human-centered, and reasoning-based tool, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk, I will present several applications in which ARCH is currently being developed and tested, including health, finance, and smart buildings.

  • Quantum Matter
    6:46 pm-7:46 pm
    12/01/2024

    Title: Three-particle mechanism for pairing and superconductivity

    Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

    [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
    [2] V. Crepel and L. Fu, arXiv:2103.12060
    [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

  • Interdisciplinary Science Seminar

    Interdisciplinary Science Seminar
    11/4/21 CMSA Interdisciplinary Science Seminar

    6:46 pm-8:46 pm
    12/01/2024
    CMSA-Interdisciplinary-Science-Seminar-11.04.21-1583x2048-1

    Title: Exploring Invertibility in Image Processing and Restoration

    Abstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., image-to-video conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    10-26-2016 Random Matrix & Probability Theory Seminar

    6:46 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:47 pm-7:47 pm
    12/01/2024

    Title: The Hilbert Space of large N Chern-Simons matter theories

    Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

  • Member Seminar
    6:52 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-24-16 Mathematical Physics Seminar

    6:53 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    6:54 pm-7:54 pm
    12/01/2024

    Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

    Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

  • Random Matrix & Probability Theory Seminar

    Random Matrix & Probability Theory Seminar
    11-30-2016 Random Matrix & Probability Theory Seminar

    6:54 pm
    12/01/2024

    No additional detail for this event.

  • Special Seminar
    6:59 pm
    12/01/2024

    No additional detail for this event.

  • Yip Lecture Series

    Yip Lecture Series Event
    Third Annual Yip Lecture

    7:00 pm-8:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138

    Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

    Time: 7:00-8:00 pm ET

    Location: Harvard Science Center Hall A

    Registration is required.

    In-person Registration

    Zoom Webinar Registration

    Title: Black Holes: The Most Mysterious Objects in the Universe

    Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.

    Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.

    Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)

    Moderator: Daniel Kapec (Harvard CMSA)

    The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

     

    https://youtu.be/RpQhQ855WUY


    The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

  • Seminars
    7:00 pm
    12/01/2024

    No additional detail for this event.

  • Yip Lecture Series
    7:00 pm-8:00 pm
    12/01/2024
    1 Oxford Street, Cambridge MA 02138
    Yip2022_poster_web

    Harvard CMSA hosted the second annual Yip Lecture on April 4, 2022.

    The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.
    This year’s speaker was Avi Loeb (Harvard).

     

    Extraterrestrial Life

    Abstract: Are we alone? It would be arrogant to think that we are, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System, such as `Oumuamua.

    Abraham (Avi) Loeb is the Frank B. Baird, Jr., Professor of Science at Harvard University and a bestselling author (in lists of the New York Times, Wall Street Journal, Publishers Weekly, Die Zeit, Der Spiegel, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986), led the first international project supported by the Strategic Defense Initiative (1983–1988), and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books, including most recently, Extraterrestrial (Houghton Mifflin Harcourt, 2021), and nearly a thousand papers (with an h-index of 118) on a wide range of topics, including black holes, the first stars, the search for extraterrestrial life, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences, the American Physical Society, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade.

    Click here for Loeb’s commentaries on innovation and diversity.

    Website: https://www.cfa.harvard.edu/~loeb/

    See the Harvard Gazette article featuring Avi Loeb: “Oh, if I could talk to the aliens” published March 8, 2022.

    Prof. Loeb’s books:
    Extraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)
    Life in the Cosmos: From Biosignatures to Technosignatures (2021)

    Avil Loeb is the head of the Galileo Project at Harvard.


    The previous Yip Lecture featured Peter Galison (Harvard), who spoke on the EHT’s hunt for an objective image of a black hole.

  • Seminars
    7:03 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    10-31-16 Mathematical Physics Seminar

    7:05 pm
    12/01/2024

    No additional detail for this event.

  • Quantum Matter
    7:30 pm-9:00 pm
    12/01/2024
  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
    CMSA-QMMP-02.09.2022-1544x2048-1

    Speaker: Yuji Tachikawa (Kavli IPMU, U Tokyo)

    Title: On the absence of global anomalies of heterotic string theories

    Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.

    In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.

    The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.

  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
    CMSA-QMMP-02.02.2022-1544x2048

    Title: Kramers-Wannier-like duality defects in higher dimensions

    Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

  • Quantum Matter
    8:00 pm-9:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/15/2020 Quantum Matter Seminar

    8:30 pm-10:00 pm
    12/01/2024
  • Quantum Matter
    8:30 pm-10:00 pm
    12/01/2024
    CMSA-QMMP-Seminar-04.13.22-1583x2048-1

    Youtube Video

    Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.

    We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.

    We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.

    Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.

  • Quantum Matter
    8:30 pm-10:30 pm
    12/01/2024
    CMSA-QMMP-Seminar-05.18.22-1583x2048-1

    Speaker: Linhao Li (ISSP, U Tokyo)

    Title: Boundary conditions and LSM anomalies of conformal field theories in 1+1 dimensions

    Abstract: In this talk, we will study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state which is invariant under a symmetry, then the CFT can be gapped with a unique ground state by adding the corresponding gapping potential. This means that the symmetry of the CFT is anomaly free. Using this approach, we will systematically deduce the anomaly-free conditions for various types of CFTs with several different symmetries. When the symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis type ingappability of the system. Our results are consistent with, where available, known results in the literature. Moreover, we extend the discussion to other symmetries including spin groups and generalized time-reversal symmetries. As an application, we propose 1d LSM theorem involving magnetic space group symmetries on the lattice. The extended LSM theorems apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and chiral three-spin interactions.

  • Quantum Matter
    8:30 pm-10:00 pm
    12/01/2024

    Speaker: Nima Arkani-Hamed (IAS Princeton)

    Title: UV/IR and Effective Field Theory

  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Tropical disk counts

    8:30 pm-9:30 pm
    12/01/2024

    Abstract: (joint with S. Venugopalan)  I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan)  which is an open analog of the twenty-seven lines.  As an application, I will explain why the Floer cohomology of such tropical fibers is well-defined; this is a generalization fo a result of Fukaya-Oh-Ohta-Ono for toric varieties.

  • Quantum Matter
    8:30 pm-9:30 pm
    12/01/2024
    CMSA-QMMP-03.10.2022-1544x2048-1-1

    Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field.

    This work is based on arxiv: 2201.11681

  • Mathematical Physics Seminar

    Mathematical Physics Seminar
    12/10/2018 Mathematical Physics Seminar

    8:42 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/10/2018 Topology Seminar

    8:43 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    12/12/2018 Hodge Seminar

    8:43 pm
    12/01/2024

    No additional detail for this event.

  • Mathematical Physics Seminar
    8:45 pm
    12/01/2024

    No additional detail for this event.

  • Seminars

    Seminars Colloquia & Seminar
    1/16/2019 Hodge Seminar

    8:46 pm
    12/01/2024

    No additional detail for this event.

  • Fluid Dynamics Seminar

    Fluid Dynamics Seminar
    4/3/2019 Fluid Dynamics Seminar

    8:54 pm
    12/01/2024

    No additional detail for this event.

  • Program
    9:27 pm
    12/01/2024-12/31/2021

    The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications. This program is funded by the Simons Foundation.

    Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model).

    We envision that our goal of proving HMS in full generality can be accomplished by combining three main viewpoints:

    1. categorical algebraic geometry and non-commutative (nc) spaces: in this language, homological mirror symmetry is the statement that the same nc-spaces can arise either from algebraic geometry or from symplectic geometry.
    2. the Strominger-Yau-Zaslow (SYZ) approach, which provides a global geometric prescription for the construction of mirror pairs.
    3. Lagrangian Floer theory and family Floer cohomology, which provide a concrete path from symplectic geometry near a given Lagrangian submanifold to an open domain in a mirror analytic space.

    The Center of Mathematical Sciences and Applications is hosting the following short-term visitors for an HMS focused semester:

    • Jacob Bourjaily (Neils Bohr Institute)  4/1/2018 – 4/14/2018
    • Colin Diemer (IHES)  2/25/2018 – 3/10/2018
    • Charles Doran (University of Alberta) 5/13/2018 – 5/25/2018
    • Baohua Fu (Chinese Academy of Sciences)  4/15/2018 – 4/28/2018
    • Andrew Harder (University of Miami)  4/15/2018 – 4/28/2018
    • Shinobu Hosono (Gakushuin University) 2/25/2018 – 3/10/2018
    • Adam Jacob (UC Davis) 3/5/2018 – 3/16/2018
    • Tsung-Ju Lee (National Taiwan University) 4/18/2018 – 5/13/2018
    • Ivan Loseu (Northeastern University) 1/21/2018 – 2/3/2018
    • Cheuk-Yu Mak (Cambridge University) 4/1/2018 – 4/15/2018
    • Daniel Pomerleano (Imperial College) 3/19/2018 – 3/23/2018
    • Mauricio Romo (Tsinghua University) 4/1/2018 – 4/18/ 2018
    • Emanuel Scheidegger (Albert Ludwigs University of Freiburg) 2/22/2018 – 3/22/2018
    • Dmytro Shklyarov (Technische Universität Chemnitz) 3/4/2018 – 3/17/2018
    • Alan Thompson (University of Cambridge) 4/15/2018 – 4/21/2018
    • Weiwei Wu (University of Georgia) 4/27/2018 – 5/6/2018
    • Matt Young (Chinese University of Hong Kong) 1/15/2018 – 2/9/2018
    • Jeng-Daw Yu (National Taiwan University) 4/2/2018 – 4/6/2018
    • Minxian Zhu (Yau Mathematical Sciences Center, Tsinghua University) 1/ 22/2018 – 2/25/2018

    As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester.  Click here for information.

    The Collaboration will include two workshops hosted by The Center. The workshops will take place January 10-13, 2018  and April 5-7, 2018 at CMSA. Click here for more information.

  • Seminars

    Seminars Colloquia & Seminar
    7/13/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    7/27/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/8/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/16/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Seminars

    Seminars Colloquia & Seminar
    6/22/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Joint Harvard-CUHK-YMSC Differential Geometry

    Joint Harvard-CUHK-YMSC Differential Geometry
    Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds

    9:30 pm-10:30 pm
    12/01/2024

    Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

  • Seminars

    Seminars Colloquia & Seminar
    7/20/2020 Geometry and Physics Seminar

    9:30 pm-10:30 pm
    12/01/2024
  • Program
    9:32 pm
    12/01/2024-12/31/2021

    The methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example, the first topological states of matter discovered were the integer quantum Hall states. The two dimensional integer quantum Hall effect was characterized by an integral number which can be understood as a Chern number of the Berry phase. Chern numbers are topological invariants that play an important role in different areas of mathematics. More recently, new topological states of matter known as topological insulators and topological superconductors have been realized theoretically and experimentally. The characterization of new phases of matter using topological invariants has allowed for a better understanding and even predictions of new phases of matter. The use of topology could lead to the discovery of new electronic, photonic, and ultracold atomic states of matter previously unknown. The concrete problems in the physical phenomena could inspire new developments in the study of topological invariants in mathematics.

    Here is a list of the scholars participating in this program.

  • Program
    9:35 pm
    12/01/2024-12/31/2021

    A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as
    cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs, using tools such as random walk theory and harmonic analysis.

     

    Here is a list of the scholars participating in this program.

  • Program
    9:36 pm
    12/01/2024-12/31/2021

    In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory, general relativity, and quantum many-body theory.

    String theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as dramatic progress in old branches.

    Several examples from the recent past exemplifying this synergy include the prediction from string theory of mirror symmetry, a highly unexpected mathematical equivalence between distinct pairs of Calabi-Yau manifolds. This fueled exciting developments in algebraic, enumerative and symplectic geometry. At the same time the realization of string theory as a phenomenologically viable physical theory depends crucially on detailed mathematical properties of these manifolds. In Einstein’s theory of general relativity the proofs of the positive energy theorem and the stability of flat spacetime were accompanied by fundamental new results in functional analysis, differential geometry and minimal surface theory. In the coming decades we expect many more important discoveries to arise from the interface of mathematics and physics. The Cheng Fund will foster these efforts.

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

    NameTentative Visiting Dates
    Po-Ning Chen2/1/15-4/30/15
    Hong-Jian He3/5/15-5/5/15
    Monica Guica12/1/14-3/15/15
    Amer Iqbal1/8/15-4/8/15
    Suvrat Raju2/25/15-5/25/15
    Mithat Ünsal9/1/15-12/31/15
  • Program
    9:37 pm
    12/01/2024-12/31/2021

    Most physical phenomena, from the gravitating universe to fluid dynamics, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations.

    The subject underwent rapid developments in the last century and foundational results were established. Compared to linear equations, the difficulty of solving nonlinear equations is of a different order of magnitude and the methods employed in solving them are also much more diversified. To this date, it is an active field with recent exciting discoveries and renewed interests, and several long standing problems seem to be within reach. The special year aims to spur activity in this subject, to provide a natural setting for the most cutting edge results to be communicated, and to facilitate interaction among researchers of different backgrounds.

    During the year, there will be two weekly seminar programs.  Each program participants will be asked to give a talk on geometric analysis, or the evolution of equations, hyperbolic equations, and fluid dynamics.   

    Seminar on Geometric Analysis

    Seminar on Evolution Equations

    Seminar on General Relativity

    Concluding Conference on Nonlinear Equations Program

    Mini-School on Nonlinear Equations, Dec. 2016

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

    NameHome InstitutionTentative Visiting Dates
    Stefano BianchiniSISSA04/01/2016 – 05/31/2016
    Lydia BieriUniversity of Michigan02/01/2016 – 04/30/2016
    Albert ChauUniversity of British Columbia02/26/2016 – 05/26/2016
    Binglong ChenSun Yat-sen University09/01/2015 – 11/30/2015
    Qingtao ChenETHZ (Swiss Federal Institute of Technology in Zurich)03/17/2016 – 04/04/2016
    Piotr ChruscielUniversity of Vienna03/01/2016 – 05/30/2016
    Fernando Coda MarquesPrinceton University04/25/2016 – 04/29/2016 05/23/2016 – 05/27/2016
    Mihalis DafermosPrinceton University04/01/2016 – 04/30/2016
    Camillo De LellisUniversity of Zurich02/01/2016 – 4/30/2016
    Michael EichmairUniversity of Vienna03/21/2016 – 04/01/2016
    Felix FinsterUniversitat Regensburg09/20/2015 – 10/20/2015 03/20/2016 – 04/20/2016
    Xianfeng David GuSUNY at Stony Brook04/01/2016 – 04/30/2016
    Zheng-Cheng GuPerimeter Institute for Theoretical Physics08/15/2015 – 09/15/2015
    Pengfei GuanMcGill University10/10/2015 – 10/17/2015
    Xiaoli HanTsinghua University01/20/2016 – 04/19/2016
    Thomas HouCalifornia Institute of Technology11/01/2016 – 11/30/2016
    Feimin HuangChinese Academy of Sciences02/15/2016 – 04/15/2016
    Xiangdi HuangChinese Academy of Sciences09/10/2015 – 12/10/2015
    Tom IlmanenETH Zurich10/19/2015 – 12/18/2015
    Niky KamranMcGill Univeristy04/04/2016 – 04/08/2016
    Nicolai KrylovUniversity of Minnesota11/01/2015 – 11/30/2015
    Junbin LiSun Yat-sen University02/01/2016 – 04/30/2016
    Yong LinRenmin University of China02/01/2016 – 03/31/2016
    Andre NevesImperial College London4/25/2016 – 4/29/2016; 5/23/2016 – 5/27/2016
    Duong H. PhongColumbia University04/08/2016 – 04/10/2016
    Ovidiu SavinColumbia University10/15/2015 – 12/14/2015
    Richard SchoenStanford University03/21/2016 – 03/25/2016
    Mao ShengUniversity of Science and Technology of China01/15/2016 – 01/28/2016
    Valentino TosattiNorthwestern University02/01/2016 – 04/15/2016
    John TothMcGill University04/04/2016 – 04/08/2016
    Chung-Jun TsaiNational Taiwan University05/01/2016 – 05/08/2016
    Tai-Peng TsaiUniversity of British Columbia03/20/2016 – 05/31/2016
    Li-Sheng TsengUC Irvine02/08/2016 – 02/19/2016; 04/27/2016 – 05/11/2016
    Chun Peng WangJilin University02/01/2016 – 04/30/2016
    Xu-Jia WangAustralian National University04/01/2016 – 05/31/2016
    Ben WeinkoveNorthwestern University02/28/2016 – 03/18/2016
    Sijue WuUniversity of Michigan04/01/2016 – 04/30/2016
    Chunjing XieShanghai Jiao Tong University09/08/2015 – 12/07/2015
    Zhou Ping XinThe Chinese University of Hong Kong10/01/2015 – 11/30/2015
    Hongwei XuZhejiang University09/01/2015 – 11/30/2015
    Peng YeUniversity of Illinois at Urbana-Champaign11/15/2015 – 11/22/2015
    Pin YuTshinghua University09/07/2015 – 12/10/2015
    Yi ZhangFudan University01/18/2016 – 05/31/2016
  • Program
    9:39 pm
    12/01/2024-12/18/2014

    arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

    Here is a partial list of the mathematicians who are participating in this program

  • Program
    9:44 pm
    12/01/2024-12/28/2013

    During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

    As part of the Program, the CMSA will be hosting two workshops:

    .

    Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

    Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
    NameTentative Visiting Dates

    Jason Alicea

    11/12/2018-11/16/2018
    Maissam Barkeshli4/22/2019 – 4/26/2019
    Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

    Lukasz Fidkowski

    1/7/2019-1/11/2019

    Zhengcheng Gu

    8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

    Yin Chen He

    10/14/2018-10/27/2018
    Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

    Michael Levin

    3/11/2019-3/15/2019
    Yuan-Ming Lu4/29/2019-6/01/2019

    Adam Nahum

    4/2/2019- 4/19/2019

    Masaki Oshikawa

    4/22/2019-5/22/2019
    Chong Wang 10/22/2018-11/16/2018

    Juven Wang

    4/1/2019-4/16/2019
    Cenke Xu 8/26/2018-10/1/2018

    Yi-Zhuang You

    4/1/2019-4/19/2019

    Mike Zaletel

    5/1/2019-5/10/2019
  • Program
    9:45 pm-9:46 pm
    12/01/2024-12/31/2010

    During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

    Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

    In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

    In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

    The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

    A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

    A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

  • Program
    9:48 pm
    12/01/2024-12/31/2010

    Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

    Organizers:

    .

    Workshops:

     

    Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

  • Program
    9:49 pm
    12/01/2024-12/23/2010

    The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

    A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


    Directors:


    Shing-Tung Yau (Harvard University)

    Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


    Professor Bong Lian (Brandeis University)

    BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


    Denis Auroux (Harvard University)

    AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
    Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




    Senior Personnel:

    Artan Sheshmani (Harvard CMSA)

    unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

    Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

    An Huang (Brandeis University)

    unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

    An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



    Siu Cheong Lau (Boston University)
    unnamed

    The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

    Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


    Affiliates:

    • Netanel Rubin-Blaier (Cambridge)
    • Kwokwai Chan (Chinese University of Hong Kong)
    • Mandy Cheung (Harvard University, BP)
    • Chuck Doran (University of Alberta)
    • Honsol Hong (Yonsei University)
    • Shinobu Hosono (Gakushuin University, Japan)
    • Conan Leung (Chinese University of Hong Kong)
    • Yu-shen Lin (Boston University)
    • Hossein Movassati (IMPA Brazil)
    • Arnav Tripathhy (Harvard University, BP)

     

    Postdocs:

    • Dennis Borisov
    • Tsung-Ju Lee
    • Dingxin Zhang
    • Jingyu Zhao
    • Yang Zhou

    Jobs:

    Postdoctoral Fellowship in Algebraic Geometry

    Postdoctoral Fellowship in Mathematical Sciences

     

    To learn about previous programming as part of the Simons Collaboration, click here.

  • More events
    • Quantum Matter
      12:00 am-1:30 pm
      12/01/2024-03/19/2021
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-9-2018 Math Physics Seminar
      12:00 am
      12/01/2024
    • Program
      All day
      12/01/2024-03/29/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Arithmetic Quantum Field Theory Program

      To receive email updates and program announcements, visit this link to sign up for the CMSA Arithmetic Quantum Field Theory Program mailing list.

      Dates: Feb. 5–Mar. 29, 2024

      Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138

      Directions to CMSA

      Organizers:

      This program will feature a weekly seminar series, workshops, and a conference.

      The object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions.

      On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions.

      The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions. Conversely, we will explore potential geometric and physical consequences of arithmetic ideas, for example, the Langlands correspondence theory of L-functions for 3-manifolds.


      Schedule

      The first week of the program will feature several lecture series aimed at a broad local community of mathematicians and physicists, aiming to introduce the main ideas underlying our program and help establish a common reference point.

      The program will host a weekly seminar series on Fridays.

      The speakers will be selected with the aim of covering a wide panorama of the subjects over the course of the program.

      The program will conclude with a week-long Conference on Arithmetic Quantum Field Theory March 25–29, 2024.


      AQFT Youtube Playlist

      Lecture series

      All lectures take place in Room G10, Harvard CMSA, 20 Garden Street Cambridge.

      Week 1: Feb. 5–9, 2024

      Abstract: In this lecture series we will introduce some of the themes underlying the CMSA program on Arithmetic Quantum Field Theory taking place this winter and the upcoming conference March 25-29, 2024.

      Some of the themes we plan to discuss include:

      Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.

      The setup of arithmetic topology as a bridge between the background of QFT to that of arithmetic (both “global” and “local”), including the “middle realm” of positive characteristic function fields.

      Questions and structures in arithmetic that have been / might be amenable to inspiration from QFT, in particular the theory of L-functions and the Langlands program.

      Schedule

       

      Monday, Feb. 5, 2024  
      11:00 am – 12:00 pm Minhyong KimArithmetic topology and field theory (Slides part 1 pdf)
      1:30 – 2:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
      2:30 – 3:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      Wednesday, Feb. 7, 2024  
      11:00 am – 12:00 pmMinhyong KimArithmetic topology and field theory (Slides part 2 pdf)
      2:30 – 3:30 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
      Thursday, Feb.8, 2024  
      2:30 – 3:30 pmMinhyong KimArithmetic topology and field theory (Slides part 3 pdf)
      4:00 – 5:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      Friday, Feb. 9, 2024  
      1:00 – 2:00 pmBrian WilliamsAlgebraic quantum field theory (Lecture Notes)
      2:00 – 3:00 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      3:30 – 4:30 pmDavid Ben-ZviThe Langlands program via arithmetic QFT
      Monday, Feb. 26, 2024
      1:00 – 2:00 pmOmer Offen (Brandeis)Period integrals of automorphic forms and the residue method
      Tuesday, Feb. 27, 2024
      2:00 – 3:00 pmWei Zhang (MIT)Shtuka special cycles and their generating series
      Friday, March 1, 2024
      11:00 am – 12:00 pmChen Wan (Rutgers Newark)Some examples of the relative Langlands duality
      2:00 – 3:00 pmPeng Shan (Tsinghua)Skein algebras and quantized Coulomb branches
      Thursday, March 7, 2024
      1:30 – 2:30 pmAn Huang (Brandeis)Tate’s thesis and p-adic strings
      3:00 – 4:00 pmJohn Francis (Northwestern)Integrating braided categories over 3-manifolds
      Friday, March 8, 2024
      1:00 – 2:00 pmDihua Jiang (U Minnesota)Shalika Periods: Functoriality and Arithmetic
      Friday, March 15, 2024
      11:45 – 1:00 pmBaiying Liu (Purdue)Recent progress on certain problems related to local Arthur packets of classical groups
      2:15 – 3:30 pmTasho Kaletha (Michigan)Covers of reductive groups and functoriality
      Monday, March 18, 2024
      1:00 – 3:00 pmXinwen Zhu (Stanford)The tame categorical local Langlands correspondence (Slides)
      4:30 – 5:30 pmNatalie Paquette (U  Washington)Koszul duality & twisted holography for asymptotically flat spacetimes (CMSA)
      Wednesday, March 20, 2024
      11:00 – 12:15 pmStephen D. Miller (Rutgers)What 4-graviton scattering amplitudes had to say about the unitary dual
      Friday, March 22, 2024
      1:45 – 3:00 pmJayce Getz (Duke)The Poisson summation conjecture and the fiber bundle method
      3:30 – 4:30 pmTBATBA

       


      Program Visitors

      • Mina Aganagic, University of California, Berkeley
      • Anne-Marie Aubert, Institut de Mathématiques de Jussieu-Paris Rive Gauche, March 15-29
      • Clark Barwick, University of Edinburgh, February 19-March 15
      • Alexander Braverman, Perimeter Institute
      • Alejandra Castro, Cambridge University, March 25-29
      • YoungJu Choie, Pohang University of Science and Technology, February 12-16; March 22-28
      • John Francis, Northwestern University, March 1-14
      • David Gaiotto, Perimeter Institute, March 25-29
      • Jayce Getz, Duke University, March 18-22
      • Ezra Getzler, Northwestern University, March 11-22
      • Sam Gunningham, Montana State University, February 9-12
      • Sarah Harrison, Northeastern University
      • Dihua Jiang, University of Minnesota, February 29-March 9
      • Tasho Kaletha, University of Michigan, March 12-20
      • Minhyong Kim, University of Edinburgh, February 1-29
      • Axel Kleinschmidt, Max Planck Institute for Gravitational Physics, Potsdam, March 18-28
      • Kim Klinger-Logan, Kansas State University, March 25-29
      • Kobi Kremnitzer, Oxford University, March 25-29
      • Baiying Liu, Purdue University, March 13-16
      • Steven Miller, Rutgers University
      • Greg Moore, Rutgers University, February 5-9
      • David Nadler, University of California, Berkeley, March 17-30
      • Bảo Châu Ngô, University of Chicago, March 25-29
      • George Pappas, Michigan State University, March 25-29
      • Daniel Persson, Chalmers Institute of Technology, March 25-29
      • Sam Raskin, Yale University, March 26-29
      • Yiannis Sakellaridis, Johns Hopkins University, March 18-22
      • Peng Shan, Tsinghua University, February 12-April 14
      • Akshay Venkatesh, Institute for Advanced Study
      • Roberto Volpato, University of Padova, February 4-10
      • Chen Wan, Rutgers University, February 29-March 9
      • Fei Yan, Brookhaven National Laboratory, March 18-29
      • Xinwen Zhu, Stanford University

       

    • CMSA EVENT: Big Data Conference 2021
      All day
      12/01/2024

      On August 24, 2021, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The 2021 Big Data Conference took place virtually on Zoom.

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
      • Sergiy Verstyuk, CMSA, Harvard University

      Speakers:

      Time (ET; Boston time)SpeakerTitle/Abstract
      9:00AMConference OrganizersIntroduction and Welcome
      9:10AM – 9:55AMAndrew Blumberg, University of Texas at AustinTitle: Robustness and stability for multidimensional persistent homology

      Abstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However, for many data sets, it is very natural to consider multiple filtrations, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.

      10:00AM – 10:45AMKatrina Ligett, The Hebrew University of JerusalemTitle: Privacy as Stability, for Generalization

      Abstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity, via a connection to the notion of differential privacy. In this talk, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open.

      Joint work with: Christopher Jung (UPenn), Seth Neel (Harvard), Aaron Roth (UPenn), Saeed Sharifi-Malvajerdi (UPenn), and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020

      10:50AM – 11:35AMHima Lakkaraju, Harvard UniversityTitle: Towards Reliable and Robust Model Explanations

      Abstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP, and also introduce novel methods to address some of these vulnerabilities. More specifically, I will first demonstrate that these methods are brittle, unstable, and are vulnerable to a variety of adversarial attacks. Then, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.

      11:40AM – 12:25PMMoran Koren, Harvard CMSATitle: A Gatekeeper’s Conundrum

      Abstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e., ignore her private information with some probability).

      12:25PMConference OrganizersClosing Remarks
    • CMSA EVENT: Mathematics in Science: Perspectives and Prospects
      All day
      12/01/2024-10/28/2023
      1 Oxford Street, Cambridge MA 02138
      Mathematics in Science: Perspectives and Prospects

      A showcase of mathematics in interaction with physics, computer science, biology, and beyond.

      October 27–28, 2023

      Location: Harvard University Science Center Hall D & via Zoom.

      Directions and Recommended Lodging

      Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

      Youtube Playlist

       

      Speakers

      Organizers

      • Michael R. Douglas (Harvard CMSA)
      • Dan Freed (Harvard Math & CMSA)
      • Mike Hopkins (Harvard Math)
      • Cumrun Vafa (Harvard Physics)
      • Horng-Tzer Yau (Harvard Math)

      Schedule

      Friday, October 27, 2023

      2:00–3:15 pmGreg Moore (Rutgers)

      Title: Remarks on Physical Mathematics

      Abstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting, I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet, so I don’t know how it will end any more than you do.

      Slides (PDF)

      3:15–3:45 pmBreak
      3:45–5:00 pmBernd Sturmfels (MPI Leipzig)

      Title: Algebraic Varieties in Quantum Chemistry

      Abstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.

      Slides (PDF)

       

      Saturday, October 28, 2023

      9:00 amBreakfast
      9:30–10:45 amMike Freedman (Harvard CMSA)

      Title: ML, QML, and Dynamics: What mathematics can help us understand and advance machine learning?

      Abstract: Vannila deep neural nets DNN repeatedly stretch and fold. They are reminiscent of the logistic map and the Smale horseshoe.  What kind of dynamics is responsible for their expressivity and trainability. Is chaos playing a role? Is the Kolmogorov Arnold representation theorem relevant? Large language models are full of linear maps. Might we look for emergent tensor structures in these highly trained maps in analogy with emergent tensor structures at local minima of certain loss functions in high-energy physics.

      Slides (PDF)

      10:45–11:15 amBreak
      11:15 am–12:30 pm
      via Zoom
      Nima Arkani-Hamed (IAS)

      Title: All-Loop Scattering as A Counting Problem

      Abstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model, the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

      12:30–2:00 pmLunch break
      2:00–3:15 pmConstantinos Daskalakis (MIT)

      Title: How to train deep neural nets to think strategically

      Abstract: Many outstanding challenges in Deep Learning lie at its interface with Game Theory: from playing difficult games like Go to robustifying classifiers against adversarial attacks, training deep generative models, and training DNN-based models to interact with each other and with humans. In these applications, the utilities that the agents aim to optimize are non-concave in the parameters of the underlying DNNs; as a result, Nash equilibria fail to exist, and standard equilibrium analysis is inapplicable. So how can one train DNNs to be strategic? What is even the goal of the training? We shed light on these challenges through a combination of learning-theoretic, complexity-theoretic, game-theoretic and topological techniques, presenting obstacles and opportunities for Deep Learning and Game Theory going forward.

      Slides (PDF)

      3:15–3:45 pmBreak
      3:45–5:00 pmAlison Etheridge (Oxford)

      Title: Modelling hybrid zones

      Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection, spatial structure, and, if time permits, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection.

      Slides (PDF)

       


      Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to mathsci2023@cmsa.fas.harvard.edu no later than October 9, 2023.

      Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV.

       

    • Holiday
      All day
      12/01/2024

      Holiday: Friday after Thanksgiving

      The CMSA will be closed on Friday, November 25, 2022.

    • Seminars
      Seminars Colloquia & Seminar
      1/27/2020 Math Physics Seminar
      12:00 am-1:00 pm
      12/01/2024
    • CMSA EVENT: Quantum Matter Workshop
      All day
      12/01/2024
      Layer-2-600x338

      Please note: this workshop has been postponed to a later date. Details will be posted to this page when they are available.

      Throughout the summer, scheduled speakers for the Quantum Matter Workshop will give talks on Zoom for the Quantum Matter/Condensed Matter seminar.

      The CMSA will be hosting our second workshop on Quantum Matter. Both of these workshops are part of our program on Quantum Matter in Mathematics and Physics. The first workshop took place in December 2019, and was extremely successful, attracting participants worldwide. Learn more about the first workshop here.

       

      Organizers: Du Pei, Ryan Thorngren, Juven Wang, Yifan Wang, and Shing-Tung Yau.

      Speakers:

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-16-2018 Mathematical Physics Seminar
      12:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/7/2018 Hodge Seminar
      1:30 am-3:00 pm
      12/01/2024
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Some remarks on contact Calabi-Yau 7-manifolds
      3:00 am-4:00 am
      12/01/2024

      Abstract: In geometry and physics it has proved useful to relate G2 and Calabi-Yau geometry via circle bundles. Contact Calabi-Yau 7-manifolds are, in the simplest cases, such circle bundles over Calabi-Yau 3-orbifolds. These 7-manifolds provide testing grounds for the study of geometric flows which seek to find torsion-free G2-structures (and thus Ricci flat metrics with exceptional holonomy). They also give useful backgrounds to examine the heterotic G2 system (also known as the G2-Hull-Strominger system), which is a coupled set of PDEs arising from physics that involves the G2-structure and gauge theory on the 7-manifold. I will report on recent progress on both of these directions in the study of contact Calabi-Yau 7-manifolds, which is joint work with H. Sá Earp and J. Saavedra.

    • Colloquium
      5:00 am
      12/01/2024

      No additional detail for this event.

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Arthur Jaffe (Harvard University)

      Title: Is relativity compatible with quantum theory?

      Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.”  Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed.

      Talk chair: Zhengwei Liu

      Video

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Edward Witten (IAS)

      Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions

      Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification.

      Talk chair: Cliff Taubes

      Video

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Nigel Hitchin (University of Oxford)

      Title: Michael Atiyah: Geometry and Physics

      Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists.

      Talk chair: Peter Kronheimer

      Video

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Alain Connes (Collège de France)

      Title: Noncommutative Geometry, the Spectral Aspect

      Abstract: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function.

      Talk chair: Peter Kronheimer

      Video 

    • CMSA EVENT: Workshop on Quantum Information
      8:00 am-6:07 pm
      12/01/2024-04/24/2017
      banner-image-1

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 23-24, 2018. In the days leading up to the conference, the American Mathematical Society will also be hosting a sectional meeting on quantum information on April 21-22. You can find more information here.

      Register for the event here.

      The following speakers are confirmed:

    • Math Science Literature Lecture Series
      8:00 am-9:00 am
      12/01/2024
      Lecture-Series-Don-pdf

      Donald Rubin (Harvard)

      Title: Why do some universities have separate departments of statistics? And are they all anachronisms, destined to follow the path of other dinosaurs?

      Video | Slides

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Yuri Manin (Max Planck Institute for Mathematics)

      Title: Homotopy spectra and Diophantine equations

      Abstract: For a long stretch of time in the history of mathematics, Number Theory and Topology formed vast, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC)  that contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory, named after Diophantus of Alexandria (about 250 BC). Topology was born much later, but arguably, its cousin — modern measure theory, — goes back to Archimedes, author of Psammites (“Sand Reckoner”), who was approximately a contemporary of Diophantus. In modern language, Archimedes measures the volume of observable universe by counting the number of small grains of sand necessary to fill this volume. Of course, many qualitative geometric models and quantitative estimates of the relevant distances precede his calculations. Moreover, since the estimated numbers of grains of sand are quite large (about $10^{64}$), Archimedes had to invent and describe a system of notation for large numbers going far outside the possibilities of any of the standard ancient systems. The construction of the first bridge between number theory and topology was accomplished only about fifty years ago: it is the theory of spectra in stable homotopy theory. In particular, it connects $Z$, the initial object in the theory of commutative rings, with the sphere spectrum $S$. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this talk based upon the authors’ (Yu. Manin and M. Marcolli) joint research project, I suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.

      Talk chair: Michael Hopkins

      Slides | Video

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrations
      8:00 am-9:30 am
      12/01/2024

      Caucher Birkar (University of Cambridge)

      Title: Log Calabi-Yau fibrations

      Abstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry, differential geometry, arithmetic geometry, mathematical physics, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties, their fibrations, as well as their local birational counterparts such as flips and singularities. Such fibrations can be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations, to remind some known results, and to state some open problems.

      Video

       

    • Special Seminar
      8:00 am-9:00 am
      12/01/2024
      Gromov-Witten

      During the Spring 2021 Semester Artan Sheshmani (CMSA/ I.M. A.U.) will be teaching a CMSA special lecture series on Gromov-Witten/Donaldson Thomas theory and Birational/Symplectic invariants for algebraic surfaces.

      In order to attend this series, please fill out this form.

      The lectures will be held Mondays from 8:00 – 9:30 AM ET and Wednesdays from 8:00 – 9:00 AM ET beginning January 25 on Zoom.

      You can watch Prof. Sheshmani describe the series here. 

    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Andrei Okounkov (Columbia University)

      Title: Classical and quantum integrable systems in enumerative geometry

      Abstract: For more than a quarter of a century, thanks to the ideas and questions originating in modern high-energy physics, there has been a very fruitful interplay between enumerative geometry and integrable system, both classical and quantum. While it is impossible to summarize even the most important aspects of this interplay in one talk, I will try to highlight a few logical points with the goal to explain the place and the role of certain more recent developments.

      Talk chair: Cumrun Vafa

      Video

    • Quantum Matter
      8:00 am-9:30 am
      12/01/2024
    • Math Science Literature Lecture Series
      8:00 am-9:30 am
      12/01/2024

      Yujiro Kawamata (University of Tokyo)

      Title: Kunihiko Kodaira and complex manifolds

      Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions.  After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces.  Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts.

      Talk chair: Baohua Fu

      Video 

    • CMSA EVENT: Geometric Analysis Approach to AI Workshop
      8:30 am-5:30 pm
      12/01/2024-01/21/2019
      Geo-Analysis-Poster-final-e1547584167900

      Geo-Analysis-1-e1543848888343

      Due to inclement weather on Sunday, the second half of the workshop has been moved forward one day. Sunday and Monday’s talks will now take place on Monday and Tuesday.

      On January 18-21, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on the Geometric Analysis Approach to AI.

      This workshop will focus on the theoretic foundations of AI, especially various methods in Deep Learning. The topics will cover the relationship between deep learning and optimal transportation theory, DL and information geometry, DL Learning and information bottle neck and renormalization theory, DL and manifold embedding and so on. Furthermore, the recent advancements, novel methods, and real world applications of Deep Learning will also be reported and discussed.

      The workshop will take place from January 18th to January 23rd, 2019. In the first four days, from January 18th to January 21, the speakers will give short courses; On the 22nd and 23rd, the speakers will give conference representations. This workshop is organized by Xianfeng Gu and Shing-Tung Yau.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please register here

      Speakers: 

    • CMSA EVENT: Big Data Conference 2018
      8:30 am-2:50 pm
      12/01/2024-08/24/2018
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2018-1

       

      shutterstock_547250785-e1527881194717

      On August 23-24, 2018 the CMSA will be hosting our fourth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The talks will take place in Science Center Hall B, 1 Oxford Street.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

      Please register here. 

      Confirmed Speakers: 

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Richard Freeman, Herbert Ascherman Professor of Economics, Harvard University
      • Jun Liu, Professor of Statistics, Harvard University
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
    • CMSA EVENT: 2019 Big Data Conference
      8:30 am-4:40 pm
      12/01/2024-08/20/2019
      1 Oxford Street, Cambridge MA 02138
      Big-Data-2019-Poster-5-2

      shutterstock_547250785-e1527881194717

      On August 19-20, 2019 the CMSA will be hosting our fifth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The talks will take place in Science Center Hall D, 1 Oxford Street.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

      Videos can be found in this Youtube playlist or in the schedule below.

    • CMSA EVENT: Workshop on Aspects of General Relativity
      8:30 am-3:30 pm
      12/01/2024-05/26/2017

      The Center of Mathematical Sciences and Applications will be hosting a workshop on General Relativity from May 23 – 24, 2016. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138The workshop will start on Monday, May 23 at 9am and end on Tuesday, May 24 at 4pm.

      Speakers:

      1. Po-Ning Chen, Columbia University
      2. Piotr T. Chruściel, University of Vienna
      3. Justin Corvino, Lafayette College
      4. Greg Galloway, University of Miami
      5. James Guillochon, Harvard University
      6. Lan-Hsuan Huang, University of Connecticut
      7. Dan Kapec, Harvard University
      8. Dan Lee, CUNY
      9. Alex Lupsasca, Harvard University
      10. Pengzi Miao, University of Miami
      11. Prahar Mitra, Harvard University
      12. Lorenzo Sironi, Harvard University
      13. Jared Speck, MIT
      14. Mu-Tao Wang, Columbia University

      Please click Workshop Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Please click here for registration – Registration is capped at 70 participants.

      Schedule:

      May 23 – Day 1
      8:30amBreakfast
      8:55amOpening remarks
      9:00am – 9:45amGreg Galloway, “Some remarks on photon spheres and their uniqueness
      9:45am – 10:30amPrahar Mitra, “BMS supertranslations and Weinberg’s soft graviton theorem
      10:30am – 11:00amBreak
      11:00am – 11:45amDan Kapec, “Area, Entanglement Entropy and Supertranslations at Null Infinity
      11:45am – 12:30pmPiotr T. Chruściel, “The cosmological constant and the energy of gravitational radiation”
      12:30pm – 2:00pmLunch
      2:00pm – 2:45pmJames Guillochon, “Tidal disruptions of stars by supermassive black holes: dynamics, light, and relics”
      2:45pm – 3:30pmMu-Tao Wang, “Quasi local conserved quantities in general relativity
      3:30pm – 4:00pmBreak
      4:00pm – 4:45pmPo-Ning Chen, “Quasi local energy in presence of gravitational radiations
      4:45pm – 5:30pmPengzi Miao, “Total mean curvature, scalar curvature, and a variational analog of Brown York mass
      May 24 – Day 2
      8:45amBreakfast
      9:00am – 9:45amJustin Corvino, “Scalar curvature deformation and the Bartnik mass
      9:45am – 10:30amLan-Hsuan Huang, “Constraint Manifolds with the Dominant Energy Condition
      10:30am – 11:00amBreak
      11:00am – 11:45amDan Lee, “Lower semicontinuity of Huisken’s isoperimetric mass
      11:45am – 12:30pmJared Speck, “Shock Formation in Solutions to the Compressible Euler Equations
      12:30pm – 2:00pmLunch
      2:00pm – 2:45pmLorenzo Sironi, “Electron Heating and Acceleration in the Vicinity of Supermassive Black Holes
      2:45pm – 3:30pmAlex Lupsasca, “Near Horizon Extreme Kerr Magnetospheres
      * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Workshop on Aspects on General Relativity“.
      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

      Organizers: Piotr T. Chruściel and Shing-Tung Yau

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Angular momentum in general relativity
      8:30 am-9:30 am
      12/01/2024

      Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

    • CMSA EVENT: F-Theory Conference
      8:30 am-3:00 pm
      12/01/2024-09/30/2018

      The CMSA will be hosting an F-Theory workshop September 29-30, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. 

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Click here for videos of the talks. 

      Organizers:

      Speakers:

    • CMSA EVENT: Workshop on Morphometrics, Morphogenesis and Mathematics
      8:30 am-2:00 pm
      12/01/2024-10/24/2018

      In Fall 2018, the CMSA will host a Program on Mathematical Biology, which aims to describe recent mathematical advances in using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.

      The plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale, the   shapes seen in a garden at the scale of a pollen grain, a seed, a sapling, a root, a flower or leaf are so numerous that “it is enough to drive the sanest man mad,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively?

      In biology, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists, to understand how polymeric assemblies grow and shrink (in the cytoskeleton), and how cells divide, change size and shape, and move to organize tissues, change their topology and geometry, and link multiple scales and connect biochemical to mechanical aspects of these problems, all in a self-regulated setting.

      To understand these questions, we need to describe shape (biomathematics), predict shape (biophysics), and design shape (bioengineering).

      For example, in mathematics there are some beautiful links to Nash’s embedding theorem,  connections to quasi-conformal geometry, Ricci flows and geometric PDE, to Gromov’s h principle, to geometrical singularities and singular geometries, discrete and computational differential geometry, to stochastic geometry and shape characterization (a la Grenander, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor, Adler) to look for similarities and differences across species during development, and across evolution.

      In physics, there are questions of generalizing classical theories to include activity, break the usual Galilean invariance, as well as isotropy, frame indifference, homogeneity, and create both agent (cell)-based and continuum theories for ordered, active machines, linking statistical to continuum mechanics, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals, polar materials, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied.

      The CMSA will be hosting a Workshop on Morphometrics, Morphogenesis and Mathematics from October 22-24 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Videos of the talks

      Confirmed Speakers:

    • CMSA EVENT: Workshop on Foundations of Computational Science
      8:30 am-2:45 pm
      12/01/2024-08/31/2019
      AI-Poster-3

      On August 29-31, 2019 the Center of Mathematical Sciences and Applications will be hosting a workshop on Foundations of Computational Science. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA This workshop is organized by David Xianfeng Gu.

      Please register here. 

      Speakers:

      Videos of the talks are contained in the Youtube playlist below. They can also be found through links in the schedule.

    • Quantum Matter
      8:30 am-10:00 am
      12/01/2024
    • CMSA EVENT: Morphogenesis: Geometry and Physics
      8:30 am-2:30 pm
      12/01/2024-12/05/2018

      Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book – a literary masterpiece – is a visionary synthesis of the geometric biology of form. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. So, how far are we from realizing the century-old vision that “Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed” ?

      To address this requires an appreciation of the enormous ‘morphospace’ in terms of the potential shapes and sizes that living forms take, using the language of mathematics. In parallel, we need to consider the biological processes that determine form in mathematical terms is based on understanding how instabilities and patterns in physical systems might be harnessed by evolution.

      In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.
      The first workshop will focus on the interface between Morphometrics and Mathematics, while the second will focus on the interface between Morphogenesis and Physics.The workshop is organized by L. Mahadevan (Harvard), O. Pourquie (Harvard), A. Srivastava (Florida).

      As part of the program on Mathematical Biology a workshop on Morphogenesis: Geometry and Physics will take place on December 3-5, 2018.  The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Videos

      Please Register Here

      PDF of the Schedule

      Speakers:

    • CMSA EVENT: From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford
      8:30 am-5:20 pm
      12/01/2024-08/20/2018
      Mumford-3

      David_Mumford-1

      On August 18 and 20, 2018, the Center of Mathematic Sciences and Applications and the Harvard University Mathematics Department hosted a conference on From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford. The talks took place in Science Center, Hall B.

       Saturday, August 18th:  A day of talks on Vision, AI and brain sciences
      Monday, August 20th: a day of talks on Math

      Speakers:

      Organizers:

       

      Publication:

      Pure and Applied Mathematics Quarterly

      Special Issue: In Honor of David Mumford

      Guest Editors: Ching-Li Chai, Amnon Neeman

       

    • Member Seminar
      8:45 am-10:15 am
      12/01/2024

      Speaker: Jörn Boehnke

      Title: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning

      Abstract:  In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.

    • CMSA EVENT: 2015 Conference on Big Data
      8:45 am-4:00 pm
      12/01/2024-10/26/2015
      1 Oxford Street, Cambridge MA 02138

      The Center of Mathematical Sciences and Applications will be having a conference on Big Data August 24-26, 2015, in Science Center Hall B at Harvard University.  This conference will feature many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      For more info, please contact Sarah LaBauve at slabauve@math.harvard.edu.

       

      Registration for the conference is now closed.

      Please click here for a downloadable version of this schedule.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found here.

      Monday, August 24

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amSendhil MullainathanPrediction Problems in Social Science: Applications of Machine Learning to Policy and Behavioral Economics
      9:45amMike LucaDesigning Disclosure for the Digital Age
      10:30Break
      10:45Jianqing FanBig Data Big Assumption: Spurious discoveries and endogeneity
      11:30amDaniel GoroffPrivacy and Reproducibility in Data Science
      12:15pmBreak for Lunch
      2:00pmRyan AdamsExact Markov Chain Monte Carlo with Large Data
      2:45pmDavid DunsonScalable Bayes: Simple algorithms with guarantees
      3:30pmBreak
      3:45pmMichael JordanComputational thinking, inferential thinking and Big Data
      4:30pmJoel TroppApplied Random Matrix Theory
      5:15pmDavid WoodruffInput Sparsity and Hardness for Robust Subspace Approximation

      Tuesday, August 25

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amGunnar CarlssonPersistent homology for qualitative analysis and feature generation
      9:45amAndrea MontanariSemidefinite Programming Relaxations for Graph and Matrix Estimation: Algorithms and Phase Transitions
      10:30amBreak
      10:45amSusan AtheyMachine Learning and Causal Inference for Policy Evaluation
      11:30amDenis NekipelovRobust Empirical Evaluation of Large Competitive Markets
      12:15pmBreak for Lunch
      2:00pmLucy ColwellUsing evolutionary sequence variation to make inferences about protein structure and function: Modeling with Random Matrix Theory
      2:45pmSimona CoccoInverse Statistical Physics approaches for the modeling of protein families
      3:30pmBreak
      3:45pmRemi MonassonInference of top components of correlation matrices with prior informations
      4:30pmSayan MukherjeeRandom walks on simplicial complexes and higher order notions of spectral clustering

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

       

      A Banquet from 7:00 – 8:30pm will follow Tuesday’s talks. This event is by invitation only.

       Wednesday, August 26 

      TimeSpeakerTitle
      8:45amMeet and Greet
      9:00amAnkur MoitraBeyond Matrix Completion
      9:45amFlorent KrzakalaOptimal compressed sensing with spatial coupling and message passing
      10:30amBreak
      10:45amPiotr IndykFast Algorithms for Structured Sparsity
      11:30amGuido ImbensExact p-values for network inference
      12:15pmBreak for lunch
      2:00pmEdo AiroldiSome fundamental ideas for causal inference on large networks
      2:45pmRonitt RubinfeldSomething for almost nothing: sublinear time approximation algorithms
      3:30pmBreak
      3:45pmLenka ZdeborovaClustering of sparse networks:  Phase transitions and optimal algorithms
      4:30pmJelani NelsonDimensionality reductions via sparse matrices
    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024
      Lecture_Fukaya-pdf

      Kenji Fukaya (Simons Center for Geometry and Physics)

      Title: Homological (homotopical) algebra and moduli spaces in Topological Field theories

      Abstract: Moduli spaces of various gauge theory equations and of various versions of (pseudo) holomorphic curve equations have played important role in geometry in these 40 years. Started with Floer’s work people start to obtain more sophisticated object such as groups, rings, or categories from (system of) moduli spaces. I would like to survey some of those works and the methods to study family of moduli spaces systematically.

      Talk chair: Peter Kronheimer

      Slides | Video

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Don Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics)

      Title: Quantum topology and new types of modularity

      Abstract: The talk concerns two fundamental themes of modern 3-dimensional topology and their unexpected connection with a theme coming from number theory. A deep insight of William Thurston in the mid-1970s is that the vast majority of complements of knots in the 3-sphere, or more generally of 3-manifolds, have a unique metric structure as hyperbolic manifolds of constant curvature -1, so that 3-dimensional topology is in some sense not really a branch of topology at all, but of differential geometry. In a different direction, the work of Vaughan Jones and Ed Witten in the late 1980s gave rise to the field of Quantum Topology, in which new types of invariants of knot complements and 3-manifolds are introduced that have their origins in ideas coming from quantum field theory. These two themes then became linked by Kashaev’s famous Volume Conjecture, now some 25 years old, which says that the Kashaev invariant _N of a hyperbolic knot K (this is a quantum invariant defined for each positive integer N and whose values are algebraic numbers) grows exponentially as N tends to infinity with an exponent proportional to the hyperbolic volume of the knot complement. About 10 years ago, I was led by numerical experiments to the discovery that Kashaev’s invariant could be upgraded to an invariant having rational numbers as its argument (with the original invariant being the value at 1/N) and that the Volume Conjecture then became part of a bigger story saying that the new invariant has some sort of strange transformation property under the action x -> (ax+b)/(cx+d) of the modular group SL(2,Z) on the argument. This turned out to be only the beginning of a fascinating and multi-faceted story relating quantum invariants, q-series, modularity, and many other topics. In the talk, which is intended for a general mathematical audience, I would like to recount some parts of this story, which is joint work with Stavros Garoufalidis (and of course involving contributions from many other authors). The “new types of modularity” in the title refer to a specific byproduct of these investigations, namely that there is a generalization of the classical notion of holomorphic modular form – which plays an absolutely central role in modern number theory – to a new class of holomorphic functions in the upper half-plane that no longer satisfy a transformation law under the action of the modular group, but a weaker extendability property instead. This new class, called “holomorphic quantum modular forms”, turns out to contain many other functions of a more number-theoretical nature as well as the original examples coming from quantum invariants.

      Talk chair: Mark Kisin

      Video

    • Combinatorics Physics and Probability
      9:00 am-10:00 am
      12/01/2024

      Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Liang Kong (Sustech)

      Title: Topological Wick Rotation and Holographic duality

      Abstract: I will explain a new type of holographic dualities between
      n+1D topological orders with a chosen boundary condition and nD
      (potentially gapless) quantum liquids. It is based on the idea of
      topological Wick rotation, a notion which was first used in
      arXiv:1705.01087 and was named, emphasized and generalized later in
      arXiv:1905.04924. Examples of these holographic dualities include the
      duality between 2+1D toric code model and 1+1D Ising chain and its
      finite-group generalizations (independently discovered by many
      others); those between 2+1D topological orders and 1+1D rational
      conformal field theories; and those between n+1D finite gauge theories
      with a gapped boundary and nD gapped quantum liquids. I will also
      briefly discuss some generalizations of this holographic duality and
      its relation to AdS/CFT duality.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: João Caetano (CERN)

      Title: Unorientable Quantum Field Theories: From crosscaps to holography

      Abstract: In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state.

      In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4-manifold. I will show how to do this in the example of N=4 Supersymmetric Yang-Mills, discuss its holographic description and present a new solvable setup of AdS/CFT.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Michele Del Zotto (Uppsala University)

      Title: On the six-dimensional origin of non-invertible symmetries

      Abstract: I will present a review about recent progress in charting non-invertible symmetries for four-dimensional quantum field theories that have a six-dimensional origin. These include in particular N=4 supersymmetric Yang-Mills theories, and also a large class of N=2 supersymmetric theories which are conformal and do not have a conventional Lagrangian description (the so-called theories of “class S”). Among the main results, I will explain criteria for identifying examples of systems with intrinsic and non-intrinsic non-invertible symmetries, as well as explore their higher dimensional origin. This seminar is based on joint works with Vladimir Bashmakov, Azeem Hasan, and Justin Kaidi.

       

      https://www.youtube.com/watch?v=0Tscbn9RhF8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=31

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 11.2.22

      Topological Quantum Matter Seminar

      Speaker: Junyeong Ahn (Harvard)

      Title: Optical axion electrodynamics

      Abstract: Electromagnetic fields in a magneto-electric medium behave in close analogy to photons coupled to the hypothetical elementary particle, the axion. This emergent axion electrodynamics is expected to provide novel ways to detect and control material properties with electromagnetic fields. Despite having been studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Formulating axion electrodynamics at general optical frequencies requires resolving the difficulty of calculating optical magneto-electric coupling in periodic systems and demands a proper generalization of the axion field. In this talk, I will introduce a theory of optical axion electrodynamics that allows for a simple quantitative analysis. Then, I will move on to discuss the issue of the Kerr effect in axion antiferromagnets, refuting the conventional wisdom that the Kerr effect is a measure of the net magnetic moment. Finally, I will apply our theory to a topological antiferromagnet MnBi2Te4.

      References:
      [1] Theory of Optical Axion Electrodynamics, J. Ahn, S.Y. Xu, A.Vishwanath, arXiv:2205.06843

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Ethan Lake (MIT)

      Title: Insulating BECs and other surprises in dipole-conserving systems

      Abstract: I will discuss recent work on bosonic models whose dynamics conserves both total charge and total dipole moment, a situation which can be engineered in strongly tilted optical lattices. Related models have received significant attention recently for their interesting out-of-equilibrium dynamics, but analytic and numeric studies reveal that they also possess rather unusual ground states. I will focus in particular on a dipole-conserving variant of the Bose-Hubbard model, which realizes an unusual phase of matter that possesses a Bose-Einstein condensate, but which is nevertheless insulating, and has zero superfluid weight. Time permitting, I will also describe the physics of a regime in which these models spontaneously fracture into an exotic type of glassy state.

       

      https://www.youtube.com/watch?v=Nad45apS8TE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=29

    • Quantum Matter
      9:00 am-4:00 pm
      12/01/2024
    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Daniel A. Spielman

      Dan Spielman (Yale University)

      Title: Discrepancy Theory and Randomized Controlled Trials

      Abstract: Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other.  By “surprisingly similar” we mean much more similar than a random partition. I will begin by surveying fundamental results in discrepancy theory, including Spencer’s famous existence proofs and Bansal’s recent algorithmic realizations of them. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar.  When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we know information about the experimental subjects, called covariates, we can combine the strengths of randomization with the promises of discrepancy theory. This should allow us to obtain more accurate estimates of the effectiveness of treatments, or to conduct trials with fewer experimental subjects. I will introduce the Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, which produces random solutions to discrepancy problems. I will then explain how Chris Harshaw, Fredrik Sävje, Peng Zhang, and I use this algorithm to improve the design of randomized controlled trials. Our Gram-Schmidt Walk Designs have increased accuracy when the experimental outcomes are correlated with linear functions of the covariates, and are comparable to uniform random assignments in the worst case.

      Talk chair: Salil Vadhan

      Video

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 10.26.22

      Topological Quantum Matter Seminar

      Speaker: Bruno Mera, Tohoku University
      Title: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
      Abstract: The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect, certain geometric constraints, associated with the holomorphic character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.
      References:
      [1] Tomoki Ozawa and Bruno Mera. Relations between topology and the quantum metric for Chern insulators. Phys. Rev. B, 104:045103, Jul 2021.
      [2] Bruno Mera and Tomoki Ozawa. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Phys. Rev. B, 104:045104, Jul 2021.
      [3] Bruno Mera and Tomoki Ozawa. Engineering geometrically flat Chern bands with Fubini-Study  Kähler structure. Phys. Rev. B, 104:115160, Sep 2021.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Francisco Machado  (Berkeley/Harvard)

      Title: Kardar-Parisi-Zhang dynamics in integrable quantum magnets

      Abstract: Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.

      In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.

      Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.

      [1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
      B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
      (PRL in press) – arXiv:2205.02853

      [2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
      D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
      Science (2022) — arXiv:2107.00038

       

      https://www.youtube.com/watch?v=65DjgbX30FU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=27

    • Math Science Literature Lecture Series
      9:00 am-12:13 pm
      12/01/2024

      Harry Shum (Tsinghua University)

      Title: From Deep Learning to Deep Understanding

      Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model,  and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike GPT or similar language models learnt from data, it is a multi-turn decision making system which takes user input, updates the belief state, retrieved from the database via symbolic reasoning, and decides how to complete the task with grounded response.

      Talk chair: Shing-Tung Yau

      Video

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      10/12/2021 Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      Title: On counting algebraically defined graphs

      Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

    • Program
      9:00 am-5:00 pm
      12/01/2024-05/13/2022

      Please visit the Swampland Initiative for current events.

      The Harvard Swampland Initiative is an immersive program aiming to bring together leading experts with the goal of exploring the boundaries of the quantum gravity landscape. Through workshops, seminars, and collaborative research, participants collectively navigate the Swampland, advancing our comprehension of the fundamental principles of quantum gravity.

       


      During the 2021-2022 academic year, the CMSA hosted a program on the so-called “Swampland.”

      The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology,  which has led to a great deal of activity in the field in the last few years.

      The Swampland is intrinsically interdisciplinary, with ramifications in string compactifications, holography, black hole physics, cosmology, particle physics, and even mathematics.

      This program will include an extensive group of visitors and a slate of seminars. Additionally, the CMSA will host a school oriented toward graduate students.

      Seminars

      Swampland Seminar Series & Group Meetings

      Program Visitors

      • Pieter Bomans, Princeton, 10/30/21 – 11/02/21
      • Irene Valenzuela, Instituto de Física Teórica, 02/14/22 – 02/21/22
      • Mariana Grana, CEA/Saclay, 03/21/22 – 03/25/22
      • Hector Parra De Freitas, IPHT Saclay, 03/21/22 – 04/01/22
      • Timo Weigand, 03/21/22 – 03/28/22
      • Gary Shiu, University of Wisconsin-Madison, 04/03/22 – 04/10/22
      • Thomas van Riet, Leuven University, 04/03/22 – 04/09/22
      • Lars Aalsma, University of Wisconsin-Madison, 04/11/22 – 04/15/22
      • Sergio Cecotti, 05/08/22 – 05/21/22
      • Tom Rudelius, 05/09/22 – 05/13/22

      https://sites.harvard.edu/swampland-initiative/

    • Math Science Literature Lecture Series
      9:00 am-9:06 am
      12/01/2024

      Claire Voisin (Collège de France)

      Title: Hodge structures and the topology of algebraic varieties

      Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results  we will discuss  rely on Hodge theory, which  has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization,  is missing in the general Kaehler context. We will also discuss some results and problems related to algebraic cycles and motives.

      Talk chair: Joe Harris

      Video | Slides | Article

    • Conference
      9:00 am-5:30 pm
      12/01/2024-03/01/2023
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Poster_GeometryStatistics_8.5x11.final

      On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

      Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

      This conference will be held in person. Directions and Recommended Lodging

      Registration is required.

      Register here to attend in-person.

      Organizing Committee:
      Stephan Huckemann (Georg-August-Universität Göttingen)
      Ezra Miller (Duke University)
      Zhigang Yao (Harvard CMSA and Committee Chair)

      Scientific Advisors:
      Horng-Tzer Yau (Harvard CMSA)
      Shing-Tung Yau (Harvard CMSA)

      Speakers:

      • Tamara Broderick (MIT)
      • David Donoho (Stanford)
      • Ian Dryden (Florida International University in Miami)
      • David Dunson (Duke)
      • Charles Fefferman (Princeton)
      • Stefanie Jegelka (MIT)
      • Sebastian Kurtek (OSU)
      • Lizhen Lin (Notre Dame)
      • Steve Marron (U North Carolina)
      • Ezra Miller (Duke)
      • Hans-Georg Mueller (UC Davis)
      • Nicolai Reshetikhin (UC Berkeley)
      • Wolfgang Polonik (UC Davis)
      • Amit Singer (Princeton)
      • Zhigang Yao (Harvard CMSA)
      • Bin Yu (Berkeley)

      Moderator: Michael Simkin (Harvard CMSA)

       

      SCHEDULE

      Monday, Feb. 27, 2023 (Eastern Time)

      8:30 amBreakfast
      8:45–8:55 amZhigang YaoWelcome Remarks
      8:55–9:00 amShing-Tung Yau*Remarks
      Morning Session Chair: Zhigang Yao
      9:00–10:00 amDavid DonohoTitle: ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise

      Abstract: Truncation of the singular value decomposition is a true scientific workhorse. But where to Truncate?

      For 55 years the answer, for many scientists, has been to eyeball the scree plot, an approach which still generates hundreds of papers per year.

      I will describe ScreeNOT, a mathematically solid alternative deriving from the many advances in Random Matrix Theory over those 55 years. Assuming a model of low-rank signal plus possibly correlated noise, and adopting an asymptotic viewpoint with number of rows proportional to the number of columns, we show that ScreeNOT has a surprising oracle property.

      It typically achieves exactly, in large finite samples, the lowest possible MSE for matrix recovery, on each given problem instance – i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure.

      The talk is based on joint work with Matan Gavish and Elad Romanov, Hebrew University.

      10:00–10:10 amBreak
      10:10–11:10 amSteve MarronTitle: Modes of Variation in Non-Euclidean Spaces

      Abstract: Modes of Variation provide an intuitive means of understanding variation in populations, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts, including shapes as data objects, vectors of directional data, amplitude and phase variation and compositional data.

      11:10–11:20 amBreak
      11:20 am–12:20 pmZhigang YaoTitle: Manifold fitting: an invitation to statistics

      Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference:https://arxiv.org/abs/1909.10228

       12:20–1:50 pm12:20 pm Group Photo

      followed by Lunch

      Afternoon Session Chair: Stephan Huckemann
      1:50–2:50 pmBin Yu*Title: Interpreting Deep Neural Networks towards Trustworthiness

      Abstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.

      2:50–3:00 pmBreak
      3:00-4:00 pmHans-Georg MuellerTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression

      Abstract: Random objects, i.e., random variables that take values in a separable metric space, pose many challenges for statistical analysis, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions, covariance matrices or surfaces, graph Laplacians to represent networks, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics, an emerging collection of statistical tools to characterize, infer and relate samples of random objects. Recent developments include depth profiles, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey, Y. Chen 2022).

      These distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.

      4:00-4:10 pmBreak
      4:10-5:10 pmStefanie JegelkaTitle: Some benefits of machine learning with invariances

      Abstract: In many applications, especially in the sciences, data and tasks have known invariances. Encoding such invariances directly into a machine learning model can improve learning outcomes, while it also poses challenges on efficient model design. In the first part of the talk, we will focus on the invariances relevant to eigenvectors and eigenspaces being inputs to a neural network. Such inputs are important, for instance, for graph representation learning. We will discuss targeted architectures that can universally express functions with the relevant invariances – sign flips and changes of basis – and their theoretical and empirical benefits.

      Second, we will take a broader, theoretical perspective. Empirically, it is known that encoding invariances into the machine learning model can reduce sample complexity. For the simplified setting of kernel ridge regression or random features, we will discuss new bounds that illustrate two ways in which invariances can reduce sample complexity. Our results hold for learning on manifolds and for invariances to (almost) any group action, and use tools from differential geometry.

      This is joint work with Derek Lim, Joshua Robinson, Behrooz Tahmasebi, Lingxiao Zhao, Tess Smidt, Suvrit Sra, and Haggai Maron.

       

       

       

      Tuesday, Feb. 28, 2023 (Eastern Time)

      8:30-9:00 amBreakfast
      Morning Session Chair: Zhigang Yao
      9:00-10:00 amCharles Fefferman*Title: Lipschitz Selection on Metric Spaces

      Abstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.

      10:00-10:10 amBreak
      10:10-11:10 amDavid DunsonTitle: Inferring manifolds from noisy data using Gaussian processes

      Abstract: In analyzing complex datasets, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm, we provide simulated and real data examples to illustrate the performance. Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478

      11:10-11:20 amBreak
      11:20 am-12:20 pmWolfgang PolonikTitle: Inference in topological data analysis

      Abstract: Topological data analysis has seen a huge increase in popularity finding applications in numerous scientific fields. This motivates the importance of developing a deeper understanding of benefits and limitations of such methods. Using this angle, we will present and discuss some recent results on large sample inference in topological data analysis, including bootstrap for Betti numbers and the Euler characteristics process.

      12:20–1:50 pmLunch
      Afternoon Session Chair: Stephan Huckemann
      1:50-2:50 pmEzra MillerTitle: Geometric central limit theorems on non-smooth spaces

      Abstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data, such as angles or phylogenetic trees, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures, correct analogues of Gaussian random variables, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers, starting with a review of the usual linear CLT and its generalization to smooth manifolds, viewed through a lens that casts the singular CLT as a natural outgrowth, and concluding with how this investigation opens gateways to further advances in geometric probability, topology, and statistics. Joint work with Jonathan Mattingly and Do Tran.

      2:50-3:00 pmBreak
      3:00-4:00 pmLizhen LinTitle: Statistical foundations of deep generative models

      Abstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in empirical performance, theoretical understanding of such models is largely lacking. We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates, and ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.

      4:00-4:10 pmBreak
      4:10-5:10 pmConversation session

       

       

       

      Wednesday, March 1, 2023 (Eastern Time)

      8:30-9:00 amBreakfast
      Morning Session Chair: Ezra Miller
      9:00-10:00 amAmit Singer*Title: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning

      Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.

      10:00-10:10 amBreak
      10:10-11:10 amIan DrydenTitle: Statistical shape analysis of molecule data

      Abstract: Molecular shape data arise in many applications, for example high dimension low sample size cryo-electron microscopy (cryo-EM) data and large temporal sequences of peptides from molecular dynamics simulations. In both applications it is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D sub-shape spaces and provide some practical fitting algorithms. The methodology is applied to cryo-EM data of a large sliding clamp multi-protein complex and to cluster analysis of peptides, where different states of the molecules can be identified. Further molecular modeling tasks include resolution matching, where coarse resolution models are back-mapped into high resolution (atomistic) structures. This is joint work with Kwang-Rae Kim, Charles Laughton and Huiling Le.

      11:10-11:20 amBreak
      11:20 am-12:20 pmTamara BroderickTitle: An Automatic Finite-Sample Robustness Metric: Can Dropping a Little Data Change Conclusions?

      Abstract: One hopes that data analyses will be used to make beneficial decisions regarding people’s health, finances, and well-being. But the data fed to an analysis may systematically differ from the data where these decisions are ultimately applied. For instance, suppose we analyze data in one country and conclude that microcredit is effective at alleviating poverty; based on this analysis, we decide to distribute microcredit in other locations and in future years. We might then ask: can we trust our conclusion to apply under new conditions? If we found that a very small percentage of the original data was instrumental in determining the original conclusion, we might not be confident in the stability of the conclusion under new conditions. So we propose a method to assess the sensitivity of data analyses to the removal of a very small fraction of the data set. Analyzing all possible data subsets of a certain size is computationally prohibitive, so we provide an approximation. We call our resulting method the Approximate Maximum Influence Perturbation. Our approximation is automatically computable, theoretically supported, and works for common estimators. We show that any non-robustness our method finds is conclusive. Empirics demonstrate that while some applications are robust, in others the sign of a treatment effect can be changed by dropping less than 0.1% of the data — even in simple models and even when standard errors are small.

       12:20-1:50 pmLunch
      Afternoon Session Chair: Ezra Miller
      1:50-2:50 pmNicolai Reshetikhin*Title: Random surfaces in exactly solvable models in statistical mechanics.

      Abstract: In the first part of the talk I will be an overview of a few models in statistical mechanics where a random variable is a geometric object such as a random surface or a random curve. The second part will be focused on the behavior of such random surfaces in the thermodynamic limit and on the formation of the so-called “limit shapes”.

      2:50-3:00 pmBreak
      3:00-4:00 pmSebastian KurtekTitle: Robust Persistent Homology Using Elastic Functional Data Analysis

      Abstract: Persistence landscapes are functional summaries of persistence diagrams designed to enable analysis of the diagrams using tools from functional data analysis. They comprise a collection of scalar functions such that birth and death times of topological features in persistence diagrams map to extrema of functions and intervals where they are non-zero. As a consequence, variation in persistence diagrams is encoded in both amplitude and phase components of persistence landscapes. Through functional data analysis of persistence landscapes, under an elastic Riemannian metric, we show how meaningful statistical summaries of persistence landscapes (e.g., mean, dominant directions of variation) can be obtained by decoupling their amplitude and phase variations. This decoupling is achieved via optimal alignment, with respect to the elastic metric, of the persistence landscapes. The estimated phase functions are tied to the resolution parameter that determines the filtration of simplicial complexes used to construct persistence diagrams. For a dataset obtained under geometric, scale and sampling variabilities, the phase function prescribes an optimal rate of increase of the resolution parameter for enhancing the topological signal in a persistence diagram. The proposed approach adds to the statistical analysis of data objects with rich structure compared to past studies. In particular, we focus on two sets of data that have been analyzed in the past, brain artery trees and images of prostate cancer cells, and show that separation of amplitude and phase of persistence landscapes is beneficial in both settings. This is joint work with Dr. James Matuk (Duke University) and Dr. Karthik Bharath (University of Nottingham).

      4:00-4:10 pmBreak
      4:10-5:10 pmConversation session
      5:10-5:20 pmStephan Huckemann, Ezra Miller, Zhigang YaoClosing Remarks

      * Virtual Presentation


       

    • Algebraic Geometry in String Theory Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 02.24.2023

      Algebraic Geometry in String Theory Seminar

      Speaker: Chao-Ming Lin (University of California, Irvine)

      Title: On the convexity of general inverse $\sigma_k$ equations and some applications

      Abstract: In this talk, I will show my recent work on general inverse $\sigma_k$ equations and the deformed Hermitian-Yang-Mills equation (hereinafter the dHYM equation). First, I will show my recent results. This result states that if a level set of a general inverse $\sigma_k$ equation (after translation if needed) is contained in the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the Monge-Ampère equation, the J-equation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special class of univariate polynomials and give a Positivstellensatz type result. These give a numerical criterion to verify whether the level set will be contained in the positive orthant. Last, as an application, I will prove one of the conjectures by Collins-Jacob-Yau when the dimension equals four. This conjecture states that under the supercritical phase assumption, if there exists a C-subsolution to the dHYM equation, then the dHYM equation is solvable.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Geodesics and minimal surfaces
      9:00 am-10:00 am
      12/01/2024
      20220209_Andre-Neves_poster

      Abstract: There are several properties of closed geodesics which are proven using its Hamiltonian formulation, which has no analogue for minimal surfaces. I will talk about some recent progress in proving some of these properties for minimal surfaces.

    • Colloquium
      9:00 am-10:00 am
      12/01/2024
    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Camillo De Lellis (IAS)

      Title: Area-minimizing integral currents and their regularity

      Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will also touch upon several fundamental open problems which still defy our understanding. 

      Talk Chair: William Minicozzi

      Video

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Rational Polypols
      9:00 am-10:00 am
      12/01/2024

      Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics, positive geometries are real semialgebraic sets together with a rational canonical form. We combine these two worlds by providing an explicit formula for the canonical form of a rational polypol in terms of defining equations of the adjoint curve and the facets of the polypol. For the special case of polygons, we show that the adjoint curve is hyperbolic and provide an explicit description of its nested ovals. Finally, we discuss the map that associates the adjoint curve to a given rational polypol, in particular the cases where this map is finite. For instance, using monodromy we find that a general quartic curve is the adjoint of 864 heptagons.

      This talk is based on joint work with R. Piene, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn,  M.-S. Sorea, and S. Telen.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Greedy maximal independent sets via local limits
      9:00 am-10:00 am
      12/01/2024

      Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge.

      In this talk, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs, such as paths and various random graphs, and by providing new results for other models such as random trees.

      If time allows, I will discuss a more delicate (and combinatorial) result, according to which, in expectation, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order.

      The talk is based on joint work with Michael Krivelevich, Tamás Mészáros and Clara Shikhelman.

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Theorems of Torelli type
      9:00 am-10:30 am
      12/01/2024
      Lecture_Looijenga-pdf

      Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University)

      Title: Theorems of Torelli type

      Abstract: Given a closed manifold of even dimension 2n, then Hodge showed around 1950 that a  kählerian complex structure on that manifold determines a decomposition of its complex cohomology. This decomposition, which can potentially vary continuously with the complex structure, extracts from a non-linear given,  linear data. It can contain a lot of information. When there is essentially no loss of data in this process, we say that the Torelli theorem holds.  We review the underlying theory and then survey some cases where this is the case. This will include the classical case n=1, but the emphasis will be on K3 manifolds (n=2) and more generally, on hyperkählerian manifolds. These cases stand out, since one can then also tell which decompositions occur.

      Talk chair: Gerard van der Geer

      Video 

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Yang Qi (Fudan)

      Title: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon

      Abstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon, leading to a significant broadening of the single-particle spectral functions. Quantitatively, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.

      https://www.youtube.com/watch?v=p1q0ots1X5s&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=20

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 10.12.22

      Topological Quantum Matter Seminar

      Speaker: Jennifer Cano (Stony Brook and Flatiron Institute)

      Title: Engineering topological phases with a superlattice potential
      Abstract: We propose an externally imposed superlattice potential as a platform for manipulating topological phases, which has both advantages and disadvantages compared to a moire superlattice. In the first example, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long sought-after goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example, we show that a superlattice potential applied to Bernal-stacked bilayer graphene can generate flat Chern bands, similar to in twisted bilayer graphene, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry, making it a promising alternative to achieve designer flat bands without a moire heterostructure.
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      10/5/2021 Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      Title: Geodesic Geometry on Graphs

      Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

      We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

      Joint work with Nati Linial.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Federico Bonetti (Oxford)

      Title: Non-Invertible Symmetries from Holography and Branes

      Abstract:  The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects, and of their action on extended operators of the 4d QFT.

      https://www.youtube.com/watch?v=opvlpWdTXr4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=21

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Junkai Dong (Harvard University)

      Title: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

      Abstract: Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

       

      https://www.youtube.com/watch?v=RfUKlzKs70o&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=23

    • Workshop
      9:00 am-3:30 pm
      12/01/2024-12/01/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Videos are available on the CMSA Youtube Playlist.

      On November 28 – Dec 1, 2022, the CMSA hosted a Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.

      Organizers: An Huang (Brandeis University) | Siu-Cheong Lau (Boston University) | Tsung-Ju Lee (CMSA, Harvard) | Andrew Linshaw (University of Denver)

      Scientific Advisor: Shing-Tung Yau (Harvard, Tsinghua)

      Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

      Directions and Recommended Lodging

      The conference was held in hybrid format, both in-person and online.

      The workshop was partially supported by Simons and NSF Grant DMS-2227199.

       

      Speakers: 

      • Tomoyuki Arakawa (Kyoto)
      • Thomas Creutzig (Edmonton)
      • Jonathan Mboyo Esole (Northeastern)
      • Fei Han (National University of Singapore)
      • Shinobu Hosono (Gakushuin University)
      • Flor Orosz Hunziker (Colorado)
      • Cuipo Jiang (Shanghai)
      • Shashank Kanade (Denver)
      • Matt Kerr (Washington University in St. Louis)
      • Carl Lian (Humboldt-Universität zu Berlin)
      • Nai-Chung Conan Leung (CUHK)
      • Ivan Loseu (Yale)
      • Robert McRae (Tsinghua University)
      • Anne Moreau (Université Paris-Saclay, Orsay)
      • Tony Pantev (University of Pennsylvania)
      • Mauricio Romo (Tsinghua University)
      • Bailin Song (USTC)
      • Cumrun Vafa (Harvard University)
      • Chin-Lung Wang (National Taiwan University)
      • Weiqiang Wang (Virginia)
      • Yaping Yang (University of Melbourne)
      • Shing-Tung Yau (Tsinghua University)
      • Chenglong Yu (Tsinghua University)
      • Gufang Zhao (University of Melbourne)

       

      Schedule (Eastern Time)

      Schedule (pdf)

      11/28 (Monday)

      08:30am – 08:55amRefreshments
      08:55am – 09:00amOpening remarks by Horng-Tzer Yau
      09:00am – 09:45amShing-Tung Yau*Title: The Hull-Strominger system through conifold transitions

      Abstract: In this talk I discuss the geometry of C-Y manifolds outside of the Kähler regime and especially describe the Hull-Strominger system through the conifold transitions.

      10:00am – 10:45amChenglong Yu*Title: Commensurabilities among Lattices in PU(1,n)

      Abstract: In joint work with Zhiwei Zheng, we study commensurabilities among certain subgroups in PU(1,n). Those groups arise from the monodromy of hypergeometric functions. Their discreteness and arithmeticity are classified by Deligne and Mostow. Thurston also obtained similar results via flat conic metrics. However, the classification of the lattices among them up to conjugation and finite index (commensurability) is not completed. When n=1, it is the commensurabilities of hyperbolic triangles. The cases of n=2 are almost resolved by Deligne-Mostow and Sauter’s commensurability pairs, and commensurability invariants by Kappes-Möller and McMullen. Our approach relies on the study of some higher dimensional Calabi-Yau type varieties instead of complex reflection groups. We obtain some relations and commensurability indices for higher n and also give new proofs for existing pairs in n=2.

      11:00am – 11:45amThomas Creutzig*Title: Shifted equivariant W-algebras

      Abstract: The CDO of a compact Lie group is a family of VOAs whose top level is the space of functions on the Lie group. Similar structures appear at the intersections of boundary conditions in 4-dimensional gauge theories, I will call these new families of VOAs shifted equivariant W-algebras. I will introduce these algebras, construct them and explain how they can be used to quickly prove the GKO-coset realization of principal W-algebras.

      11:45am – 1:30 pmLunch
      01:30pm – 02:15pmCumrun VafaTitle: Reflections on Mirror Symmetry

      Abstract: In this talk I review some of the motivations leading to the search and discovery of mirror symmetry as well as some of the applications it has had.

      02:30pm – 03:15pmJonathan Mboyo EsoleTitle: Algebraic topology and matter representations in F-theory

      Abstract: Recently, it was observed that representations appearing in geometric engineering in F-theory all satisfy a unique property: they correspond to characteristic representations of embedding of Dynkin index one between Lie algebras. However, the reason why that is the case is still being understood. In this talk, I will present new insights, giving a geometric explanation for this fact using K-theory and the topology of Lie groups and their classifying spaces. In physics, this will be interpreted as conditions on the charge of instantons and the classifications of Wess-Zumino-Witten terms.

      03:15pm – 03:45 pmBreak
      03:45pm – 04:30pmWeiqiang WangTitle: A Drinfeld presentation of affine i-quantum groups

      Abstract: A quantum symmetric pair of affine type (U, U^i) consists of a Drinfeld-Jimbo affine quantum group (a quantum deformation of a loop algebra) U and its coideal subalgebra U^i (called i-quantum group). A loop presentation for U was formulated by Drinfeld and proved by Beck. In this talk, we explain how i-quantum groups can be viewed as a generalization of quantum groups, and then we give a Drinfeld type presentation for the affine quasi-split i-quantum group U^i. This is based on joint work with Ming Lu (Sichuan) and Weinan Zhang (Virginia).

      04:45pm – 05:30pmTony PantevTitle: Decomposition, anomalies, and quantum symmetries

      Abstract: Decomposition is a phenomenon in quantum physics which converts quantum field theories with non-effectively acting gauge symmetries into equivalent more tractable theories in which the fields live on a disconnected space. I will explain the mathematical content of decomposition which turns out to be a higher categorical version of Pontryagin duality. I will examine how this duality interacts with quantum anomalies and secondary quantum symmetries and will show how the anomalies can be canceled by homotopy coherent actions of diagrams of groups. I will discuss in detail the case of 2-groupoids which plays a central role in anomaly cancellation, and will describe a new duality operation that yields decomposition in the presence of anomalies. The talk is based on joint works with Robbins, Sharpe, and Vandermeulen.

       

      11/29 (Tuesday)

       

      Refreshments
      09:00am – 09:45amRobert MacRae*Title: Rationality for a large class of affine W-algebras

      Abstract: One of the most important results in vertex operator algebras is Huang’s theorem that the representation category of a “strongly rational” vertex operator algebra is a semisimple modular tensor category. Conversely, it has been conjectured that every (unitary) modular tensor category is the representation category of a strongly rational (unitary) vertex operator algebra. In this talk, I will describe my results on strong rationality for a large class of affine W-algebras at admissible levels. This yields a large family of modular tensor categories which generalize those associated to affine Lie algebras at positive integer levels, as well as those associated to the Virasoro algebra.

      10:00am – 10:45amBailin Song*Title: The global sections of chiral de Rham complexes on compact Calabi-Yau manifolds

      Abstract: Chiral de Rham complex is a sheaf of vertex algebras on a complex manifold. We will describe the space of global sections of the chiral de Rham complexes on compact Calabi-Yau manifolds.

      11:00am – 11:45amCarl Lian*Title: Curve-counting with fixed domain

      Abstract: The fixed-domain curve-counting problem asks for the number of pointed curves of fixed (general) complex structure in a target variety X subject to incidence conditions at the marked points. The question comes in two flavors: one can ask for a virtual count coming from Gromov-Witten theory, in which case the answer can be computed (in principle) from the quantum cohomology of X, or one can ask for the “honest” geometric count, which tends to be more subtle. The answers are conjectured to agree in the presence of sufficient positivity, but do not always. I will give an overview of some recent results and open directions. Some of this work is joint with Alessio Cela, Gavril Farkas, and Rahul Pandharipande.

      11:45am – 01:30pmLunch
      01:30pm – 02:15pmChin-Lung WangTitle: A blowup formula in quantum cohomology

      Abstract: We study analytic continuations of quantum cohomology $QH(Y)$ under a blowup $\phi: Y \to X$ of complex projective manifolds along the extremal ray variable $q^{\ell}$. Under $H(Y) = \phi^* H(X) plus K$ where $K = \ker \phi_*$, we show that (i) the restriction of quantum product along the $\phi^*H(X)$ direction, denoted by $QH(Y)_X$, is meromorphic in $x := 1/q^\ell$, (ii) $K$ deforms uniquely to a quantum ideal $\widetilde K$ in $QH(Y)_X$, (iii) the quotient ring $QH(Y)_X/\widetilde K$ is regular over $x$, and its restriction to $x = 0$ is isomorphic to $QH(X)$. This is a joint work (in progress) with Y.-P. Lee and H.-W. Lin.

      02:30pm – 03:15pmIvan LoseuTitle: Quantizations of nilpotent orbits and their Lagrangian subvarieties

      Abstract: I’ll report on some recent progress on classifying quantizations of the algebras of regular functions of nilpotent orbits (and their covers) in semisimple Lie algebras, as well as the classification of quantizations of certain Lagrangian subvarieties. An ultimate goal here is to understand the classification of unitary representations of real semisimple Lie groups.

      03:15pm – 03:45pmBreak
      03:45pm – 04:30pmMatt Kerr*Title: $K_2$ and quantum curves

      Abstract: The basic objects for this talk are motives consisting of a curve together with a $K_2$ class, and their mixed Hodge-theoretic invariants.

      My main objective will be to explain a connection (recently proved in joint work with C. Doran and S. Sinha Babu) between (i) Hodge-theoretically distinguished points in the moduli of such motives and (ii) eigenvalues of operators on L^2(R) obtained by quantizing the equations of the curves.

      By local mirror symmetry, this gives evidence for a conjecture in topological string theory (due to M. Marino, A. Grassi, and others) relating enumerative invariants of toric CY 3-folds to spectra of quantum curves.

      04:45pm – 05:30pmFlor Orosz HunzikerTitle: Tensor structures associated to the N=1 super Virasoro algebra

      Abstract:  We have recently shown that there is a natural category of representations associated to the N=1 super Virasoro vertex operator algebras that have braided tensor structure. We will describe this category and discuss the problem of establishing its rigidity at particular central charges. This talk is based on joint work in progress with Thomas Creutzig, Robert McRae and Jinwei Yang.

       

       

       

      11/30 (Wednesday)

      08:30am – 09:00amRefreshments
      09:00am – 09:45amTomoyuki ArakawaTitle: 4D/2D duality and representation theory

      Abstract: This talk is about the 4D/2D duality discovered by Beem et al. rather recently in physics. It associates a vertex operator algebra (VOA) to any 4-dimensional superconformal field theory, which is expected to be a complete invariant of thl theory. The VOAs appearing in this manner may be regarded as chiralization of various symplectic singularities and their representations are expected to be closely related with the Coulomb branch of the 4D theory. I will talk about this remarkable 4D/2D duality from a representation theoretic perspective.

      10:00am – 10:45amShashank KanadeTitle: Combinatorics of principal W-algebras of type A

      Abstract: The combinatorics of principal W_r(p,p’) algebras of type A is controlled by cylindric partitions. However, very little seems to be known in general about fermionic expressions for the corresponding characters. Welsh’s work explains the case of Virasoro minimal models W_2(p,p’). Andrews, Schilling and Warnaar invented and used an A_2 version of the usual (A_1) Bailey machinery to give fermionic characters (up to a factor of (q)_\infty) of some, but not all, W_3(3,p’) modules. In a recent joint work with Russell, we have given a complete set of conjectures encompassing all of the remaining modules for W_3(3,p’), and proved our conjectures for small values of p’. In another direction, characters of W_r(p,p’) algebras also arise as appropriate limits of certain sl_r coloured Jones invariants of torus knots T(p,p’), and we expect this to provide further insights on the underlying combinatorics.

      11:00am – 11:45amGufang ZhaoTitle: Quasimaps to quivers with potentials

      Abstract: This talk concerns non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of the potential. The construction borrows ideas from the theory of gauged linear sigma models as well as recent development in shifted symplectic geometry and Donaldson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual counts arising from quivers with potentials are discussed. This is based on work in progress, in collaboration with Yalong Cao.

      11:45am – 01:30pmGroup Photo, Lunch
      01:30pm – 02:15pmYaping YangTitle: Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

      Abstract: Let X be a smooth local toric Calabi-Yau 3-fold. On the cohomology of the moduli spaces of certain sheaves on X, there is an action of the cohomological Hall algebra (COHA) of Kontsevich and Soibelman via “raising operators”. I will discuss the “double” of the COHA that acts on the cohomology of the moduli space by adding the “lowering operators”. We associate a root system to X. The double COHA is expected to be the shifted Yangian of this root system. We also give a prediction for the shift in terms of an intersection pairing. We provide evidence of the aforementioned expectation in various examples. This is based on my joint work with M. Rapcak, Y. Soibelman, and G. Zhao

      02:30pm – 03:15pmFei HanTitle: Graded T-duality with H-flux for 2d sigma models

      Abstract: T-duality in string theory can be realised as a transformation acting on the worldsheet fields in the two-dimensional nonlinear sigma model. Bouwknegt-Evslin-Mathai established the T-duality in a background flux for the first time upon compactifying spacetime in one direction to a principal circle by constructing the T-dual maps transforming the twisted cohomology of the dual spacetimes. In this talk, we will describe our recent work on how to promote the T-duality maps of Bouwknegt-Evslin-Mathai in two aspects. More precisely, we will introduce (1) graded T-duality, concerning the graded T-duality maps of all levels of twistings; (2) the 2-dimensional sigma model picture, concerning the double loop space of spacetimes. This represents our joint work with Mathai.

      03:15pm – 3:45pmBreak
      03:45pm – 04:30pmMauricio RomoTitle: Networks and BPS Counting: A-branes view point

      Abstract: I will review the countings of BPS invariants via exponential/spectral networks and present an interpretation of this counting as a count of certain points in the moduli space of A-branes corresponding to degenerate Lagrangians.

      04:45pm – 05:30pmShinobu HosonoTitle: Mirror symmetry of abelian fibered Calabi-Yau manifolds with ρ = 2

      Abstract: I will describe mirror symmetry of Calabi-Yau manifolds fibered by (1,8)-polarized abelian surfaces, which have Picard number two. Finding a mirror family over a toric variety explicitly, I  observe that mirror symmetry of all related Calabi-Yau manifods arises from the corresponding boundary points, which are not necessarily toric boundary points.  Calculating Gromov-Witten invariants up to genus 2, I find that the generating functions are expressed elliptic (quasi-)modular forms, which reminds us the modular anomaly equation found for elliptic surfaces. This talk is based on a published work with Hiromichi Takaki (arXiv:2103.08150).

      06:00pmBanquet @ Royal East Restaurant, 782 Main St, Cambridge, MA 02139

       

      12/1 (Thursday)

      08:30am – 09:00amRefreshments
      09:00am – 09:45amConan Nai Chung Leung*Title: Quantization of Kahler manifolds

      Abstract: I will explain my recent work on relationships among geometric quantization, deformation quantization, Berezin-Toeplitz quantization and brane quantization.

      10:00am – 10:45amCuipo Jiang*Title: Cohomological varieties associated to vertex operator algebras

      Abstract: We define and examine the cohomological variety of a vertex algebra, a notion cohomologically dual to that of the associated variety, which measures the smoothness of the associated scheme at the vertex point.  We study its basic properties. As examples, we construct a closed subvariety of the cohomological variety for rational affine vertex operator algebras constructed from finite dimensional simple Lie algebras. We also determine the cohomological varieties of the simple Virasoro vertex operator algebras. These examples indicate that, although the associated variety for a rational $C_2$-cofinite vertex operator algebra is always a simple point, the cohomological variety can have as large a dimension as possible. This talk is based on joint work with Antoine Caradot and Zongzhu Lin.

      11:00am – 11:45amAnne Moreau*Title: Action of the automorphism group on the Jacobian of Klein’s quartic curve

      Abstract: In a joint work with Dimitri Markouchevitch, we prove that the quotient variety of the 3-dimensional Jacobian of the plane Klein quartic curve by its full automorphism group of order 336 is isomorphic to the 3-dimensional weighted projective space with weights 1,2,4,7.

      The latter isomorphism is a particular case of the general conjecture of Bernstein and Schwarzman suggesting that a quotient of the n-dimensional complex space by the action of an irreducible complex crystallographic group generated by reflections is a weighted projective space.

      In this talk, I will explain this conjecture and the proof of our result. An important ingredient is the computation of the Hilbert function of the algebra of invariant theta-functions on the Jacobian.

      11:45am – 11:50amClosing remarks
      11:50amFree discussions and departure

      * = Online speaker

      CMSA COVID-19 Policies

       

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 11.23.22

      Topological Quantum Matter Seminar

      Speaker: Jian Kang, School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

      Title: Continuum field theory of graphene bilayer system

      Abstract: The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the magic-angle twisted bilayer graphene (MATBG), and nowadays is a starting point for most theoretical works. In this talk, I will briefly review the BM model and then present a continuum field theory [1] for graphene bilayer system allowing any smooth lattice deformation including the small twist angle. With the gradient expansion to the second order, the continuum theory for MATBG [2] produces the spectrum that almost perfectly matches the spectrum of the microscopic model, suggesting the validity of this theory. In the presence of the lattice deformation, the inclusion of the pseudo-vector potential does not destroy but shift the flat band chiral limit to a smaller twist angle. Furthermore, the continuum theory contains another important interlayer tunneling term that was overlooked in all previous works. This term non-negligibly breaks the particle-hole symmetry of the narrow bands and may be related with the experimentally observed particle-hole asymmetry.

      1. O. Vafek and JK, arXiv: 2208.05933.
      2. JK and O. Vafek, arXiv: 2208.05953.

       

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Sungwoo Hong (U Chicago & KAIST)

      Title: Neutrino Masses from Generalized Symmetry Breaking

      Abstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

       

      https://www.youtube.com/watch?v=4eZa06kiPCs&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=22

    • Program
      9:00 am-5:00 pm
      12/01/2024-05/24/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Mathematical Aspects of Scattering Amplitudes Program

      To receive email updates and program announcements, visit this link to sign up for the CMSA Mathematical Aspects of Scattering Amplitudes Program mailing list.

      Dates: April 15 – May 24, 2024

      Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138

      Organizers:

      Participants:

      This program will feature a weekly seminar series.
      Further Details TBA.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Justin Kulp (Perimeter Institute)

      Title: Holomorphic Twists and Confinement in N=1 SYM

      Abstract: Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

    • Workshop
      9:00 am-5:00 pm
      12/01/2024-05/05/2022
      GR Workshop Poster

      General Relativity Workshop on scalar curvature, minimal surfaces, and initial data sets

      Dates: May 2–5, 2022

      Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138 and via Zoom webinar.
      Advanced registration for in-person components is required.

      Organizers: Dan Lee (CMSA/CUNY), Martin Lesourd (CMSA/BHI), and Lan-Hsuan Huang (University of Connecticut).

      Speakers:

      • Zhongshan An, University of Connecticut
      • Paula Burkhardt-Guim, NYU
      • Hyun Chul Jang, University of Miami
      • Chao Li, NYU
      • Christos Mantoulidis, Rice University
      • Robin Neumayer, Carnegie Mellon University
      • Andre Neves, University of Chicago
      • Tristan Ozuch, MIT
      • Annachiara Piubello, University of Miami
      • Antoine Song, UC Berkeley
      • Tin-Yau Tsang, UC Irvine
      • Ryan Unger, Princeton
      • Zhizhang Xie, Texas A & M
      • Xin Zhou, Cornell University
      • Jonathan Zhu, Princeton University

      Schedule

      Download PDF

      Monday, May 2, 2022

      9:30–10:30 amHyun Chul JangTitle: Mass rigidity for asymptotically locally hyperbolic manifolds with boundary

      Abstract: Asymptotically locally hyperbolic (ALH) manifolds are a class of manifolds whose sectional curvature converges to −1 at infinity. If a given ALH manifold is asymptotic to a static reference manifold, the Wang-Chruściel-Herzlich mass integrals are well-defined, which is a geometric invariant that essentially measure the difference from the reference manifold. In this talk, I will present the result that an ALH manifold which minimize the mass integrals admits a static potential. To show this, we proved the scalar curvature map is locally surjective when it is defined on (1) the space of ALH metrics that coincide exponentially toward the boundary or (2) the space of ALH metrics with arbitrarily prescribed nearby Bartnik boundary data. And then, we establish the rigidity of the known positive mass theorems by studying the static uniqueness. This talk is based on joint work with L.-H. Huang.

      10:40–11:40 amAnnachiara PiubelloTitle: Estimates on the Bartnik mass and their geometric implications.

      Abstract: In this talk, we will discuss some recent estimates on the Bartnik mass for data with non-negative Gauss curvature and positive mean curvature. In particular, if the metric is round the estimate reduces to an estimate found by Miao and if the total mean curvature approaches 0, the estimate tends to 1/2 the area radius, which is the bound found by Mantoulidis and Schoen in the blackhole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.

      LUNCH BREAK
      1:30–2:30 pmRyan UngerTitle: Density and positive mass theorems for black holes and incomplete manifolds

      Abstract: We generalize the density theorems for the Einstein constraint equations of Corvino-Schoen and Eichmair-Huang-Lee-Schoen to allow for marginally outer trapped boundaries (which correspond physically to apparent horizons). As an application, we resolve the spacetime positive mass theorem in the presence of MOTS boundary in the non-spin case. This also has a surprising application to the Riemannian setting, including a non-filling result for manifolds with negative mass. This is joint work with Martin Lesourd and Dan Lee.

      2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications I

      Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

      TEA BREAK
      4:10–5:10 pmAntoine Song (virtual)Title: The spherical Plateau problem

      Abstract: For any closed oriented manifold with fundamental group G, or more generally any group homology class for a group G, I will discuss an infinite codimension Plateau problem in a Hilbert classifying space for G. For instance, for a closed oriented 3-manifold M, the intrinsic geometry of any Plateau solution is given by the hyperbolic part of M.

      Tuesday, May 3, 2022

      9:30–10:30 amChao LiTitle: Stable minimal hypersurfaces in 4-manifolds

      Abstract: There have been a classical theory for complete minimal surfaces in 3-manifolds, including the stable Bernstein conjecture in R^3 and rigidity results in 3-manifolds with positive Ricci curvature. In this talk, I will discuss how one may extend these results in four dimensions. This leads to new comparison theorems for positively curved 4-manifolds.

      10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds I

      Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

      LUNCH BREAK
      1:30–2:30 pmZhongshan AnTitle: Local existence and uniqueness of static vacuum extensions of Bartnik boundary data

      Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data — the induced metric and mean curvature of the boundary — is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang.

      2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications II

      Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

      TEA BREAK
      4:10–5:10 pmTin-Yau TsangTitle: Dihedral rigidity, fill-in and spacetime positive mass theorem

      Abstract: For compact manifolds with boundary, to characterise the relation between scalar curvature and boundary geometry, Gromov proposed dihedral rigidity conjecture and fill-in conjecture. In this talk, we will see the role of spacetime positive mass theorem in answering the corresponding questions for initial data sets.

      Speakers Banquet

      Wednesday, May 4, 2022

      9:30–10:30 amTristan OzuchTitle: Weighted versions of scalar curvature, mass and spin geometry for Ricci flows

      Abstract: With A. Deruelle, we define a Perelman-like functional for ALE metrics which lets us study the (in)stability of Ricci-flat ALE metrics. With J. Baldauf, we extend some classical objects and formulas from the study of scalar curvature, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.

      10:40–11:40 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds II

      Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

      LUNCH BREAK
      1:30–2:30 pmChristos MantoulidisTitle: Metrics with lambda_1(-Delta+kR) > 0 and applications to the Riemannian Penrose Inequality

      Abstract: On a closed n-dimensional manifold, consider the space of all Riemannian metrics for which -Delta+kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally, for different values of k, in the study of scalar curvature in dimension n + 1 via minimal surfaces, the Yamabe problem in dimension n, and Perelman’s surgery for Ricci flow in dimension n = 3. We study these spaces in unison and generalize, as appropriate, scalar curvature results that we eventually apply to k = 1/2, where the space above models apparent horizons in time-symmetric initial data sets to the Einstein equations and whose flexibility properties are intimately tied with the instability of the Riemannian Penrose Inequality. This is joint work with Chao Li.

      2:40–3:40 pmZhizhang XieTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications III

      Abstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.

      TEA BREAK
      4:10–5:10 pmXin Zhou
      (Virtual)
      Title: Min-max minimal hypersurfaces with higher multiplicity

      Abstract: It is well known that minimal hypersurfaces produced by the Almgren-Pitts min-max theory are counted with integer multiplicities. For bumpy metrics (which form a generic set), the multiplicities are one thanks to the resolution of the Marques-Neves Multiplicity One Conjecture. In this talk, we will exhibit a set of non-bumpy metrics on the standard (n+1)-sphere, in which the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere. Such non-bumpy metrics form the first set of examples where the min-max theory must produce higher multiplicity minimal hypersurfaces. The talk is based on a joint work with Zhichao Wang (UBC).

      May 5, 2022

      9:00–10:00 amAndre NevesTitle: Metrics on spheres where all the equators are minimal

      Abstract: I will talk about joint work with Lucas Ambrozio and Fernando Marques where we study the space of metrics where all the equators are minimal.

      10:10–11:10 amRobin NeumayerTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds III

      Abstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge, and what the limiting objects look like. In this mini-course, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.

      11:20–12:20 pmPaula Burkhardt-GuimTitle: Lower scalar curvature bounds for C^0 metrics: a Ricci flow approach

      Abstract: We describe some recent work that has been done to generalize the notion of lower scalar curvature bounds to C^0 metrics, including a localized Ricci flow approach. In particular, we show the following: that there is a Ricci flow definition which is stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C^0 initial data.

      LUNCH BREAK
      1:30–2:30 pmJonathan ZhuTitle: Widths, minimal submanifolds and symplectic embeddings

      Abstract: Width or waist inequalities measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels.

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.26.2022-1583x2048-1

      Abstract: In spatial population genetics, it is important to understand the probability of extinction in multi-species interactions such as growing bacterial colonies, cancer tumor evolution and human migration. This is because extinction probabilities are instrumental in determining the probability of coexistence and the genealogies of populations. A key challenge is the complication due to spatial effect and different sources of stochasticity. In this talk, I will discuss about methods to compute the probability of extinction and other long-time behaviors for stochastic reaction-diffusion equations on metric graphs that flexibly parametrizes the underlying space. Based on recent joint work with Adrian Gonzalez-Casanova and Yifan (Johnny) Yang.

    • Colloquium
      Colloquium Colloquia & Seminar
      Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a seminar on Combinatorics, Physics and Probability, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu).

      The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/25/2022
      *note special time 9:00–10:00 AM ET
      Jacob Bourjaily (Penn State University, Eberly College of ScienceTitle: Adventures in Perturbation Theory

      Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

      2/3/2022Ran Tessler
      (Weizmann Institute of Science)
      Title: The Amplituhedron BCFW Triangulation

      Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

      2/8/2022Anna Seigal (Harvard)Title: Invariant theory for maximum likelihood estimation

      Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

      2/15/2022Igor Balla, Hebrew University of JerusalemTitle: Equiangular lines and regular graphs

      Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

      Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
      the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/21/2021Nima Arkani-Hamed
      IAS (Institute for Advanced Study), School of Natural Sciences
      Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes
      9/28/2021Melissa Sherman-Bennett
      University of Michigan, Department of Mathematics
      Title: The hypersimplex and the m=2 amplituhedron

      Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

      10/5/2021Daniel Cizma, Hebrew UniversityTitle: Geodesic Geometry on Graphs

      Abstract: In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

      We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

      Joint work with Nati Linial.

      10/12/2021Lisa Sauermann, MITTitle: On counting algebraically defined graphs

      Abstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane), the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials), and this lower bound essentially matches the upper bound from Warren’s theorem.

      10/19/2021Pavel Galashin
      UCLA, Department of Mathematics
      Title: Ising model, total positivity, and criticality

      Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
      The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
      I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model.

      10/26/2021Candida Bowtell, University of OxfordTitle: The n-queens problem

      Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

      In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

      This is joint work with Peter Keevash.

      11/9/2021Steven Karp
      Universite du Quebec a Montreal, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)
      Title: Gradient flows on totally nonnegative flag varieties

      Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.
      11/16/2021
      *note special time 12:30–1:30 ET*
      Yinon Spinka (University of British Columbia)Title: A tale of two balloons

      Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
      Joint work with Omer Angel and Gourab Ray.

      11/23/2021Lutz Warnke (UC San Diego)Title: Prague dimension of random graphs

      Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

      11/30/2021Karel Devriendt (University of Oxford)Title: Resistance curvature – a new discrete curvature on graphs

      Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
      In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
      Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
      This work was done in collaboration with Renaud Lambiotte.

      12/7/2021Matthew Jenssen (University of Birmingham)Title: The singularity probability of random symmetric matrices

      Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

      12/14/2021Stefan Glock (ETH Zurich)Title: The longest induced path in a sparse random graph

      Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

      12/21/2021
      01/25/2022Jacob Bourjaily
      Penn State University, Department of Physics
    • Program
      9:00 am-5:00 pm
      12/01/2024-06/12/2022
      CMSA-2-600x338

      The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

      Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

      In this course, we will start with an introduction to computer programming, algorithms, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, and differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

      The program hopes to provide several research mentors from various disciplines who will give some of the course lectures. Students will have the opportunity to work with one of the research mentors offered by the program.

      Prerequisites: Basic coding ability in some programming language (C/Python/Matlab or CS50 experience). Some background in calculus and linear algebra is needed too. If you wish to work with a research mentor on differential geometry, more background in geometry such as from Math 132 or 136 will be useful. If you wish to work with a research mentor on computer science, coding experience mentioned above will be very useful. If you wish to work with a medical scientist, some background in life science or basic organic chemistry is recommended.

      The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

      This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard-related perks (such as a place to live if you are in Boston over the summer.)

      However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third-year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

      If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited, so don’t wait too long to apply.

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.19.22-1583x2048-1

      Abstract: Conditional independence (CI) is an important tool instatistical modeling, as, for example, it gives a statistical interpretation to graphical models. In general, given a list of dependencies among random variables, it is difficult to say which constraints are implied by them. Moreover, it is important to know what constraints on the random variables are caused by hidden variables. On the other hand, such constraints are corresponding to some determinantal conditions on the tensor of joint probabilities of the observed random variables. Hence, the inference question in statistics relates to understanding the algebraic and geometric properties of determinantal varieties such as their irreducible decompositions or determining their defining equations. I will explain some recent progress that arises by uncovering the link to point configurations in matroid theory and incidence geometry. This connection, in particular, leads to effective computational approaches for (1) giving a decomposition for each CI variety; (2) identifying each component in the decomposition as a matroid variety; (3) determining whether the variety has a real point or equivalently there is a statistical model satisfying a given collection of dependencies. The talk is based on joint works with Oliver Clarke, Kevin Grace, and Harshit Motwani.

      The papers are available on arxiv: https://arxiv.org/pdf/2011.02450
      and https://arxiv.org/pdf/2103.16550.pdf

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/22/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Conference
      9:00 am-6:00 pm
      12/01/2024
      150 Western Ave, Allston, MA 02134
      SMaSH_2022-2

      SMaSH: Symposium for Mathematical Sciences at Harvard

      On Tuesday, May 17, 2022, from 9:00 am – 5:30 pm, the Harvard John A Paulson School of Engineering and Applied Sciences (SEAS) and the Harvard Center of Mathematical Sciences and Applications (CMSA) held a Symposium for Mathematical Sciences for the mathematical sciences community at Harvard.

      Organizing Committee

      • Michael Brenner, Applied Mathematics (SEAS)
      • Michael Desai, Organismic and Evolutionary Biology (FAS)
      • Sam Gershman, Psychology (FAS)
      • Michael Hopkins, Mathematics (FAS)
      • Gary King, Government (FAS)
      • Peter Koellner, Philosophy (FAS)
      • Scott Kominers, Economics (FAS) & Entrepreneurial Management (HBS)
      • Xihong Lin, Biostatistics (HSPH) & Statistics (FAS)
      • Yue Lu, Electrical Engineering (SEAS)
      • Susan Murphy, Statistics (FAS) & Computer Science (SEAS)
      • Lisa Randall, Physics (SEAS)
      • Eugene Shakhnovich, Chemistry (FAS)
      • Salil Vadhan, Computer Science (SEAS)
      • Horng-Tzer Yau, Mathematics (FAS)

      This event was held in-person at the Science and Engineering Complex (SEC) at 150 Western Ave, Allston, MA 02134, and streamed on Zoom.

      Harvard graduate students and postdocs presented Poster Sessions.


      Venue: Science and Engineering Complex (SEC)


      Speakers

      • Anurag Anshu, Computer Science (SEAS)
      • Morgane Austern, Statistics (FAS)
      • Demba Ba, Electrical Engineering & Bioengineering (SEAS)
      • Michael Brenner, Applied Mathematics (SEAS)
      • Rui Duan, Biostatistics (HSPH)
      • Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)
      • Kosuke Imai, Government & Statistics (FAS)
      • Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)
      • Seth Neel, Technology & Operations Management (HBS)
      • Melanie Matchett Wood, Mathematics (FAS)

      Schedule PDF

      Schedule

      9:00–9:30 amCoffee and Breakfast
      West Atrium (ground floor of the SEC)
      9:30–10:30 amFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumKosuke Imai, Government & Statistics (FAS): Use of Simulation Algorithms for Legislative Redistricting Analysis and EvaluationYannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS): The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization
      10:30–11:00 amCoffee Break
      West Atrium (ground floor of the SEC)
      11:00–12:00 pmFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumSeth Neel, Technology & Operations Management (HBS): “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy LawDemba Ba, Electrical Engineering & Bioengineering (SEAS): Geometry, AI, and the Brain
      12:00–1:00 pmLunch Break
      Engineering Yard Tent
      1:00–2:30 pmFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMelanie Matchett Wood, Mathematics (FAS): Understanding distributions of algebraic structures through their momentsMorgane Austern, Statistics (FAS): Limit theorems for structured random objectsAnurag Anshu, Computer Science (SEAS): Operator-valued polynomial approximations and their use.
      2:30–3:00 pmCoffee Break
      West Atrium (ground floor of the SEC)
      3:00–4:30 pmFaculty Talks
      Winokur Family Hall Classroom (Room 1.321) located just off of the West AtriumMichael Brenner, Applied Mathematics (SEAS): Towards living synthetic materialsRui Duan, Biostatistics (HSPH): Federated and transfer learning for healthcare data integrationSham M. Kakade, Computer Science (SEAS) & Statistics (FAS): What is the Statistical Complexity of Reinforcement Learning?
      4:30–5:30 pmReception with Jazz musicians
      & Poster Session
      Engineering Yard Tent

      Faculty Talks

      SpeakerTitle / Abstract / Bio
      Anurag Anshu, Computer Science (SEAS)Title: Operator-valued polynomial approximations and their use.

      Abstract: Approximation of complicated functions with low degree polynomials is an indispensable tool in mathematics. This becomes particularly relevant in computer science, where the complexity of interesting functions is often captured by the degree of the approximating polynomials. This talk concerns the approximation of operator-valued functions (such as the exponential of a hermitian matrix, or the intersection of two projectors) with low-degree operator-valued polynomials. We will highlight the challenges that arise in achieving similarly good approximations as real-valued functions, as well as recent methods to overcome them. We will discuss applications to the ground states in physics and quantum complexity theory: correlation lengths, area laws and concentration bounds.

      Bio: Anurag Anshu is an Assistant Professor of computer science at Harvard University. He spends a lot of time exploring the rich structure of quantum many-body systems from the viewpoint of quantum complexity theory, quantum learning theory and quantum information theory. He held postdoctoral positions at University of California, Berkeley and University of Waterloo and received his PhD from National University of Singapore, focusing on quantum communication complexity.

      Morgane Austern, Statistics (FAS)Title: Limit theorems for structured random objects

      Abstract: Statistical inference relies on numerous tools from probability theory to study the properties of estimators. Some of the most central ones are the central limit theorem and the free central limit theorem. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting. We consider distributionally “structured’ and dependent random object i.e random objects whose distribution is invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory.

      Bio: Morgane Austern is an assistant professor in the Statistics Department of Harvard University. Broadly, she is interested in developing probability tools for modern machine learning and in establishing the properties of learning algorithms in structured and dependent data contexts. She graduated with a PhD in statistics from Columbia University in 2019 where she worked in collaboration with Peter Orbanz and Arian Maleki on limit theorems for dependent and structured data. She was a postdoctoral researcher at Microsoft Research New England from 2019 to 2021.

      Demba Ba, Electrical Engineering & Bioengineering (SEAS)Title: Geometry, AI, and the Brain

      Abstract: A large body of experiments suggests that neural computations reflect, in some sense, the geometry of “the world”. How do artificial and neural systems learn representations of “the world” that reflect its geometry? How, for instance, do we, as humans, learn representations of objects, e.g. fruits, that reflect the geometry of object space? Developing artificial systems that can capture/understand the geometry of the data they process may enable them to learn representations useful in many different contexts and tasks. My talk will describe an artificial neural-network architecture that, starting from a simple union-of-manifold model of data comprising objects from different categories, mimics some aspects of how primates learn, organize, and retrieve concepts, in a manner that respects the geometry of object space.

      Bio: Demba Ba serves as an Associate Professor of electrical engineering and bioengineering in Harvard University’s School of Engineering and Applied Sciences, where he directs the CRISP group. Recently, he has taken a keen interest in the connection between artificial neural networks and sparse signal processing. His group leverages this connection to solve data-driven unsupervised learning problems in neuroscience, to understand the principles of hierarchical representations of sensory signals in the brain, and to develop explainable AI. In 2016, he received a Research Fellowship in Neuroscience from the Alfred P. Sloan Foundation. In 2021, Harvard’s Faculty of Arts and Sciences awarded him the Roslyn Abramson award for outstanding undergraduate teaching.

      Michael Brenner, Applied Mathematics (SEAS)Title: Towards living synthetic materials

      Abstract: Biological materials are much more complicated and functional than synthetic ones. Over the past several years we have been trying to figure out why. A sensible hypothesis is that biological materials are programmable. But we are very far from being able to program materials we create with this level of sophistication.  I will discuss our (largely unsuccessful) efforts to bridge this gap, though as of today I’m somewhat optimistic that we are arriving at a set of theoretical models that is rich enough to produce relevant emergent behavior.

      Bio: I’ve been at Harvard for a long time. My favorite part of Harvard is the students.

      Rui Duan, Biostatistics (HSPH)Title: Federated and transfer learning for healthcare data integration

      Abstract: The growth of availability and variety of healthcare data sources has provided unique opportunities for data integration and evidence synthesis, which can potentially accelerate knowledge discovery and improve clinical decision-making. However, many practical and technical challenges, such as data privacy, high dimensionality, and heterogeneity across different datasets, remain to be addressed. In this talk, I will introduce several methods for the effective and efficient integration of multiple healthcare datasets in order to train statistical or machine learning models with improved generalizability and transferability. Specifically, we develop communication-efficient federated learning algorithms for jointly analyzing multiple datasets without the need of sharing patient-level data, as well as transfer learning approaches that leverage shared knowledge learned across multiple datasets to improve the performance of statistical models in target populations of interest. We will discuss both the theoretical properties and examples of implementation of our methods in real-world research networks and data consortia.

      Bio: Rui Duan is an Assistant Professor of Biostatistics at the Harvard T.H. Chan School of Public Health. She received her Ph.D. in Biostatistics in May 2020 from the University of Pennsylvania. Her research interests focus on developing statistical, machine learning, and informatics tools for (1) efficient data integration in biomedical research, (2) understanding and accounting for the heterogeneity of biomedical data, and improving the generalizability and transferability of models across populations (3) advancing precision medicine research on rare diseases and underrepresented populations.

      Yannai A. Gonczarowski, Economics (FAS) & Computer Science (SEAS)Title: The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization

      Abstract: We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε > 0, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples.

      Our fully nonparametric approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that are not necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art.

      Joint work with S. Matthew Weinberg

      Bio: Yannai A. Gonczarowski is an Assistant Professor of Economics and of Computer Science at Harvard University—the first faculty member at Harvard to have been appointed to both of these departments. Interested in both economic theory and theoretical computer science, Yannai explores computer-science-inspired economics: he harnesses approaches, aesthetics, and techniques traditionally originating in computer science to derive economically meaningful insights. Yannai received his PhD from the Departments of Math and CS, and the Center for the Study of Rationality, at the Hebrew University of Jerusalem, where he was advised by Sergiu Hart and Noam Nisan. Yannai is also a professionally-trained opera singer, having acquired a bachelor’s degree and a master’s degree in Classical Singing at the Jerusalem Academy of Music and Dance. Yannai’s doctoral dissertation was recognized with several awards, including the 2018 Michael B. Maschler Prize of the Israeli Chapter of the Game Theory Society, and the ACM SIGecom Doctoral Dissertation Award for 2018. For the design and implementation of the National Matching System for Gap-Year Programs in Israel, he was awarded the Best Paper Award at MATCH-UP’19 and the inaugural INFORMS AMD Michael H. Rothkopf Junior Researcher Paper Prize (first place) for 2020. Yannai is also the recipient of the inaugural ACM SIGecom Award for Best Presentation by a Student or Postdoctoral Researcher at EC’18. His first textbook, “Mathematical Logic through Python” (Gonczarowski and Nisan), which introduces a new approach to teaching the material of a basic Logic course to Computer Science students, tailored to the unique intuitions and strengths of this cohort of students, is forthcoming in Cambridge University Press.

      Kosuke Imai, Government & Statistics (FAS)Title: Use of Simulation Algorithms for Legislative Redistricting Analysis and Evaluation

      Abstract: After the 2020 Census, many states have been redrawing the boundaries of Congressional and state legislative districts. To evaluate the partisan and racial bias of redistricting plans, scholars have developed Monte Carlo simulation algorithms. The idea is to generate a representative sample of redistricting plans under a specified set of criteria and conduct a statistical hypothesis test by comparing a proposed plan with these simulated plans. I will give a brief overview of these redistricting simulation algorithms and discuss how they are used in real-world court cases.

      Bio: Kosuke Imai is Professor in the Department of Government and Department of Statistics at Harvard University. Before moving to Harvard in 2018, Imai taught at Princeton University for 15 years where he was the founding director of the Program in Statistics and Machine Learning. Imai specializes in the development of statistical methods and machine learning algorithms and their applications to social science research. His areas of expertise include causal inference, computational social science, program evaluation, and survey methodology.

      Sham M. Kakade, Computer Science (SEAS) & Statistics (FAS)Title: What is the Statistical Complexity of Reinforcement Learning?

      Abstract: This talk will highlight much of the recent progress on the following fundamental question in the theory of reinforcement learning: what (representational or structural) conditions govern our ability to generalize and avoid the curse of dimensionality?  With regards to supervised learning, these questions are reasonably well understood, both practically and theoretically: practically, we have overwhelming evidence on the value of representational learning (say through modern deep networks) as a means for sample efficient learning, and, theoretically, there are well-known complexity measures (e.g. the VC dimension and Rademacher complexity) that govern the statistical complexity of learning.  Providing an analogous theory for reinforcement learning is far more challenging, where even characterizing structural conditions which support sample efficient generalization has been far less well understood, until recently.

      This talk will survey recent advances towards characterizing when generalization is possible in RL, focusing on both necessary and sufficient conditions. In particular, we will introduce a new complexity measure, the Decision-Estimation Coefficient, that is proven to be necessary (and, essentially, sufficient) for sample-efficient interactive learning.

      Bio: Sham Kakade is a professor at Harvard University and a co-director of the Kempner Institute for the Study of Artificial and Natural Intelligence.  He works on the mathematical foundations of machine learning and AI. Sham’s thesis helped lay the statistical foundations of reinforcement learning. With his collaborators, his additional contributions include foundational results on: policy gradient methods in reinforcement learning; regret bounds for linear bandit and Gaussian process bandit models; the tensor and spectral methods for latent variable models; and a number of convergence analyses for convex and non-convex algorithms.  He is the recipient of the ICML Test of Time Award, the IBM Pat Goldberg best paper award, and INFORMS Revenue Management and Pricing Prize. He has been program chair for COLT 2011.

      Sham was an undergraduate at Caltech, where he studied physics and worked under the guidance of John Preskill in quantum computing. He completed his Ph.D. with Peter Dayan in computational neuroscience at the Gatsby Computational Neuroscience Unit. He was a postdoc with Michael Kearns at the University of Pennsylvania.

      Seth Neel, Technology & Operations Management (HBS)Title: “Machine (Un)Learning” or Why Your Deployed Model Might Violate Existing Privacy Law

      Abstract:  Businesses like Facebook and Google depend on training sophisticated models on user data. Increasingly—in part because of regulations like the European Union’s General Data Protection Act and the California Consumer Privacy Act—these organizations are receiving requests to delete the data of particular users. But what should that mean? It is straightforward to delete a customer’s data from a database and stop using it to train future models. But what about models that have already been trained using an individual’s data? These are not necessarily safe; it is known that individual training data can be exfiltrated from models trained in standard ways via model inversion attacks. In a series of papers we help formalize a rigorous notion of data-deletion and propose algorithms to efficiently delete user data from trained models with provable guarantees in both convex and non-convex settings.

      Bio: Seth Neel is a first-year Assistant Professor in the TOM Unit at Harvard Business School, and Co-PI of the SAFR ML Lab in the D3 Institute, which develops methodology to incorporate privacy and fairness guarantees into techniques for machine learning and data analysis, while balancing other critical considerations like accuracy, efficiency, and interpretability. He obtained his Ph.D. from the University of Pennsylvania in 2020 where he was an NSF graduate fellow. His work has focused primarily on differential privacy, notions of fairness in a variety of machine learning settings, and adaptive data analysis.

      Melanie Matchett Wood, Mathematics (FAS)Title: Understanding distributions of algebraic structures through their moments

      Abstract: A classical tool of probability and analysis is to use the moments (mean, variance, etc.) of a distribution to recognize an unknown distribution of real numbers.  In recent work, we are interested in distributions of algebraic structures that can’t be captured in a single number.  We will explain one example, the fundamental group, that captures something about the shapes of possibly complicated or high dimensional spaces.  We are developing a new theory of the moment problem for random algebraic structures which helps to to identify distributions of such, such as fundamental groups of random three dimensional spaces.  This talk is based partly on joint work with Will Sawin.

      Bio: Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study.  Her work spans number theory, algebraic geometry, algebraic topology, additive combinatorics, and probability. Wood has been awarded a CAREER grant, a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, and the AWM-Microsoft Research Prize in Algebra and Number Theory, and she is a Fellow of the American Mathematical Society. In 2021, Wood received the National Science Foundation’s Alan T. Waterman Award, the nation’s highest honor for early-career scientists and engineers.


    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Frances Kirwan (University of Oxford)

      TitleMoment maps and the Yang-Mills functional

      Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led.

      This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

      Talk chair: Peter Kronheimer

      Video

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/29/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Conference in Memory of Professor Masatake Kuranishi
      9:00 am-12:30 pm
      12/01/2024-05/12/2022
      150 Western Ave, Allston, MA 02134
      Kuranishi_Harvard_10x12-2

      On May 9–12, 2022, the CMSA hosted the conference Deformations of structures and moduli in geometry and analysis: A Memorial in honor of Professor Masatake Kuranishi.

      Organizers:  Tristan Collins (MIT) and Shing-Tung Yau (Harvard and Tsinghua)

      Videos are available on the conference playlist.

       

      Speakers:

      Charles Fefferman (Princeton University)

      Teng Fei (Rutgers University)

      Robert Friedman (Columbia University)

      Kenji Fukaya (Simons Center, Stony Brook)

      Akito Futaki (Tsinghua University)

      Victor Guillemin (Massachusetts Institute of Technology)

      Nigel Hitchin (Oxford University)

      Blaine Lawson (Stony Brook University)

      Yu-Shen Lin (Boston University)

      Melissa C.C. Liu (Columbia University)

      Takeo Ohsawa (Nagoya University)

      Duong H. Phong (Columbia University)

      Sebastien Picard (University of British Columbia)

      Paul Seidel (Massachusetts Institute of Technology)

      Gabor Szekelyhidi (University of Notre Dame)

      Claire Voisin (Institut de Mathematiques, Jussieu, France)

      Shing-Tung Yau (Harvard University)

       

      Schedule (download pdf)


      Monday, May 9, 2022

      8:15 amLight breakfast & coffee/tea
      8:45–9:00 amOpening Remarks
      9:00–10:00 amKenji FukayaTitle: Gromov Hausdorff convergence of filtered A infinity category

      Abstract: In mirror symmetry a mirror to a symplectic manifold is actually believed to be a family of complex manifold parametrized by a disk (of radius 0). The coordinate ring of the parameter space is a kind of formal power series ring the Novikov ring. Novikov ring is a coefficient ring of Floer homology. Most of the works on homological Mirror symmetry so far studies A infinity category over Novikov field, which corresponds to the study of generic fiber. The study of A infinity category over Novikov ring is related to several interesting phenomenon of Hamiltonian dynamics. In this talk I will explain a notion which I believe is useful to study mirror symmetry.

      Video

      10:15–11:15 amNigel Hitchin (Zoom)Title: Deformations: A personal perspective

      Abstract: The talk, largely historical, will focus on different deformation complexes I have encountered in my work, starting with instantons on 4-manifolds, but also monopoles, Higgs bundles and generalized complex structures. I will also discuss some speculative ideas related to surfaces of negative curvature.

      Video

      11:30–12:30 pmH. Blaine LawsonTitle: Projective Hulls, Projective Linking, and Boundaries of Varieties

      Abstract: In 1958 John Wermer proved that the polynomial hull of a compact real analytic curve γ ⊂ Cn was a 1-dim’l complex subvariety of Cn − γ. This result engendered much subsequent activity, and was related to Gelfand’s spectrum of a Banach algebra. In the early 2000’s Reese Harvey and I found a projective analogue of these concepts and wondered whether Wermer’s Theorem could be generalized to the projective setting. This question turned out to be more subtle and quite intriguing, with unexpected consequences. We now know a great deal, a highpoint of which s a result with Harvey and Wermer. It led to conjectures (for Cω-curves in P2C) which imply several results. One says, roughly, that a (2p − 1)-cycle Γ in Pn bounds a positive holomorphic p-chain of mass ≤ Λ ⇐⇒ its normalized linking number with all positive (n − p)-cycles in Pn − |Γ| is ≥ −Λ. Another says that a class τ ∈ H2p(Pn,|Γ|;Z) with ∂τ = Γ contains a positive holomorphic p-chain ⇐⇒ τ•[Z]≥0 for all positive holomorphic (n−p)-cycles Z in Pn−|Γ|

      Video

      12:30–2:30 pmLunch Break
      2:30–3:30 pmGabor SzekelyhidiTitle: Singularities along the Lagrangian mean curvature flow.

      Abstract: We study singularity formation along the Lagrangian mean curvature flow of surfaces. On the one hand we show that if a tangent flow at a singularity is the special Lagrangian union of two transverse planes, then the flow undergoes a “neck pinch”, and can be continued past the flow. This can be related to the Thomas-Yau conjecture on stability conditions along the Lagrangian mean curvature flow. In a different direction we show that ancient solutions of the flow, whose blow-down is given by two planes meeting along a line, must be translators. These are joint works with Jason Lotay and Felix Schulze.

      Video

      3:30–4:00 pmCoffee Break 
      4:00–5:00 pmTakeo OhsawaTitle: Glimpses of embeddings and deformations of CR manifolds

      Abstract: Basic results on the embeddings and the deformations of CR manifolds will be reviewed with emphasis on the reminiscences of impressive moments with Kuranishi since his visit to Kyoto in 1975.

      Video

       

       

       

      Tuesday, May 10, 2022

       

      8:15 amLight breakfast & coffee/tea
      9:00–10:00 amCharles Fefferman (Zoom)Title: Interpolation of Data by Smooth Functions

      Abstract: Let X be your favorite Banach space of continuous functions on R^n. Given an (arbitrary) set E in R^n and an arbitrary function f:E->R, we ask: How can we tell whether f extends to a function F \in X? If such an F exists, then how small can we take its norm? What can we say about its derivatives (assuming functions in X have derivatives)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F as above with norm nearly as small as possible? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few data points (x, f(x)) as “outliers”? Which points should we discard?

      The results were obtained jointly with A. Israel, B. Klartag, G.K. Luli and P. Shvartsman over many years.

      Video

      10:15–11:15 amClaire VoisinTitle: Deformations of K-trivial manifolds and applications to hyper-Kähler geometry

      Summary: I will explain the Ran approach via the T^1-lifting principle to the BTT theorem stating that deformations of K-trivial compact Kähler manifolds are unobstructed. I will explain a similar unobstructedness result for Lagrangian submanifolds of hyper-Kähler manifolds and I will describe important consequences on the topology and geometry of hyper-Kähler manifolds.

      Video

      11:30– 2:30 pmVictor GuilleminTitle: Semi-Classical Functions of Isotropic Type

      Abstract: The world of semiclassical analysis is populated by objects of “Lagrangian type.” The topic of this talk however will be objects in semi-classical analysis that live instead on isotropic submanifolds. I will describe in my talk a lot of interesting examples of such objects.

      Video

      12:30–2:30 pmLunch Break
      2:30–3:30 pmTeng FeiTitle: Symplectic deformations and the Type IIA flow

      Abstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong, Picard and Zhang.

      Video

      Speakers Banquet

       

       

       

      Wednesday, May 11, 2022

       

      8:15 amLight breakfast & coffee/tea
      9:00–10:00 amShing-Tung Yau (Zoom)Title: Canonical metrics and stability in mirror symmetry

      Abstract: I will discuss the deformed Hermitian-Yang-Mills equation, its role in mirror symmetry and its connections to notions of stability.  I will review what is known, and pose some questions for the future.

      Video

      10:15–11:15 amDuong H. PhongTitle: $L^\infty$ estimates for the Monge-Ampere and other fully non-linear equations in complex geometry

      Abstract: A priori estimates are essential for the understanding of partial differential equations, and of these, $L^\infty$ estimates are particularly important as they are also needed for other estimates. The key $L^\infty$ estimates were obtained by S.T. Yau in 1976 for the Monge-Ampere equation for the Calabi conjecture, and sharp estimates obtained later in 1998 by Kolodziej using pluripotential theory. It had been a long-standing question whether a PDE proof of these estimates was possible. We provide a positive answer to this question, and derive as a consequence sharp estimates for general classes of fully non-linear equations. This is joint work with B. Guo and F. Tong.

      Video

      11:30–2:30 pmPaul SeidelTitle: The quantum connection: familiar yet puzzling

      Abstract: The small quantum connection on a Fano variety is possibly the most basic piece of enumerative geometry. In spite of being really easy to write down, it is the subject of far-reaching conjectures (Dubrovin, Galkin, Iritani), which challenge our understanding of mirror symmetry. I will give a gentle introduction to the simplest of these questions.

      Video

      12:30–2:30 pmLunch Break
      2:30–3:30 pmMelissa C.C. LiuTitle: Higgs-Coulumb correspondence for abelian gauged linear sigma models

      Abstract: The underlying geometry of a gauged linear sigma model (GLSM) consists of a GIT quotient of a complex vector space by the linear action of a reductive algebraic group G (the gauge group) and a polynomial function (the superpotential) on the GIT quotient. The Higgs-Coulomb correspondence relates (1) GLSM invariants which are virtual counts of curves in the critical locus of the superpotential (Higgs branch), and (2) Mellin-Barnes type integrals on the Lie algebra of G (Coulomb branch). In this talk, I will describe the correspondence when G is an algebraic torus, and explain how to use the correspondence to study dependence of GLSM invariants on the stability condition. This is based on joint work with Konstantin Aleshkin.

      Video

      3:30–4:00 pmCoffee Break 
      4:00–5:00 pmSebastien PicardTitle: Topological Transitions of Calabi-Yau Threefolds

      Abstract: Conifold transitions were proposed in the works of Clemens, Reid and Friedman as a way to travel in the parameter space of Calabi-Yau threefolds with different Hodge numbers. This process may deform a Kahler Calabi-Yau threefold into a non-Kahler complex manifold with trivial canonical bundle. We will discuss the propagation of differential geometric structures such as balanced hermitian metrics, Yang-Mills connections, and special submanifolds through conifold transitions. This is joint work with T. Collins, S. Gukov and S.-T. Yau.

      Video

       

       

       

      Thursday, May 12, 2022

       

      8:15 amLight breakfast & coffee/tea
      9:00 am–10:00 amAkito Futaki (Zoom)Title: Transverse coupled Kähler-Einstein metrics and volume minimization

      Abstract:
      We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kählercone, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.Video
      10:15 am–11:15 amYu-Shen LinTitle: SYZ Mirror Symmetry of Log Calabi-Yau Surfaces

      Abstract: Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admits special Lagrangian fibrations. The conjecture serves as one of the guiding principles in mirror symmetry. In this talk, I will explain the existence of the special Lagrangian fibrations in some log Calabi-Yau surfaces and their dual fibrations in their expected mirrors. The journey leads us to the study of the moduli space of Ricci-flat metrics with certain asymptotics on these geometries and the discovery of new semi-flat metrics. If time permits, I will explain the application to the Torelli theorem of ALH^* gravitational instantons. The talk is based on joint works with T. Collins and A. Jacob.

      Video

      11:30 am – 12:30 pmRobert FriedmanTitle: Deformations of singular Fano and Calabi-Yau varieties

      Abstract: This talk will describe recent joint work with Radu Laza on deformations of generalized Fano and Calabi-Yau varieties, i.e. compact analytic spaces whose dualizing sheaves are either duals of ample line bundles or are trivial. Under the assumption of isolated hypersurface canonical singularities, we extend results of Namikawa and Steenbrink in dimension three and discuss various generalizations to higher dimensions.

      Video

      12:30 pmConcluding Remarks

       

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/6/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Symposium on Foundations of Responsible Computing (FORC)
      9:00 am-5:00 pm
      12/01/2024-06/08/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Screen-Shot-2020-03-05-at-11.54.28-AM-600x338

      On June 6-8, 2022, the CMSA hosted the 3rd annual Symposium on Foundations of Responsible Computing (FORC).

      The Symposium on Foundations of Responsible Computing (FORC) is a forum for mathematical research in computation and society writ large.  The Symposium aims to catalyze the formation of a community supportive of the application of theoretical computer science, statistics, economics and other relevant analytical fields to problems of pressing and anticipated societal concern.

      Organizers: Cynthia Dwork, Harvard SEAS | Omer Reingold, Stanford | Elisa Celis, Yale

      Schedule

      DOWNLOAD PDF

      June 6, 2022

      9:15 am–10:15 amOpening Remarks

      Keynote Speaker: Caroline Nobo, Yale University

      Title: From Theory to Impact: Why Better Data Systems are Necessary for Criminal Legal Reform

      Abstract: This talk will dive into the messy, archaic, and siloed world of local criminal justice data in America. We will start with a 30,000 foot discussion about the current state of criminal legal data systems, then transition to the challenges of this broken paradigm, and conclude with a call to measure new things – and to measure them better! This talk will leave you with an understanding of criminal justice data infrastructure and transparency in the US, and will discuss how expensive case management software and other technology are built on outdated normative values which impede efforts to reform the system. The result is an infuriating paradox: an abundance of tech products built without theoretical grounding, in a space rich with research and evidence.

      10:15 am–10:45 amCoffee Break
      10:45 am–12:15 pmPaper Session 1Session Chair: Ruth Urner
      Georgy Noarov, University of PennsylvaniaTitle: Online Minimax Multiobjective Optimization

      Abstract: We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. The learner’s objective is to minimize the maximum cumulative loss over all coordinates. We give a simple algorithm that lets the learner do almost as well as if she knew the adversary’s actions in advance. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains, ranging from multicalibration to a large set of no-regret algorithms, to a variant of Blackwell’s approachability theorem for polytopes with fast convergence rates. As a new application, we show how to “(multi)calibeat” an arbitrary collection of forecasters — achieving an exponentially improved dependence on the number of models we are competing against, compared to prior work.

      Matthew Eichhorn, Cornell UniversityTitle: Mind your Ps and Qs: Allocation with Priorities and Quotas

      Abstract: In many settings, such as university admissions, the rationing of medical supplies, and the assignment of public housing, decision-makers use normative criteria (ethical, financial, legal, etc.) to justify who gets an allocation. These criteria can often be translated into quotas for the number of units available to particular demographics and priorities over agents who qualify in each demographic. Each agent may qualify in multiple categories at different priority levels, so many allocations may conform to a given set of quotas and priorities. Which of these allocations should be chosen? In this talk, I’ll formalize this reserve allocation problem and motivate Pareto efficiency as a natural desideratum. I’ll present an algorithm to locate efficient allocations that conform to the quota and priority constraints. This algorithm relies on beautiful techniques from integer and linear programming, and it is both faster and more straightforward than existing techniques in this space. Moreover, its clean formulation allows for further refinement, such as the secondary optimization of some heuristics for fairness.

      Haewon Jeong, Harvard UniversityTitle: Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values

      Abstract: We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature, most of them require a complete training set as input. In practice, data can have missing values, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead, we train a tree with missing incorporated as attribute (MIA), which does not require explicit imputation, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset, through several experiments on real-world datasets.

      Emily Diana, University of PennsylvaniaTitle: Multiaccurate Proxies for Downstream Fairness

      Abstract: We study the problem of training a model that must obey demographic fairness conditions when the sensitive features are not available at training time — in other words, how can we train a model to be fair by race when we don’t have data about race? We adopt a fairness pipeline perspective, in which an “upstream” learner that does have access to the sensitive features will learn a proxy model for these features from the other attributes. The goal of the proxy is to allow a general “downstream” learner — with minimal assumptions on their prediction task — to be able to use the proxy to train a model that is fair with respect to the true sensitive features. We show that obeying multiaccuracy constraints with respect to the downstream model class suffices for this purpose, provide sample- and oracle efficient-algorithms and generalization bounds for learning such proxies, and conduct an experimental evaluation. In general, multiaccuracy is much easier to satisfy than classification accuracy, and can be satisfied even when the sensitive features are hard to predict.

      12:15 pm–1:45 pmLunch Break
      1:45–3:15 pmPaper Session 2Session Chair: Guy Rothblum
      Elbert Du, Harvard UniversityTitle: Improved Generalization Guarantees in Restricted Data Models

      Abstract: Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis — even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that, under this assumption, it is possible to “re-use” privacy budget on different portions of the data, significantly improving accuracy without increasing the risk of overfitting.

      Ruth Urner, York UniversityTitle: Robustness Should not be at Odds with Accuracy

      Abstract: The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability and trustworthiness: in many instances an imperceptible perturbation can falsely flip a neural network’s prediction. Applied research in this area has mostly focused on developing novel adversarial attack strategies or building better defenses against such. It has repeatedly been pointed out that adversarial robustness may be in conflict with requirements for high accuracy. In this work, we take a more principled look at modeling the phenomenon of adversarial examples. We argue that deciding whether a model’s label change under a small perturbation is justified, should be done in compliance with the underlying data-generating process. Through a series of formal constructions, systematically analyzing the the relation between standard Bayes classifiers and robust-Bayes classifiers, we make the case for adversarial robustness as a locally adaptive measure. We propose a novel way defining such a locally adaptive robust loss, show that it has a natural empirical counterpart, and develop resulting algorithmic guidance in form of data-informed adaptive robustness radius. We prove that our adaptive robust data-augmentation maintains consistency of 1-nearest neighbor classification under deterministic labels and thereby argue that robustness should not be at odds with accuracy.

      Sushant Agarwal, University of WaterlooTitle: Towards the Unification and Robustness of Perturbation and Gradient Based Explanations

      Abstract: As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method, and a variant of LIME which is a perturbation based method. More specifically, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation, i.e., when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties, such as robustness and linearity, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally, we empirically validate our theory using extensive experimentation on both synthetic and real world datasets.

      Tijana Zrnic, University of California, BerkeleyTitle: Regret Minimization with Performative Feedback

      Abstract: In performative prediction, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time, the learner needs to deploy a model to get feedback about the distribution it induces. We study the problem of finding near-optimal models under performativity while maintaining low regret. On the surface, this problem might seem equivalent to a bandit problem. However, it exhibits a fundamentally richer feedback structure that we refer to as performative feedback: after every deployment, the learner receives samples from the shifted distribution rather than only bandit feedback about the reward. Our main contribution is regret bounds that scale only with the complexity of the distribution shifts and not that of the reward function. The key algorithmic idea is careful exploration of the distribution shifts that informs a novel construction of confidence bounds on the risk of unexplored models. The construction only relies on smoothness of the shifts and does not assume convexity. More broadly, our work establishes a conceptual approach for leveraging tools from the bandits literature for the purpose of regret minimization with performative feedback.

      3:15 pm–3:45 pmCoffee Break
      3:45 pm–5:00 pmPanel DiscussionTitle: What is Responsible Computing?

      Panelists: Jiahao Chen, Cynthia Dwork, Kobbi Nissim, Ruth Urner

      Moderator: Elisa Celis

       

      June 7, 2022

      9:15 am–10:15 amKeynote Speaker: Isaac Kohane, Harvard Medical SchoolTitle: What’s in a label? The case for and against monolithic group/ethnic/race labeling for machine learning

      Abstract: Populations and group labels have been used and abused for thousands of years. The scale at which AI can incorporate such labels into its models and the ways in which such models can be misused are cause for significant concern. I will describe, with examples drawn from experiments in precision medicine, the task dependence of how underserved and oppressed populations can be both harmed and helped by the use of group labels. The source of the labels and the utility models underlying their use will be particularly emphasized.

      10:15 am–10:45 amCoffee Break
      10:45 am–12:15 pmPaper Session 3Session Chair: Ruth Urner
      Rojin Rezvan, University of Texas at AustinTitle: Individually-Fair Auctions for Multi-Slot Sponsored Search

      Abstract: We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from Chawla and Jagadeesan.

      Judy Hanwen Shen, StanfordTitle: Leximax Approximations and Representative Cohort Selection

      Abstract: Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency, exploiting significant utility improvements, and robustness to noise. Among other definitional contributions, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.

      Jiayuan Ye,
      National University of Singapore
      Title: Differentially Private Learning Needs Hidden State (or Much Faster Convergence)

      Abstract: Differential privacy analysis of randomized learning algorithms typically relies on composition theorems, where the implicit assumption is that the internal state of the iterative algorithm is revealed to the adversary. However, by assuming hidden states for DP algorithms (when only the last-iterate is observable), recent works prove a converging privacy bound for noisy gradient descent (on strongly convex smooth loss function) that is significantly smaller than composition bounds after a few epochs. In this talk, we extend this hidden-state analysis to various stochastic minibatch gradient descent schemes (such as under “shuffle and partition” and “sample without replacement”), by deriving novel bounds for the privacy amplification by random post-processing and subsampling. We prove that, in these settings, our privacy bound is much smaller than composition for training with a large number of iterations (which is the case for learning from high-dimensional data). Our converging privacy analysis, thus, shows that differentially private learning, with a tight bound, needs hidden state privacy analysis or a fast convergence. To complement our theoretical results, we present experiments for training classification models on MNIST, FMNIST and CIFAR-10 datasets, and observe a better accuracy given fixed privacy budgets, under the hidden-state analysis.

      Mahbod Majid, University of WaterlooTitle: Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism

      Abstract: We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution from O(d) independent samples (up to logarithmic factors) subject to pure differential privacy.

      Our main technique is a new approach to use the powerful Sum of Squares method (SoS) to design differentially private algorithms. SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics – estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees. We demonstrate a similar proofs to private algorithms phenomenon: instances of the workhorse exponential mechanism which apparently require exponential time but which can be analyzed with low-degree SoS proofs can be automatically turned into polynomial-time differentially private algorithms. We prove a meta-theorem capturing this phenomenon, which we expect to be of broad use in private algorithm design.

      12:15 pm–1:45 pmLunch Break
      1:45–3:15 pmPaper Session 4Session Chair: Kunal Talwar
      Kunal Talwar,
      Apple
      Title: Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

      Abstract: Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation (SMC) protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected.
      In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.

      Giuseppe Vietri, University of MinnesotaTitle: Improved Regret for Differentially Private Exploration in Linear MDP

      Abstract: We study privacy-preserving exploration in sequential decision-making for environments that rely on sensitive data such as medical records. In particular, we focus on solving the problem of reinforcement learning (RL) subject to the constraint of (joint) differential privacy in the linear MDP setting, where both dynamics and rewards are given by linear functions. Prior work on this problem due to Luyo et al. (2021) achieves a regret rate that has a dependence of O(K^{3/5}) on the number of episodes K. We provide a private algorithm with an improved regret rate with an optimal dependence of O(K^{1/2}) on the number of episodes. The key recipe for our stronger regret guarantee is the adaptivity in the policy update schedule, in which an update only occurs when sufficient changes in the data are detected. As a result, our algorithm benefits from low switching cost and only performs O(log(K)) updates, which greatly reduces the amount of privacy noise. Finally, in the most prevalent privacy regimes where the privacy parameter ? is a constant, our algorithm incurs negligible privacy cost — in comparison with the existing non-private regret bounds, the additional regret due to privacy appears in lower-order terms.

      Mingxun Zhou,
      Carnegie Mellon University
      Title: The Power of the Differentially Oblivious Shuffle in Distributed Privacy MechanismsAbstract: The shuffle model has been extensively investigated in the distributed differential privacy (DP) literature. For a class of useful computational tasks, the shuffle model allows us to achieve privacy-utility tradeoff similar to those in the central model, while shifting the trust from a central data curator to a “trusted shuffle” which can be implemented through either trusted hardware or cryptography. Very recently, several works explored cryptographic instantiations of a new type of shuffle with relaxed security, called differentially oblivious (DO) shuffles. These works demonstrate that by relaxing the shuffler’s security from simulation-style secrecy to differential privacy, we can achieve asymptotical efficiency improvements. A natural question arises, can we replace the shuffler in distributed DP mechanisms with a DO-shuffle while retaining a similar privacy-utility tradeoff?
      In this paper, we prove an optimal privacy amplification theorem by composing any locally differentially private (LDP) mechanism with a DO-shuffler, achieving parameters that tightly match the shuffle model. Moreover, we explore multi-message protocols in the DO-shuffle model, and construct mechanisms for the real summation and histograph problems. Our error bounds approximate the best known results in the multi-message shuffle-model up to sub-logarithmic factors. Our results also suggest that just like in the shuffle model, allowing each client to send multiple messages is fundamentally more powerful than restricting to a single message.
      Badih Ghazi,
      Google Research
      Title: Differentially Private Ad Conversion Measurement

      Abstract: In this work, we study conversion measurement, a central functionality in the digital advertising space, where an advertiser seeks to estimate advertiser site conversions attributed to ad impressions that users have interacted with on various publisher sites. We consider differential privacy (DP), a notion that has gained in popularity due to its strong and rigorous guarantees, and suggest a formal framework for DP conversion measurement, uncovering a subtle interplay between attribution and privacy. We define the notion of an operationally valid configuration of the attribution logic, DP adjacency relation, privacy
      budget scope and enforcement point, and provide, for a natural space of configurations, a complete characterization.

      3:15 pm–3:45 pmCoffee Break
      3:45 pm–5:00 pmOpen Poster Session

       

      June 8, 2022

      9:15 am–10:15 amKeynote Speaker: Nuria Oliver, Data-Pop AllianceTitle: Data Science against COVID-19

      Abstract: In my talk, I will describe the work that I have been doing since March 2020, leading a multi-disciplinary team of 20+ volunteer scientists working very closely with the Presidency of the Valencian Government in Spain on 4 large areas: (1) human mobility modeling; (2) computational epidemiological models (both metapopulation, individual and LSTM-based models); (3) predictive models; and (4) citizen surveys via the COVID19impactsurvey with over 600,000 answers worldwide.

      I will describe the results that we have produced in each of these areas, including winning the 500K XPRIZE Pandemic Response Challenge and best paper award at ECML-PKDD 2021. I will share the lessons learned in this very special initiative of collaboration between the civil society at large (through the survey), the scientific community (through the Expert Group) and a public administration (through the Commissioner at the Presidency level). WIRED magazine just published an article describing our story.

      10:15 am–10:45 amCoffee Break
      10:45 am–12:15 pmPaper Session 5Session Chair: Kunal Talwar
      Shengyuan Hu, Carnegie Mellon UniversityTitle: Private Multi-Task Learning: Formulation and Applications to Federated Learning

      Abstract: Many problems in machine learning rely on multi-task learning (MTL), in which the goal is to solve multiple related machine learning tasks simultaneously. MTL is particularly relevant for privacy-sensitive applications in areas such as healthcare, finance, and IoT computing, where sensitive data from multiple, varied sources are shared for the purpose of learning. In this work, we formalize notions of task-level privacy for MTL via joint differential privacy (JDP), a relaxation of differential privacy for mechanism design and distributed optimization. We then propose an algorithm for mean-regularized MTL, an objective commonly used for applications in personalized federated learning, subject to JDP. We analyze our objective and solver, providing certifiable guarantees on both privacy and utility. Empirically, our method allows for improved privacy/utility trade-offs relative to global baselines across common federated learning benchmarks

      Christina Yu,
      Cornell University
      Title: Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve

      Abstract: We consider the problem of dividing limited resources to individuals arriving over T rounds with a goal of achieving fairness across individuals. In general there may be multiple resources and multiple types of individuals with different utilities. A standard definition of `fairness’ requires an allocation to simultaneously satisfy envy-freeness and Pareto efficiency. However, in the online sequential setting, the social planner must decide on a current allocation before the downstream demand is realized, such that no policy can guarantee these desiderata simultaneously with probability 1, requiring a modified metric of measuring fairness for online policies. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to L_T necessarily suffers an efficiency loss of at least 1 / L_T. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. Our result is the first to provide guarantees for fair online resource allocation with high probability for multiple resource and multiple type settings. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.

      Hedyeh Beyhaghi, Carnegie Mellon UniversityTitle: On classification of strategic agents who can both game and improve

      Abstract: In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

      Keegan Harris, Carnegie Mellon UniversityTitle: Bayesian Persuasion for Algorithmic Recourse

      Abstract: When subjected to automated decision-making, decision subjects may strategically modify their observable features in ways they believe will maximize their chances of receiving a favorable decision. In many practical situations, the underlying assessment rule is deliberately kept secret to avoid gaming and maintain competitive advantage. The resulting opacity forces the decision subjects to rely on incomplete information when making strategic feature modifications. We capture such settings as a game of Bayesian persuasion, in which the decision maker offers a form of recourse to the decision subject by providing them with an action recommendation (or signal) to incentivize them to modify their features in desirable ways. We show that when using persuasion, both the decision maker and decision subject are never worse off in expectation, while the decision maker can be significantly better off. While the decision maker’s problem of finding the optimal Bayesian incentive-compatible (BIC) signaling policy takes the form of optimization over infinitely-many variables, we show that this optimization can be cast as a linear program over finitely-many regions of the space of possible assessment rules. While this reformulation simplifies the problem dramatically, solving the linear program requires reasoning about exponentially-many variables, even under relatively simple settings. Motivated by this observation, we provide a polynomial-time approximation scheme that recovers a near-optimal signaling policy. Finally, our numerical simulations on semi-synthetic data empirically illustrate the benefits of using persuasion in the algorithmic recourse setting.

      12:15 pm–1:45 pmLunch Break
      1:45–3:15 pmPaper Session 6Session Chair: Elisa Celis
      Mark Bun, Boston UniversityTitle: Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling

      Abstract: Sampling schemes are fundamental tools in statistics, survey design, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However, in practice, sampling designs are often more complex than the simple, data-independent sampling schemes that are addressed in prior work. In this work, we extend the study of privacy amplification results to more complex, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms, as well as provide some insight into the study of more general sampling designs.

      Samson Zhou, Carnegie Mellon UniversityTitle: Private Data Stream Analysis for Universal Symmetric Norm Estimation

      Abstract: We study how to release summary statistics on a data stream subject to the constraint of differential privacy. In particular, we focus on releasing the family of symmetric norms, which are invariant under sign-flips and coordinate-wise permutations on an input data stream and include L_p norms, k-support norms, top-k norms, and the box norm as special cases. Although it may be possible to design and analyze a separate mechanism for each symmetric norm, we propose a general parametrizable framework that differentially privately releases a number of sufficient statistics from which the approximation of all symmetric norms can be simultaneously computed. Our framework partitions the coordinates of the underlying frequency vector into different levels based on their magnitude and releases approximate frequencies for the “heavy” coordinates in important levels and releases approximate level sizes for the “light” coordinates in important levels. Surprisingly, our mechanism allows for the release of an arbitrary number of symmetric norm approximations without any overhead or additional loss in privacy. Moreover, our mechanism permits (1+\alpha)-approximation to each of the symmetric norms and can be implemented using sublinear space in the streaming model for many regimes of the accuracy and privacy parameters.

      Aloni Cohen, University of ChicagoTitle: Attacks on Deidentification’s Defenses

      Abstract: Quasi-identifier-based deidentification techniques (QI-deidentification) are widely used in practice, including k-anonymity, ?-diversity, and t-closeness. We present three new attacks on QI-deidentification: two theoretical attacks and one practical attack on a real dataset. In contrast to prior work, our theoretical attacks work even if every attribute is a quasi-identifier. Hence, they apply to k-anonymity, ?-diversity, t-closeness, and most other QI-deidentification techniques.
      First, we introduce a new class of privacy attacks called downcoding attacks, and prove that every QI-deidentification scheme is vulnerable to downcoding attacks if it is minimal and hierarchical. Second, we convert the downcoding attacks into powerful predicate singling-out (PSO) attacks, which were recently proposed as a way to demonstrate that a privacy mechanism fails to legally anonymize under Europe’s General Data Protection Regulation. Third, we use LinkedIn.com to reidentify 3 students in a k-anonymized dataset published by EdX (and show thousands are potentially vulnerable), undermining EdX’s claimed compliance with the Family Educational Rights and Privacy Act.

      The significance of this work is both scientific and political. Our theoretical attacks demonstrate that QI-deidentification may offer no protection even if every attribute is treated as a quasi-identifier. Our practical attack demonstrates that even deidentification experts acting in accordance with strict privacy regulations fail to prevent real-world reidentification. Together, they rebut a foundational tenet of QI-deidentification and challenge the actual arguments made to justify the continued use of k-anonymity and other QI-deidentification techniques.

      Steven Wu,
      Carnegie Mellon University
      Title: Fully Adaptive Composition in Differential Privacy

      Abstract: Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. The authors introduce two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the tightness of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. We also construct several general families of odometers. These odometers can match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging recent advances in time-uniform martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss, and conjecture that our results are essentially not improvable (even in constants) in general.

      3:15 pm–3:45 pmFORC Reception
      3:45 pm–5:00 pmSocial Hour
    • Workshop
      9:00 am-5:00 pm
      12/01/2024-04/29/2022
      Blockchain,Network,Concept,,,Distributed,Ledger,,Computer,Connection,Technology,,Matrix

      On April 27–29, 2022, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics.

      Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

      In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

      Speakers:

      • Federico Ardila (San Francisco State)
      • Nima Arkani-Hamed (IAS)
      • Madeline Brandt (Brown)
      • Nick Early (Max Planck Institute)
      • Chris Eur (Harvard)
      • Claudia Fevola (Max Planck Institute)
      • Christian Gaetz (Harvard)
      • Yuji Kodama (Ohio State University)
      • Yelena Mandelshtam (Berkeley)
      • Sebastian Mizera (IAS)
      • Matteo Parisi (Harvard CMSA)
      • Emma Previato (Boston University)
      • Anna Seigal (Harvard)
      • Melissa Sherman-Bennett (University of Michigan)
      • Simon Telen (Max Planck Institute)
      • Charles Wang (Harvard)

      Schedule

      Schedule PDF

      Wednesday, April 27, 2022

      9:30 am–10:30 amFederico ArdilaTitle: Nonlinear spaces from linear spaces

      Abstract: Matroid theory provides a combinatorial model for linearity, but it plays useful roles beyond linearity. In the classical setup, a linear subspace V of an n-dimensional vector space gives rise to a matroid M(V) on {1,…,n}. However, the matroid M(V) also knows about some nonlinear geometric spaces related to V. Conversely, those nonlinear spaces teach us things we didn’t know about matroids. My talk will discuss some examples.

      10:30 am–11:00 amCOFFEE BREAK
      11:00 am–11:45 amChris EurTitle: Tautological classes of matroids

      Abstract: Algebraic geometry has furnished fruitful tools for studying matroids, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (K-classes) on permutohedral varieties, which we call “tautological bundles (classes)” of matroids, as a new framework that unifies, recovers, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget, Hunter Spink, and Dennis Tseng.

      11:45 am–2:00 pmLUNCH BREAK
      2:00 pm–2:45 pmNick EarlyTitle: Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes

      Abstract: The associahedron is known to encapsulate physical properties such as the notion of tree-level factorization for one of the simplest Quantum Field Theories, the biadjoint scalar, which has only cubic interactions.  I will discuss novel instances of the associahedron and the biadjoint scalar in a class of generalized amplitudes, discovered by Cachazo, Early, Guevara and Mizera, by taking certain limits thereof. This connection leads to a simple proof of a new realization of the associahedron involving a Minkowski sum of certain positroid polytopes in the second hypersimplex.

      2:45 pm–3:30 pmAnna SeigalTitle: Invariant theory for maximum likelihood estimation

      Abstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

      3:30 pm–4:00 pmCOFFEE BREAK
      4:00 pm–4:45 pmMatteo ParisiTitle: Amplituhedra, Scattering Amplitudes, and Triangulations

      Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – introduced by physicists to encode interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory.
      Triangulations of polygons are encoded in the associahedron, studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes, constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. I will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between Amplituhedra of “m=2” type and a seemingly unrelated object – the Hypersimplex. The latter is a polytope which appears in many contexts, from matroid theory to tropical geometry.
      Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski.

      4:45 pm–5:30 pmMelissa Sherman-BennettTitle: The hypersimplex and the m=2 amplituhedron

      Abstract: In this talk, I’ll continue where Matteo left off. I’ll give some more details about the curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). The hypersimplex decompositions are closely related to matroidal subdivisions. Along the way, we prove a nice description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers, inspired by an analogous triangulation of the hypersimplex into Eulerian-number-many simplices.

       

      Thursday, April 28, 2022

      9:30 am–10:30 amClaudia FevolaTitle: Nonlinear Algebra meets Feynman integrals

      Abstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. They form a finite-dimensional vector space and the elements of a basis are named “master integrals” in the physics literature. The number of master integrals has been interpreted in different ways: it equals the dimension of a twisted de Rham cohomology group, the Euler characteristic of a very affine variety, and the holonomic rank of a D-module. In this talk, we are interested in a more general family of integrals that contains Feynman integrals as a special case. We explore this setting using tools coming from nonlinear algebra. This is an ongoing project with Daniele Agostini, Anna-Laura Sattelberger, and Simon Telen.

      10:30 am–11:00 amCOFFEE BREAK
      11:00 am–11:45 amSimon TelenTitle: Landau discriminants

      Abstract: The Landau discriminant is a projective variety containing kinematic parameters for which a Feynman integral can have singularities. We present a definition and geometric properties. We discuss how to compute Landau discriminants using symbolic and numerical methods. Our methods can be used, for instance, to compute the Landau discriminant of the pentabox diagram, which is a degree 12 hypersurface in 6-space. This is joint work with Sebastian Mizera.

      11:45 am–2:00 pmLUNCH BREAK
      2:00 pm–2:45 pmChristian GaetzTitle: 1-skeleton posets of Bruhat interval polytopes

      Abstract: Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes, despite not being simple, have interesting h-vectors. In a special case, work of Williams shows that Bruhat interval polytopes are isomorphic to bridge polytopes, so that chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs.

      2:45 pm–3:30 pmMadeleine BrandtTitle: Top Weight Cohomology of $A_g$

      Abstract: I will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of $A_g$. Thus, it can be computed combinatorially. This is joint work with Juliette Bruce, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.

      3:30 pm–4:00 pmCOFFEE BREAK
      4:00 pm–5:00 pmEmma PreviatoTitle: Sigma function on curves with non-symmetric semigroup

      Abstract: We start with an overview of the correspondence between spectral curves and commutative rings of differential operators, integrable hierarchies of non-linear PDEs and Jacobian vector fields. The coefficients of the operators can be written explicitly in terms of the Kleinian sigma function: Weierstrass’ sigma function was generalized to genus greater than one by Klein, and is a ubiquitous tool in integrability. The most accessible case is the sigma function of telescopic curves. In joint work with J. Komeda and S. Matsutani, we construct a curve with non-symmetric Weierstrass semigroup (equivalently, Young tableau), consequently non-telescopic, and its sigma function. We conclude with possible applications to commutative rings of differential operators.

      6:00 pmDinner Banquet, Gran Gusto Trattoria

       

      Friday, April 29, 2022

      9:00 am–10:00 amYuji KodamaTitle: KP solitons and algebraic curves

      Abstract: It is well-known that soliton solutions of the KdV hierarchy are obtained by singular limits of hyper-elliptic curves. However, there is no general results for soliton solutions of the KP hierarchy, KP solitons. In this talk, I will show that some of the KP solitons are related to the singular space curves associated with certain class of numerical semigroups.

      10:00 am–10:30 amCOFFEE BREAK
      10:30 am–11:15 amYelena MandelshtamTitle: Curves, degenerations, and Hirota varieties

      Abstract: The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases, Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This talk is based on joint work with Daniele Agostini, Claudia Fevola, and Bernd Sturmfels.

      11:15 am–12:00 pmCharles WangTitle: Differential Algebra of Commuting Operators

      Abstract: In this talk, we will give an overview of the problem of finding the centralizer of a fixed differential operator in a ring of differential operators, along with connections to integrable hierarchies and soliton solutions to e.g. the KdV or KP equations. Given these interesting connections, it is important to be able to compute centralizers of differential operators, and we discuss how to use techniques from differential algebra to approach this question, as well as how having these computational tools can help in understanding the structure of soliton solutions to these equations.

      12:00 pm–2:00 pmLUNCH BREAK
      2:00 pm–3:00 pmSebastian MizeraTitle: Feynman Polytopes

      Abstract: I will give an introduction to a class of polytopes that recently emerged in the study of scattering amplitudes in quantum field theory.

      3:00 pm–3:30 pmCOFFEE BREAK
      3:30 pm–4:30 pmNima Arkani-HamedTitle: Spacetime, Quantum Mechanics and Combinatorial Geometries at Infinity

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Algebraic Statistics with a View towards Physics
      9:00 am-10:00 am
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.

      **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

      All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

      LINK TO FORM

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/13/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.21.22-1583x2048-1

      Abstract:
      Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure, the adoption of MPC in real industry is still very much limited as of today, the biggest obstacle of which boils down to its efficiency.

      My research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal, my research spans both theoretical and applied cryptography. In theory, I develop new techniques for achieving general MPC with the optimal complexity, bringing theory closer to practice. In practice, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice.

      Biography:
      Peihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC, she received her Ph.D. from the University of California, Berkeley in 2019 and had brief stints at Google, Facebook, Microsoft Research, and Visa Research. Her research interests lie broadly in cryptography, theory, and security, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/20/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Workshop
      9:00 am-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series.

      Location: Room G10, 20 Garden Street, Cambridge, MA 02138.

      Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).

      Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory, algebraic geometry, and representation theory.

      At this workshop, we will bring together mathematicians, theoretical physicists, and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.

      Speakers:

      • James Halverson, Northeastern University Dept. of Physics and IAIFI
      • Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI
      • Andrew Sutherland, MIT Department of Mathematics

       

      https://youtu.be/qseSPgHHFtQ

       

       

      https://youtu.be/JN3mVazeP2E

       

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.14.22-1583x2048

      Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.

    • Member Seminar
      9:00 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Farzan Vafa

      Title: Diffusive growth sourced by topological defects

      Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time, and predict that in the presence of a positive defect, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature, we exploit the fact that for axisymmetric surfaces, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry, for polar order and small bending modulus, is a deformed football.
      We apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      5/27/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      6/3/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: The Atiyah-Singer Index Theorem
      9:00 am-10:30 am
      12/01/2024

      Dan Freed (The University of Texas at Austin)

      Title: The Atiyah-Singer Index Theorem

      Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator.

      This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer.

      Talk chair: Cumrun Vafa

      Video

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Interdisciplinary Science Seminar
      Speaker: Jianfeng Lu, Duke UniversityTitle: Surface hopping algorithms for non-adiabatic quantum systems

      Abstract: Surface hopping algorithm is widely used in chemistry for mixed quantum-classical dynamics. In this talk, we will discuss some of our recent works in mathematical understanding and algorithm development for surface hopping methods. These methods are based on stochastic approximations of semiclassical path-integral representation to the solution of multi-level Schrodinger equations; such methodology also extends to other high-dimensional transport systems.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      7/8/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Big Data Conference 2022
      9:00 am-1:00 pm
      12/01/2024
      Big Data 2022_web

      On August 26, 2022 the CMSA hosted our eighth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      The 2022 Big Data Conference took place virtually on Zoom.

      Organizers:

      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
      • Sergiy Verstyuk, CMSA, Harvard University

      Speakers:

      Schedule

      9:00 amConference OrganizersIntroduction and Welcome
      9:10 am – 9:55 amXiaohong ChenTitle: On ANN optimal estimation and inference for policy functionals of nonparametric conditional moment restrictions

      Abstract:  Many causal/policy parameters of interest are expectation functionals of unknown infinite-dimensional structural functions identified via conditional moment restrictions. Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional covariates more effectively than linear sieves. In this talk we present ANN optimal estimation and inference on  policy functionals, such as average elasticities or value functions, of unknown structural functions of endogenous covariates. We provide ANN efficient estimation and optimal t based confidence interval for regular policy functionals such as average derivatives in nonparametric instrumental variables regressions. We also present ANN quasi likelihood ratio based inference for possibly irregular policy functionals of general nonparametric conditional moment restrictions (such as quantile instrumental variables models or Bellman equations) for time series data. We conduct intensive Monte Carlo studies to investigate computational issues with ANN based optimal estimation and inference in economic structural models with endogeneity. For economic data sets that do not have very high signal to noise ratios, there are current gaps between theoretical advantage of ANN approximation theory vs inferential performance in finite samples.
      Some of the results are applied to efficient estimation and optimal inference for average price elasticity in consumer demand and BLP type demand.

      The talk is based on two co-authored papers:
      (1) Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators
      (Authors: Jiafeng Chen, Xiaohong Chen and Elie Tamer)
      https://arxiv.org/abs/2110.06763

      (2) Neural network Inference on Nonparametric conditional moment restrictions with weakly dependent data
      (Authors: Xiaohong Chen, Yuan Liao and Weichen Wang).

      View/Download Lecture Slides (pdf)

      10:00 am – 10:45 amJessica JeffersTitle: Labor Reactions to Credit Deterioration: Evidence from LinkedIn Activity

      Abstract: We analyze worker reactions to their firms’ credit deterioration. Using weekly networking activity on LinkedIn, we show workers initiate more connections immediately following a negative credit event, even at firms far from bankruptcy. Our results suggest that workers are driven by concerns about both unemployment and future prospects at their firm. Heightened networking activity is associated with contemporaneous and future departures, especially at financially healthy firms. Other negative events like missed earnings and equity downgrades do not trigger similar reactions. Overall, our results indicate that the build-up of connections triggered by credit deterioration represents a source of fragility for firms.

      10:50 am – 11:35 amMiles CranmerTitle: Interpretable Machine Learning for Physics

      Abstract: Would Kepler have discovered his laws if machine learning had been around in 1609? Or would he have been satisfied with the accuracy of some black box regression model, leaving Newton without the inspiration to discover the law of gravitation? In this talk I will explore the compatibility of industry-oriented machine learning algorithms with discovery in the natural sciences. I will describe recent approaches developed with collaborators for addressing this, based on a strategy of “translating” neural networks into symbolic models via evolutionary algorithms. I will discuss the inner workings of the open-source symbolic regression library PySR (github.com/MilesCranmer/PySR), which forms a central part of this interpretable learning toolkit. Finally, I will present examples of how these methods have been used in the past two years in scientific discovery, and outline some current efforts.

      View/Download Lecture Slides (pdf) 

      11:40 am – 12:25 pmDan RobertsTitle: A Statistical Model of Neural Scaling Laws

      Abstract: Large language models of a huge number of parameters and trained on near internet-sized number of tokens have been empirically shown to obey “neural scaling laws” for which their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model — a joint generative data model and random feature model — that captures this neural scaling phenomenology. By solving this model using tools from random matrix theory, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws (ii) how nonlinear feature maps, i.e the role played by the deep neural network, enable scaling laws when trained on these datasets, and (iii) how such scaling laws can break down, and what their behavior is when they do. A key feature is the manner in which the power laws that occur in the statistics of natural datasets are translated into power law scalings of the test loss, and how the finite extent of such power laws leads to both bottlenecks and breakdowns.

      View/Download Lecture Slides (pdf)

       

      12:30 pmConference OrganizersClosing Remarks

       

      Information about last year’s conference can be found here.

    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 09.28.22

      Topological Quantum Matter Seminar

      Speaker: Ruihua Fan, Harvard University

      Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow
      Abstract: One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance.
    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024
      CMSA QMMP Seminar 09.26.22

      Quantum Matter in Mathematics and Physics

      Speaker: Avner Karasik (University of Cambridge, UK)

      Title: Candidates for Non-Supersymmetric Dualities

      Abstract: In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

       

    • Math Science Literature Lecture Series
      9:00 am-10:30 pm
      12/01/2024

      Maxim Kontsevich  (IHÉS)

      Title: On the History of quantum cohomology and homological mirror symmetry

      Abstract: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry.  First, the usual cup-product on the cohomology of a complex projective variety admits a canonical multi-parameter deformation to so-called quantum product, satisfying a nice system of differential equations (WDVV equations).  The second discovery, even more striking,  is Mirror Symmetry, a duality between families of Calabi-Yau varieties acting as a mirror reflection on the Hodge diamond.

      Later it was realized that the quantum product belongs to the realm of symplectic geometry, and a half of mirror symmetry (called Homological Mirror Symmetry) is a duality between complex algebraic and symplectic varieties. The search of correct definitions and possible generalizations lead to great advances in many domains, giving mathematicians new glasses, through which they can see familiar objects in a completely new way.

      I will review the history of major mathematical advances in the subject of HMS, and the swirl of ideas around it.

      Talk chair: Paul Seidel

      Video

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      4/1/2021 Strongly Correlated Quantum Materials
      9:00 am-10:30 am
      12/01/2024
    • Topological Quantum Matter Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 09.21.22
      Topological Quantum Matter Seminar

      Speaker: Semyon Klevtsov, University of Strasbourg

      Title: Geometric test for topological states of matter

      Abstract: We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the

      degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille).

       

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024-04/27/2021

      In 2021, the CMSA hosted a lecture series on the literature of the mathematical sciences. This series highlights significant accomplishments in the intersection between mathematics and the sciences. Speakers include Edward Witten, Lydia Bieri, Simon Donaldson, Michael Freedman, Dan Freed, and many more.

      Videos of these talks can be found in this Youtube playlist.

      https://youtu.be/vb_JEhUW9t4

      In the Spring 2021 semester, the CMSA hosted a sub-program on this series titled A Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Below is the schedule for talks in that subprogram

      April 6, 2021 | 9:00 – 10:30am ET

      Edward Witten (IAS)

      TitleIsadore Singer’s Work on Analytic Torsion


      April 13, 2021 | 9:00 – 10:30am ET

      Claire Voisin (College de France)

      Title: K-theory and characteristic classes in topology and complex geometry  (a tribute to Atiyah and Hirzebruch)


      April 20, 2021 | 9:00 – 10:30am ET

      Dan Freed (the University of Texas at Austin)

      TitleThe Atiyah-Singer Index Theorem


      April 27, 2021 | 9:00 – 10:30am ET

      Frances Kirwan (University of Oxford)

      TitleMoment maps and the Yang-Mills functional

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Edward Witten (IAS)

      TitleIsadore Singer’s Work on Analytic Torsion

      Abstract:  I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory.

      This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and Singer.

      Talk chair: Cumrun Vafa

      Slides | Video

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Equiangular lines and regular graphs
      9:00 am-10:00 am
      12/01/2024

      Abstract: In 1973, Lemmens and Seidel asked to determine N_alpha(r), the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently, this problem has been almost completely settled when r is exponentially large relative to 1/alpha, with the approach both relying on Ramsey’s theorem, as well as being limited by it. In this talk, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5).

      Our projection method generalizes to complex equiangular lines in C^r, which may be of independent interest in quantum theory. Applying this method also allows us to obtain
      the first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha), an extension of the Alon-Boppana theorem to dense regular graphs, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r, an improvement to Welch’s bound in coding theory.

    • Quantum Matter
      9:00 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA QMMP Seminar

      Quantum Matter in Mathematics and Physics Seminar

      Speaker: Zhengyan Darius Shi (MIT)
      Title: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
      Abstract: Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity \sigma(mega) \sim mega^{-2/z} (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result \sigma(mega) \sim mega^{-2(z-2)/z}  due to Kim et al. is incorrect for inversion-odd order parameters.
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      7/1/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Interdisciplinary Science Seminar

      Speaker: Yue M. Lu, Harvard University

      Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning

      Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
      In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.

      Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007.  He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.

    • CMSA EVENT: Joint BHI/CMSA Conference on Flat Holography
      9:00 am-5:00 pm
      12/01/2024-06/24/2022

      On June 21–24, 2022, the Harvard Black Hole Initiative and the CMSA hosted the Joint BHI/CMSA Conference on Flat Holography (and related topics).

      The recent discovery of infinitely-many soft symmetries for all quantum theories of gravity in asymptotically flat space has provided a promising starting point for a bottom-up construction of a holographic dual for the real world. Recent developments have brought together previously disparate studies of soft theorems, asymptotic symmetries, twistor theory, asymptotically flat black holes and their microscopic duals, self-dual gravity, and celestial scattering amplitudes, and link directly to AdS/CFT.

      The conference was held in room G10 of the CMSA, 20 Garden Street, Cambridge, MA.

      Organizers:

      • Daniel Kapec, CMSA
      • Andrew Strominger, BHI
      • Shing-Tung Yau, Harvard & Tsinghua

      Confirmed Speakers:

      • Nima Arkani-Hamed, IAS
      • Shamik Banerjee, Bhubaneswar, Inst. Phys.
      • Miguel Campiglia, Republica U., Montevido
      • Geoffrey Compere, Brussels
      • Laura Donnay, Vienna
      • Netta Engelhardt, MIT
      • Laurent Freidel, Perimeter
      • Alex Lupsasca, Princeton
      • Juan Maldacena, IAS
      • Lionel Mason, Oxford
      • Natalie Paquette, U. Washington
      • Sabrina Pasterski, Princeton/Perimeter
      • Andrea Puhm, Ecole Polytechnique
      • Ana-Maria Raclariu, Perimeter
      • Marcus Spradlin, Brown
      • Tomasz Taylor, Northeastern
      • Herman Verlinde, Princeton
      • Anastasia Volovich, Brown
      • Bin Zhu, Northeastern

      Short talks by: Gonçalo Araujo-Regado (Cambridge), Adam Ball (Harvard), Eduardo Casali (Harvard), Jordan Cotler (Harvard), Erin Crawley (Harvard), Stéphane Detournay (Brussels), Alfredo Guevara (Harvard), Temple He (UC Davis), Elizabeth Himwich (Harvard), Yangrui Hu (Brown), Daniel Kapec (Harvard), Rifath Khan (Cambridge), Albert Law (Harvard), Luke Lippstreu (Brown), Noah Miller (Harvard), Sruthi Narayanan (Harvard), Lecheng Ren (Brown), Francisco Rojas (UAI), Romain Ruzziconi (Vienna), Andrew Strominger (Harvard), Adam Tropper (Harvard), Tianli Wang (Harvard), Walker Melton (Harvard)

      Schedule

      Monday, June 20, 2022

      Arrival
      7:00–9:00 pmWelcome Reception at Andy’s residence

       

      Tuesday, June 21, 2022

      9:00–9:30 amBreakfastlight breakfast provided
      Morning SessionChair: Dan Kapec
      9:30–10:00 amHerman VerlindeTitle: Comments on Celestial Dynamics
      10:00–10:30 amJuan MaldacenaTitle: What happens when you spend too much time looking at supersymmetric
      black holes?
      10:30–11:00Coffee break
      11:00–11:30 amMiguel CampigliaTitle: Asymptotic symmetries and loop corrections to soft theorems
      11:30–12:00 pmGeoffrey CompereTitle: Metric reconstruction from $Lw_{1+\infty}$ multipoles

      Abstract: The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be exchanged under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely determined by a set of conserved celestial charges, which uniquely label transitions among non-radiative regions caused by radiative processes. The algebra of the conserved celestial charges is derived from the real $Lw_{1+\infty}$ algebra. The celestial charges are expressed in terms of multipole moments, which allows to holographically reconstruct the metric in de Donder, Newman-Unti or Bondi gauge outside of sources.

      12:00–2:00 pmLunch break
      Afternoon SessionChair: Eduardo Casali
      2:00–2:30 pmNatalie PaquetteTitle: New thoughts on old gauge amplitudes
      2:30–3:00 pmLionel MasonTitle: An open sigma model for celestial gravity

      Abstract: A global twistor construction for conformally self-dual split signature metrics on $S2\times S2$  was developed 15 years ago by Claude LeBrun and the speaker.  This encodes the conformal metric into the location of a finite deformation of the real twistor space inside the flat complex twistor space, $\mathbb{CP}3$. This talk adapts the construction to construct global SD Einstein metrics from conformal boundary data and perturbations around the self-dual sector.  The construction entails determining a family of holomorphic discs in $\mathbb{CP}3$ whose boundaries lie on the deformed real slice and the (chiral) sigma model controls these discs in the Einstein case and provides amplitude formulae.

      3:00–3:30 pmCoffee break
      3:30–4:30 pmShort TalksDaniel Kapec: Soft Scalars and the Geometry of the Space of Celestial CFTs

      Albert Law: Soft Scalars and the Geometry of the Space of Celestial CFTs

      Sruthi Narayanan: Soft Scalars and the Geometry of the Space of Celestial CFTs

      Stéphane Detournay: Non-conformal symmetries and near-extremal black holes

      Francisco Rojas: Celestial string amplitudes beyond tree level

      Temple He: An effective description of energy transport from holography

      4:30–5:00 pmNima Arkani-Hamed(Dual) surfacehedra and flow particles know about strings

       

      Wednesday, June 22, 2022

      9:00–9:30 amBreakfastlight breakfast provided
      Morning SessionChair: Alfredo Guevara
      9:30–10:00 amLaurent FreidelTitle: Higher spin symmetry in gravity

      Abstract: In this talk, I will review how the gravitational conservation laws at infinity reveal a tower of symmetry charges in an asymptotically flat spacetime.
      I will show how the conservation laws, at spacelike infinity, give a tower of soft theorems that connect to the ones revealed by celestial holography.
      I’ll present the expression for the symmetry charges in the radiative phase space, which opens the way to reveal the structure of the algebra beyond the positive helicity sector. Then, if time permits I’ll browse through many questions that these results raise:
      such as the nature of the spacetime symmetry these charges represent, the nature of the relationship with multipole moments, and the insights their presence provides for quantum gravity.

      10:00–10:30 amAna-Maria RaclariuTitle: Eikonal approximation in celestial CFT
      10:30–11:00 amCoffee break
      11:00–11:30 amAnastasia VolovichTitle: Effective Field Theories with Celestial Duals
      11:30–12:00 pmMarcus SpradlinTitle: Loop level gluon OPE’s in celestial holography
      12:00–2:00 pmLunch break
      Afternoon SessionChair: Chiara Toldo
      2:00–2:30 pmNetta EngelhardtTitle: Wormholes from entanglement: true or false?
      2:30–3:00 pmShort TalksLuke Lippstreu: Loop corrections to the OPE of celestial gluons

      Yangrui Hu: Light transforms of celestial amplitudes

      Lecheng Ren: All-order OPE expansion of celestial gluon and graviton primaries from MHV amplitudes

      3:00–3:30 pmCoffee break
      3:30–4:30 pmShort TalksNoah Miller: C Metric Thermodynamics

      Erin Crawley: Kleinian black holes

      Rifath Khan: Cauchy Slice Holography: A New AdS/CFT Dictionary

      Gonçalo Araujo-Regado: Cauchy Slice Holography: A New AdS/CFT Dictionary

      Tianli Wang: Soft Theorem in the BFSS Matrix Model

      Adam Tropper: Soft Theorem in the BFSS Matrix Model

      7:00–9:00 pmBanquetMaharaja Restaurant, 57 JFK Street, Cambridge, MA

       

      Thursday, June 23, 2022

      9:00–9:30 amBreakfastlight breakfast provided
      Morning SessionChair: Jordan Cotler
      9:30–10:00 amLaura DonnayTitle: A Carrollian road to flat space holography
      10:00–10:30 amAndrea PuhmTitle: Celestial wave scattering on Kerr-Schild backgrounds
      10:30–11:00 amCoffee break
      11:00–11:30 amSabrina PasterskiTitle: Mining Celestial Symmetries

      Abstract: The aim of this talk is to delve into the common thread that ties together recent work with H. Verlinde, L. Donnay, A. Puhm, and S. Banerjee exploring, explaining, and exploiting the symmetries encoded in the conformally soft sector.

      Come prepared to debate the central charge, loop corrections, contour prescriptions, and orders of limits!

      11:30–12:00 pmShamik BanerjeeTitle: Virasoro and other symmetries in CCFT

      Abstract:  In this talk I will briefly describe my ongoing work with Sabrina Pasterski. In this work we revisit the standard construction of the celestial stress tensor as a shadow of the subleading conformally soft graviton.  In its original formulation, we find that there is an obstruction to reproducing the expected $TT$ OPE in the double soft limit. This obstruction is related to the existence of the $SL_2$ current algebra symmetry of the CCFT. We propose a modification to the definition of the stress tensor which circumvents this obstruction and also discuss its implications for the existence of other current algebra (w_{1+\infty}) symmetries in CCFT.

      12:00–2:00 pmLunch break
      Afternoon SessionChair: Albert Law
      2:00–2:30 pmTomasz TaylorTitle: Celestial Yang-Mills amplitudes and D=4 conformal blocks
      2:30–3:00 pmBin ZhuTitle:  Single-valued correlators and Banerjee-Ghosh equations

      Abstract:  Low-point celestial amplitudes are plagued with singularities resulting from spacetime translation. We consider a marginal deformation of the celestial CFT which is realized by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators.

      3:00–3:30 pmCoffee break
      3:30–4:00 pmAlex LupsascaTitle: Holography of the Photon Ring
      4:00–5:30 pmShort TalksElizabeth Himwich: Celestial OPEs and w(1+infinity) symmetry of massless and massive amplitudes

      Adam Ball: Perturbatively exact $w_{1+\infty}$ asymptotic symmetry of quantum self-dual gravity

      Romain Ruzziconi: A Carrollian Perspective on Celestial Holography

      Jordan Cotler: Soft Gravitons in 3D

      Alfredo Guevara: Comments on w_1+\inf

      Andrew Strominger: Top-down celestial holograms

      Eduardo Casali: Celestial amplitudes as AdS-Witten diagrams

      Walker Melton: Top-down celestial holograms

       

      Friday, June 24, 2022

      9:00–9:30 amBreakfast
      9:30–12:30 pmOpen Discussion
      12:30–2:30 pmLunch provided at the BHI
      Departure

       

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      Interdisciplinary Science Seminar
      Title: Recent Advances on Maximum Flows and Minimum-Cost Flows

      Abstract: We survey recent advances on computing flows in graphs, culminating in an almost linear time algorithm for solving minimum-cost flow and several other problems to high accuracy on directed graphs. Along the way, we will discuss intuitions from linear programming, graph theory, and data structures that influence these works, and the resulting natural open problems.

      Bio: Yang P. Liu is a final-year graduate student at Stanford University. He is broadly interested in the efficient design of algorithms, particularly flows, convex optimization, and online algorithms. For his work, he has been awarded STOC and ITCS best student papers.

    • Workshop
      9:00 am-5:00 pm
      12/01/2024-08/05/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Phase Transitions_Poster

      On August 2–5, the CMSA hosted a workshop on Phase Transitions and Topological Defects in the Early Universe.

      The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA and online via Zoom webinar.

      The next decade will see a wealth of new cosmological data, which can lead to new insights into fundamental physics. Upcoming facilities (such as LISA) will be able to probe signals of fascinating phenomena in the early universe. These include signals from “Phase Transitions and Topological Defects,” which are ubiquitously given rise to in well-motivated UV models. In-depth studies of such signals requires cross-talks between experts from a wide spectrum of fields.

      The workshop aims to provide a platform for efficient exchange of new ideas related to these topics. It will start with an overview of some of the past and future experimental efforts. Next, there will be a substantial number of talks probing different aspects of phenomenology of phase transitions and topological defects in the early universe. It will finally close with discussions on recent formal development in the field.

      Scientific Advisory: Julian B. Muñoz, Lisa Randall, Matthew Reece, Tracy Slatyer, Shing-Tung Yau

      Organizers:
      Harvard: Nick DePorzio, Katie Fraser, Sam Homiller, Rashmish Mishra, & Aditya Parikh
      MIT: Pouya Asadi, Marianne Moore, & Yitian Sun

      Schedule/Format
      There will be 20+ 10 minute talks, ample discussion time, and lightning chalkboard talks.

      Speakers:

      • Nancy Aggarwal (Northwestern)
      • Jae Hyeok Chang (UMD – JHU)
      • Yanou Cui (UC Riverside)
      • David Dunsky (UC Berkeley)
      • Isabel Garcia-Garcia (KITP – UCSB)
      • Oliver Gould (Nottingham)
      • Yann Gouttenoire (Tel Aviv)
      • Eleanor Hall (UC Berkeley)
      • Sungwoo Hong (Chicago)
      • Anson Hook (UMD)
      • Jessica Howard (UC Irvine)
      • Seth Koren (Chicago)
      • Mrunal Korwar (Wisconsin)
      • Soubhik Kumar (UC Berkeley)
      • Vuk Mandic (Minnesota)
      • Yuto Minami (Osaka)
      • Michael Nee (Oxford)
      • Kai Schmitz (CERN)
      • Stephen R. Taylor (Vanderbilt)
      • Ofri Telem (UC Berkeley)
      • Juven Wang (Harvard)
      • Yikun Wang (Caltech)

      Participants:

      • Manuel Buen Abad (UMD)
      • Pouya Asadi (MIT)
      • Sean Benevedes (MIT)
      • Sandipan Bhattacherjee (Birla Institute of Technology Mesra Ranchi India)
      • Xingang Chen (Harvard University)
      • Nicholas DePorzio (Harvard University)
      • Peizhi Du (Stony Brook University)
      • Nicolas Fernandez (University of Illinois Urbana-Champaign)
      • Joshua Foster (MIT)
      • Katherine Fraser (Harvard University)
      • Sarah Geller (MIT)
      • Aurora Ireland (University of Chicago)
      • Marius Kongsore (New York University)
      • Ho Tat Lam (Massachusetts Institute of Technology)
      • Lingfeng Li (Brown University)
      • Yingying Li (Fermilab)
      • Gustavo Marques-Tavares (UMD)
      • Rashmish Mishra (Harvard University)
      • Siddharth Mishra-Sharma (MIT/Harvard University)
      • Toby Opferkuch (UC Berkeley)
      • Tong Ou (University of Chicago)
      • Aditya Parikh (Harvard University)
      • Yitian Sun (MIT)
      • Juan Sebastian Valbuena-Bermudez (Ludwig Maximilian University of Munich and Max Planck Institute for Physics)
      • Isaac Wang (Rutgers)
      • Wei Xue (University of Florida)
      • Winston Yin (UC Berkeley)
      • Quratulain Zahoor (The Islamia University of Bahwalpur Punjab (Pakistan)

      Schedule

      Tuesday, August 2, 2022

      9:00–9:20 amBreakfast
      9:20–9:30 amRashmish MishraOpening Remarks
      9:30–10:00 amVuk MandicTitle: Searching for the Stochastic Gravitational Wave Background with LISA

      Abstract: The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) will open a window into the milliHertz band of the gravitational wave spectrum. Among the many sources in this band is the stochastic gravitational wave background (SGWB), arising as an incoherent superposition of many uncorrelated gravitational wave sources. The SGWB could be of cosmological origin, carrying unique information about the physical processes that took place within the first minute after the big bang, including possible phase transitions and topological defects. LISA therefore has the potential to illuminate particle physics at very high energy scales that may be inaccessible in laboratories. I will discuss how LISA can be used to search for the SGWB, highlighting a new pipeline developed for this purpose as well as several challenges and limitations that such a search will encounter.

      10:00–10:30 amNancy AggarwalTitle: Gravitational waves at frequencies above 10 kHz

      Abstract: Gravitational waves (GWs) at frequencies higher than the LIGO band can bring us completely new information about the universe. Besides being the most-interesting frequency region for looking at cosmological phenomena, they can also convey signatures of ultralight bosons through blackhole superradiance and light primordial blackholes (PBHs). I will introduce a new global initiative to study GW sources and detectors at ultra-high-frequencies (MHz-GHz), as well as a new experiment at Northwestern University to look for GWs in the frequency band of 10 kHz to 300 kHz using levitated optomechanical sensors. I will summarize the design, the current experimental progress, as well as a path forward for future improvements.

      10:30–11:00 amYuto MinamiTitle: New measurements of the cosmic birefringence

      Abstract: Polarised light of the cosmic microwave background, the remnant light of the Big Bang, is sensitive to parity-violating physics, cosmic birefringence. In this presentation I report on a new measurement of cosmic birefringence from polarisation data of the European Space Agency (ESA)’s Planck satellite released in 2018. The statistical significance of the measured signal is 2.4 sigma. Recently, we found a signal with 3.3 sigma statistical significance when we use the latest Planck data and consider an effect of polarised foreground emission. If confirmed with higher statistical significance in future, it would have important implications for the elusive nature of dark matter and dark energy.

      11:00–1:30 pmBreak
      1:30–3:00 pmLighting Talks 1Lingfeng Li
      Winston Yin
      Marius Kongsore
      Nick DePorzio
      3:00–3:30 pmJae Hyeok ChangTitle: Correlating gravitational wave and gamma-ray signals from primordial black holes

      Abstract: Asteroid-mass primordial black holes (PBHs) can explain the observed dark matter abundance while being consistent with the current indirect detection constraints. These PBHs can produce gamma-ray signals from Hawking radiation that are within the sensitivity of future measurements by the AMEGO and e-ASTROGAM experiments. PBHs which give rise to such observable gamma-ray signals have a cosmic origin from large primordial curvature fluctuations. There must then be a companion, stochastic gravitational wave (GW) background produced by the same curvature fluctuations. I will demonstrate that the resulting GW signals will be well within the sensitivity of future detectors such as LISA, DECIGO, BBO, and the Einstein Telescope. The multimessenger signal from the observed gamma-rays and GWs will allow a precise measurement of the primordial curvature perturbation that produces the PBH. I will also argue that the resulting correlation between the two types of observations can provide a smoking-gun signal of PBHs.

      3:30–4:00 pmAnson Hook
      (Virtual via Zoom)
      Title: Early Universe Cosmology from Stochastic Gravitational Waves

      Abstract:  The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure gstar and beta functions as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the 10^-3 level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to O(1) deviations of gstar and the QCD beta function from their Standard Model value at temperatures ~ 10^5 GeV. In this case, many motivated models such as split SUSY and other solutions to the Electroweak Hierarchy problem would be tested. Future detectors, such as DECIGO, would be 100 times more sensitive than LISA to these effects and be capable of testing other motivated scenarios such as WIMPs and axions. The amazing prospect of using precision gravitational wave measurements to test such well motivated theories provides a benchmark to aim for when developing a precise understanding of the gravitational wave spectrum both experimentally and theoretically.

       

      Wednesday, August 3, 2022

      9:00–9:30 amBreakfast
      9:30–10:00 amKai Schmitz
      (Virtual via Zoom)
      Title: Gravitational waves from metastable cosmic strings

      Abstract: Cosmic strings are predicted by many Standard Model extensions involving the cosmological breaking of an Abelian symmetry and represent a potential source of primordial gravitational waves (GWs). In many Grand Unified Theories (GUTs), cosmic strings especially turn out to be metastable, as the nucleation of GUT monopoles along strings after a finite lifetime eventually leads to the collapse of the entire string network. In this talk, I will discuss the theoretical description of such a network and its individual components as well as the consequences for the emitted GW spectrum. Remarkably, the GW signal from metastable strings may well explain the common-spectrum process recently observed in pulsar timing data, while at the same time and in contrast to stable cosmic strings predicting a signal at higher frequencies that is still within the reach of current-generation ground-based interferometers. On their way to design sensitivity, existing GW experiments will thus have a realistic chance to probe particle physics processes at energies close to the GUT scale via the observation of GWs from metastable strings. This talk is based on 2107.04578 in collaboration with Wilfried Buchmüller and Valerie Domcke.

      10:00–10:30 amOliver Gould
      (Virtual via Zoom)
      Title: Effective field theory for cosmological phase transitions

      Abstract: Phase transitions are driven by thermal loop fluctuations, which modify background fields at leading order. This breaks the loop expansion and leads to large theoretical uncertainties in typical calculations, especially for gravitational wave predictions. I will give an overview of our present understanding of these uncertainties, and of the tools that have been developed to overcome them. Effective field theory has been at the forefront of this development, and I will outline how it can be used to solve a number of decades-long-standing theoretical problems.

      10:30–11:00 amIsabel Garcia-GarciaTitle: The Rocket Science of Expanding Bubbles

      11:00–1:30 pmBreak
      1:30–3:00 pmLightning Talks 2Sarah Geller
      Peizhi Du
      Tong Ou
      Isaac Wang
      Katie Fraser
      3:00–3:30 pmDavid Dunsky
      (Virtual via Zoom)
      Title: Gravitational Wave Gastronomy

      Abstract: The symmetry breaking of grand unified gauge groups in the early universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable and can leave behind unique gravitational wave fingerprints. In this talk, I will discuss the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and “eat” the strings, 2) the collapse and decay of a monopole-string network by strings that “eat” the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and “eat” the wall, and 4) the collapse and decay of a string-bounded wall network by walls that “eat” the strings. We call the gravitational wave signals produced from the “eating” of one topological defect by another “gravitational wave gastronomy”. The gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO(10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects.

      3:30–4:00 pmYanou Cui
      (Virtual via Zoom)
      Title: Cosmic Archaeology with gravitational waves from (axion) cosmic strings

      Abstract: In this talk I will discuss important aspects of cosmology and particle physics that can be probed with GW signals from cosmic strings: probing the pre-BBN primordial dark age and axion physics.  Gravitational waves (GWs) originating from the dynamics of a cosmic string network have the ability to probe many otherwise inaccessible properties of the early universe. In particular, I will discuss how the frequency spectrum of a stochastic GW background (SGWB) from a cosmic string network can be used to probe Hubble expansion rate of the early universe prior to Big Bang Nucleosynthesis (BBN), during the “primordial dark age”. Furthermore I will show that in contrast to the standard expectation, cosmic strings formed before inflation could regrow back into the horizon and leave imprints, with GW bursts potentially being the leading signal. In relation to axion physics I will also demonstrate the detection prospect for SGWB from global/axion strings which may provide a new probe for axion-like dark matter models, considering various scenarios of cosmic history.

      4:00–4:30 pmMichael NeeTitle: The Boring Monopole

      Abstract: First order phase transitions play an important role in the cosmology of many theories of BSM physics. In this talk I will discuss how a population of magnetic monopoles present in the early universe can seed first order phase transitions, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, thus requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. Our results show that monopole-catalysed tunnelling can dominate over the homogeneous decay for a wide range of parameters.

       

      Thursday, August 4, 2022

      9:00–9:30 amBreakfast
      9:30–10:00 amYikun WangTitle: A New Approach to Electroweak Symmetry Non-Restoration

      Abstract: Electroweak symmetry non-restoration up to high temperatures well above the electroweak scale has intriguing implications for (electroweak) baryogenesis and early universe thermal histories. In this talk, I will discuss such a possible fate of the electroweak symmetry in the early universe and a new approach to realize it, via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. Examples of benchmark scenarios that allow for electroweak symmetry non-restoration all the way up to hundreds of TeV temperatures, at the same time featuring suppressed sphaleron washout factors down to the electroweak scale, will be presented. Renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures, have been implemented calculating the thermal history. This method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

      10:00–10:30 amSoubhik KumarTitle: Probing primordial fluctuations through stochastic gravitational wave background anisotropies

      Abstract: Stochastic gravitational wave backgrounds are expected to be anisotropic. While such anisotropies can be of astrophysical origin, a cosmological component of such anisotropies can carry rich information about primordial perturbations. Focusing on the case of a cosmological phase transition, I will talk about how such anisotropies can give us a powerful probe of primordial non-Gaussianities, complementary to current and future CMB and LSS searches. In the scenario where astrophysical foregrounds are also present, I will then discuss some strategies using which we can extract the cosmological signal, focusing on the case of LISA, Taiji and BBO, in particular.

      10:30–11:00 amJessica Howard
      (Virtual via Zoom)
      Title: Dark Matter Freeze-out during SU(2)_L Confinement

      Abstract: We explore the possibility that dark matter is a pair of SU(2)_L doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This phase of confinement causes the Standard Model doublets and dark matter to confine into pion-like objects. Before the weak sector deconfines, the dark pions freezeout and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the observed relic density. We determine which regions of this parameter space evade direct detection and collider bounds.

      11:00–11:30 amJuven WangTitle: Quantum Matter Adventure to Beyond the Standard Model Prediction

      Abstract: Ideas developed from the quantum matter and quantum field theory frontier may guide us to explore new physics beyond the 4d Standard Model. I propose a few such ideas. First, new physics for neutrinos: right-handed neutrinos carry a Z_{16} class mixed gauge-gravitational global anomaly index, which could be replaced by 4d or 5d topological quantum field theory, or 4d interacting conformal field theory. These theories provide possible new neutrino mass mechanisms [arXiv:2012.15860]. Second, deconfined quantum criticality between Grand Unified Theories: dictated by a Z_2 class global anomaly, a gapless quantum critical region can happen between Georgi-Glashow and Pati-Salam models as deformation of the Standard Model, where Beyond the Standard Model physics and Dark Gauge sector occur as neighbor phases [arXiv:2106.16248, arXiv:2112.14765, arXiv:2204.08393]. Third, the Strong CP problem can be solved by a new solution involving Symmetric Mass Generation [arXiv:2204.14271].

      11:30–1:30 pmBreak
      1:30–4:00 pmStephen R. TaylorTitle: Pulsar Timing Arrays: The Next Window onto the Low-frequency Gravitational-wave Universe

      Abstract: The nanohertz-frequency band of gravitational waves should be awash with signals from supermassive black-hole binaries, as well as cosmological signatures of phase transitions, cosmic strings, and other relics of the early Universe. Pulsar-timing arrays (PTAs) like the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and the International Pulsar Timing Array are poised to chart this new frontier of gravitational wave discovery within the next several years. I will present exciting new results from recent cutting-edge searches, discuss some milestones on the road to the next decade of PTA discovery, and take workshop attendees through a guided tutorial of how the broader community can use our production-level analysis pipeline to extract new science with ease.

       

      Friday, August 5, 2022

      9:00–9:30 amBreakfast
      9:30–10:00 amOfri TelemTitle: Charge-Monopole Pairwise Phases from Dressed Quantum States

      10:00–10:30 amSungwoo HongTitle: Coupling a Cosmic String to a TQFT

      Abstract: In the last few years, the notion of symmetry has been enlarged to “generalized symmetry” or “higher-form symmetry” and these more generalized symmetries have played a critical role in deepening our understanding of QFT, notably IR phases of QFT. In this talk, I will discuss a various ways of coupling the axion-Maxwell theory to a topological field theory (TQFT). Contrary to a common wisdom, I will show that such topological modifications can lead to direct changes in the local physics with possible observable consequences. This surprise can be realized by a dimensional reduction, namely, a coupling to a TQFT in 4d leads to a non-trivial and local impact on the 2d string world-sheet QFT. There also exists a topological modification of the theory, i.e. gauging a discrete subgroup of 0-form shift symmetry, and this time it results in a alteration of spectrum of cosmic strings. If time permits, I will also discuss generalized symmetries and associated higher-groups of these theories.

      10:30–11:00 amEleanor Hall
      (Virtual via Zoom)
      Title: Non-perturbative methods for false vacuum decay

      Abstract: Gravitational waves from phase transitions in the early universe are one of our most promising signal channels of BSM physics; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present the quasi-stationary effective action, a new non-perturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. This method opens the door to reliable calculation of gravitational wave signals and false vacuum decay rates for strongly-interacting theories. I will also discuss recent developments and ongoing extensions of the QSEA.

      11:00–1:30 pmBreak
      1:30–2:00 pmMrunal KorwarTitle: Electroweak Symmetric Balls

      Abstract: Electroweak symmetric balls are macroscopic objects with electroweak symmetry restored inside. Such an object can arise in models where dark sectors contain monopole or non-topological soliton with a Higgs portal interaction to the Standard Model. It could be produced in the early universe via phase transition or parametric resonance, accounting for all dark matter. In a scenario where the balls are allowed to evaporate, the observed baryon asymmetry in our universe could be explained by a mechanism of “catalyzed baryogenesis.” In this mechanism, the motion of a ball-like catalyst provides the necessary out-of-equilibrium condition, its outer wall has CP-violating interactions with the Standard Model particles, and its interior has baryon number violating interactions via electroweak Sphaleron. Because of electroweak symmetric cores, such objects have a large geometric cross-section off a nucleus, generating a multi-hit signature in large volume detectors. These objects could radiatively capture a nucleus and release GeV-scale energy for each interaction. The IceCube detector can probe dark matter balls with masses up to a gram.

      2:00–2:30 pmSeth KorenTitle: Discrete Gauged Baryon Minus Lepton Number and the Cosmological Lithium Problem

      Abstract: We study the baryon minus lepton number gauge theory broken by a scalar with charge six. The infrared discrete vestige of the gauge symmetry demands the existence of cosmic string solutions, and their production as dynamical objects in the early universe is guaranteed by causality. These topological defects can support interactions which convert three protons into three positrons, and we argue an `electric’-`magnetic’ interplay can lead to an amplified, strong-scale cross-section in an analogue of the Callan-Rubakov effect.
      The cosmological lithium problem—that theory predicts a primordial abundance thrice as high as that observed—has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We suggest cosmic strings have disintegrated O(1) of the primordial lithium nuclei and estimate the rate in a benchmark scenario. To our knowledge this is the first new physics mechanism with microphysical justification for the abundance of lithium uniquely to be modified after Big Bang Nucleosynthesis.

      2:30–3:00 pmYann GouttenoireTitle: Supercool Composite Dark Matter beyond 100 TeV

       

      Phase-Transitions_Poster

    • CMSA EVENT: Advances in Mathematical Physics
      9:00 am-1:45 pm
      12/01/2024-08/01/2022
      1 Oxford Street, Cambridge MA 02138
      Elliott-Lieb-conference-2022_banner-2-1536x734

      A Conference in Honor of Elliott H. Lieb on his 90th Birthday

      On July 30 – Aug 1, 2022 the Harvard Mathematics Department and the CMSA co-hosted a birthday conference in honor of Elliott Lieb.

      This meeting highlights Elliott’s vast contribution to math and physics. Additionally, this meeting features Prof. Lieb’s more recent impact in strong subadditivity of entropy and integrable systems (ice model, Temperley-Lieb algebra etc.).

      Venue:

      July 30–31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
      August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138

      Schedule (pdf)

      Organizers:
      Michael Aizenman, Princeton University
      Joel Lebowitz, Rutgers University
      Ruedi Seiler, Technische Universität Berlin
      Herbert Spohn, Technical University of Munich
      Horng-Tzer Yau, Harvard University
      Shing-Tung Yau, Harvard University
      Jakob Yngvason, University of Vienna

      SPEAKERS:
      Rafael Benguria, Pontificia Universidad Catolica de Chile
      Eric Carlen, Rutgers University
      Philippe Di Francesco, University of Illinois
      Hugo Duminil-Copin, IHES
      László Erdös, Institute of Science and Technology Austria
      Rupert Frank, Ludwig Maximilian University of Munich
      Jürg Fröhlich, ETH Zurich
      Alessandro Giuliani, Università degli Studi Roma Tre
      Bertrand Halperin, Harvard University
      Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
      Sabine Jansen, Ludwig Maximilian University of Munich
      Mathieu Lewin, Université Paris-Dauphine
      Bruno Nachtergaele, The University of California, Davis
      Yoshiko Ogata, University of Tokyo
      Ron Peled, Tel Aviv University
      Benjamin Schlein, University of Zurich
      Robert Seiringer, Institute of Science and Technology Austria
      Jan Philip Solovej, University of Copenhagen
      Hal Tasaki, Gakushuin University
      Simone Warzel, Technical University of Munich
      Jun Yin, The University of California, Los Angeles

       

      Elliott-Lieb-conference

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      CMSA Interdisciplinary Science Seminar

      Speaker: Sumit Sinha, Harvard University

      Title: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data (https://arxiv.org/abs/2202.10595)

      Abstract: Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.

      Bio: I am a postdoctoral fellow in Harvard SEAS (Applied Mathematics) and Dana Farber Cancer Institute (Data Science) beginning Feb 2022. I finished my PhD in Physics (Theoretical Biophysics) from UT Austin (Jan 2022) on “Theoretical and computational studies of growing tissue”.  I pursued my undergraduate degree in Physics from the Indian Institute of Technology, Kanpur in India (2015). Boradly, I am interested in developing theoretical models, inspired from many-body statistical physics, for biological processes at different length and time scales.

       

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024

      Abstract: The establishment of neural circuitry during early infancy is critical for developing visual, auditory, and motor functions. However, how cortical tissue develops postnatally is largely unknown. By combining T1 relaxation time from quantitative MRI and mean diffusivity (MD) from diffusion MRI, we tracked cortical tissue development in infants across three timepoints (newborn, 3 months, and 6 months). Lower T1 and MD indicate higher microstructural tissue density and more developed cortex. Our data reveal three main findings: First, primary sensory-motor areas (V1: visual, A1: auditory, S1: somatosensory, M1: motor) have lower Tand MD at birth than higher-level cortical areas. However, all primary areas show significant reductions in Tand MD in the first six months of life, illustrating profound tissue growth after birth. Second, significant reductions in Tand MD from newborns to 6-month-olds occur in all visual areas of the ventral and dorsal visual streams. Strikingly, this development was heterogenous across the visual hierarchies: Earlier areas are more developed with denser tissue at birth than higher-order areas, but higher-order areas had faster rates of development. Finally, analysis of transcriptomic gene data that compares gene expression in postnatal vs. prenatal tissue samples showed strong postnatal expression of genes associated with myelination, synaptic signaling, and dendritic processes. Our results indicate that these cellular processes may contribute to profound postnatal tissue growth in sensory cortices observed in our in-vivo measurements. We propose a novel principle of postnatal maturation of sensory systems: development of cortical tissue proceeds in a hierarchical manner, enabling the lower-level areas to develop first to provide scaffolding for higher-order areas, which begin to develop more rapidly following birth to perform complex computations for vision and audition.

      This work is published here: https://www.nature.com/articles/s42003-021-02706-w

    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-07.14.22-1583x2048

      Abstract:  Introducing internal degrees of freedom in the description of crystalline insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses. Here, we present a semiclassical approach to transport and accumulation of general spinor degrees of freedom in adiabatically driven, weakly inhomogeneous crystals of dimensions one, two and three under external electromagnetic fields. Our approach shows that spatio-temporal modulations of the system induce a spinor current and density that is related to geometrical and topological objects — the spinor-Chern fluxes and numbers — defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates.

      The results are available here: https://arxiv.org/abs/2203.14902

      Bio: Ioannis Petrides is a postdoctoral fellow at the School of Engineering and Applied Sciences at Harvard University. He received his Ph.D. from the Institute for Theoretical Physics at ETH Zurich. His research focuses on the topological and geometrical aspects of condensed matter systems.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/15/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
      Interdisciplinary Science Seminar
      Speaker: Fouad El Baidouri, Broad Institute

      Title: The phenotype of the last universal common ancestor and the evolution of complexity

      Abstract: A fundamental concept in evolutionary theory is the last universal common ancestor (LUCA) from which all living organisms originated. While some authors have suggested a relatively complex LUCA it is still widely assumed that LUCA must have been a very simple cell and that life has subsequently increased in complexity through time. However, while current thought does tend towards a general increase in complexity through time in Eukaryotes, there is increasing evidence that bacteria and archaea have undergone considerable genome reduction during their evolution. This raises the surprising possibility that LUCA, as the ancestor of bacteria and archaea may have been a considerably complex cell. While hypotheses regarding the phenotype of LUCA do exist, all are founded on gene presence/absence. Yet, despite recent attempts to link genes and phenotypic traits in prokaryotes, it is still inherently difficult to predict phenotype based on the presence or absence of genes alone. In response to this, we used Bayesian phylogenetic comparative methods to predict ancestral traits. Testing for robustness to horizontal gene transfer (HGT) we inferred the phenotypic traits of LUCA using two robust published phylogenetic trees and a dataset of 3,128 bacterial and archaeal species.

      Our results depict LUCA as a far more complex cell than has previously been proposed, challenging the evolutionary model of increased complexity through time in prokaryotes. Given current estimates for the emergence of LUCA we suggest that early life very rapidly evolved cellular complexity.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      6/24/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Some new algorithms in statistical genomics
      9:00 am-10:00 am
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-06.23.2022-1583x2048-1

      Abstract: The statistical analysis of genomic data has incubated many innovations for computational method development. This talk will discuss some simple algorithms that may be useful in analyzing such data. Examples include algorithms for efficient resampling-based hypothesis testing, minimizing the sum of truncated convex functions, and fitting equality-constrained lasso problems. These algorithms have the potential to be used in other applications beyond statistical genomics.

      Bio: Hui Jiang is an Associate Professor in the Department of Biostatistics at the University of Michigan. He received his Ph.D. in Computational and Mathematical Engineering from Stanford University. Before joining the University of Michigan, he was a postdoc in the Department of Statistics and Stanford Genome Technology Center at Stanford University. He is interested in developing statistical and computational methods for analyzing large-scale biological data generated using modern high-throughput technologies.

    • Math Science Literature Lecture Series
      9:00 am-10:30 am
      12/01/2024

      Peter Shor (MIT)

      TitleQuantum error correcting codes and fault tolerance

      Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field.

      Talk chair: Zhengwei Liu

      Video

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      The number of n-queens configurations
      9:00 am-10:00 am
      12/01/2024

      Speaker: Michael Simkin, Harvard CMSA

      Title: The number of n-queens configurations

      Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

      Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      6/10/2021 Interdisciplinary Science Seminar
      9:00 am-10:00 am
      12/01/2024
    • CMSA EVENT: Simons Collaboration Workshop, Jan. 10-13, 2018
      9:00 am-12:00 pm
      12/01/2024-01/13/2017
      banner-image-1

      The CMSA will be hosting a four-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on January 10-13, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

       

      Confirmed Participants:

    • CMSA EVENT: Simons Collaboration on Homological Mirror Symmetry
      9:00 am-5:00 pm
      12/01/2024-05/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 3-day workshop on Homological Mirror Symmetry and related areas on May 6 – May 8, 2016 at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Organizers:

      D. Auroux, S.C. Lau, N.C. Leung, Bong Lian, C.C. Liu, S.T. Yau

      Speakers:

      1. Netanel Blaier (MIT)
      2. Kwokwai Chan (CUHK)
      3. Bohan Fang (Peking University)
      4. Amanda Francis (BYU)
      5. Hansol Hong (CUHK)
      6. Heather Lee (Purdue University)
      7. Si Li (Tsinghua University)
      8. Yu-Shen Lin (Stanford University)
      9. Alex Perry (Harvard University)
      10. Hiro Tanaka (Harvard University)
      11. Sara Tukachinsky (HUJ)
      12. Michael Viscardi (MIT)
      13. Eric Zaslow (Northwestern University)
      14. Jingyu Zhao (Columbia University)

      Please click here for the conference Main Website.

      Please click Simons Workshop Schedule with Abstract for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Schedule:

      May 6 – Day 1
      9:00amBreakfast
      9:35amOpening remarks
      9:45am – 10:45amSi Li, “Quantum master equation, chiral algebra, and integrability”
      10:45am – 11:15amBreak
      11:15am – 12:15pmSara Tukachinsky, “Point like bounding chains and open WDVV
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmBohan Fang, “Mirror B model for toric Calabi Yau 3 folds
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHiro Tanaka, “Toward Fukaya categories over arbitrary coefficients
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmHansol Hong, “Noncommutative mirror functors
      May 7 – Day 2
      9:00amBreakfast
      9:45am – 10:45amEric Zaslow, “Lagrangian fillings what does the sheaf say?
      10:45am – 11:15amBreak
      11:15am – 12:15pmAlex Perry, “Derived categories of Gushel Mukai varieties
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmAmanda Francis, “A Landau Ginzburg mirror theorem inspired by Borcea Voisin symmetry
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmHeather Lee, “Homological mirror symmetry for open Riemann surfaces from pair of pants decompositions
      4:00pm – 4:15pmBreak
      4:15pm – 5:15pmYu-Shen Lin, “Counting Holomorphic Discs via Tropical Discs on K3 Surfaces
      May 8 – Day 3
      9:00amBreakfast
      9:45am – 10:45amKwokwai Chan, “HMS for local CY manifolds via SYZ
      10:45am – 11:15amBreak
      11:15am – 12:15pmNetanel Blaier, “The quantum Johnson homomorphism, formality and symplectic isotopy
      12:15pm – 1:45pmLunch
      1:45pm – 2:45pmJingyu Zhao, “Periodic symplectic cohomology and the Hodge filtration
      2:45pm – 3:00pmBreak
      3:00pm – 4:00pmMichael Viscardi, “Equivariant quantum cohomology and the geometric Satake equivalence
      * Click titles for talk videos. All videos are also available on “Harvard CMSA” channel on Youtube, grouped into playlist “Simons Collaboration on Homological Mirror symmetry“.

      This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Adventures in Perturbation Theory
      9:00 am-10:00 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-01.25.2022-1

      Abstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form, underlying geometric structure, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The Amplituhedron BCFW Triangulation
      9:00 am-10:00 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-2.3.2022

      Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.

    • CMSA EVENT: Workshop on Optimization in Image Processing
      9:00 am-12:30 pm
      12/01/2024-06/30/2016

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Optimization in Image Processing on June 27 – 30, 2016. This 4-day workshop aims to bring together researchers to exchange and stimulate ideas in imaging sciences, with a special focus on new approaches based on optimization methods. This is a cutting-edge topic with crucial impact in various areas of imaging science including inverse problems, image processing and computer vision. 16 speakers will participate in this event, which we think will be a very stimulating and exciting workshop. The workshop will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Speakers:

      1. Antonin Chambolle, CMAP, Ecole Polytechnique
      2. Raymond Chan, The Chinese University of Hong Kong
      3. Ke Chen, University of Liverpool
      4. Patrick Louis Combettes, Université Pierre et Marie Curie
      5. Mario Figueiredo, Instituto Superior Técnico
      6. Alfred Hero, University of Michigan
      7. Ronald Lok Ming Lui, The Chinese University of Hong Kong
      8. Mila Nikolova, Ecole Normale Superieure Cachan
      9. Shoham Sabach, Israel Institute of Technology
      10. Martin Benning, University of Cambridge
      11. Jin Keun Seo, Yonsei University
      12. Fiorella Sgallari, University of Bologna
      13. Gabriele Steidl, Kaiserslautern University of Technology
      14. Joachim Weickert, Saarland University
      15. Isao Yamada, Tokyo Institute of Technology
      16. Wotao Yin, UCLA

      Please click Workshop Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Please click here for registration – Registration Deadline: June 7, 2016; Registration is capped at 70 participants.

      Schedule:

      June 27 – Day 1
      9:00amBreakfast
      9:20amOpening remarks
      9:30am – 10:20amJoachim Weickert, “FSI Schemes: Fast Semi-Iterative Methods for Diffusive or Variational Image Analysis Problems”
      10:20am – 10:50amBreak
      10:50am – 11:40pmPatrick Louis Combettes“Block-Iterative Asynchronous Variational Image Recovery”
      11:40am – 12:30pmIsao Yamada“Spicing up Convex Optimization for Certain Inverse Problems”
      12:30pm – 2:00pmLunch
      2:30pm – 3:20pmFiorella Sgallari, “Majorization-Minimization for Nonconvex Optimization”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmShoham Sabach“A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Problems”
      June 28 – Day 2
      9:00amBreakfast
      9:30am – 10:20amAntonin Chambolle“Acceleration of alternating minimisations”
      10:20am – 10:50amBreak
      10:50am – 11:40amMario Figueiredo“ADMM in Image Restoration and Related Problems: Some History and Recent Advances”
      11:40am – 12:30pmKe Chen“Image Restoration and Registration Based on Total Fractional-Order Variation Regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 4:40pmDiscussions
      June 29 – Day 3
      9:00amBreakfast
      9:30am – 10:20amAlfred Hero“Continuum relaxations for discrete optimization”
      10:20am – 10:50amBreak
      10:50am – 11:40amWotao Yin“Coordinate Update Algorithms for Computational Imaging and Machine Learning”
      11:40am – 12:30pmMila Nikolova“Limits on noise removal using log-likelihood and regularization”
      12:30pm – 2:30pmLunch
      2:30pm – 3:20pmMartin Benning, “Nonlinear spectral decompositions and the inverse scale space method”
      3:20pm – 3:50pmBreak
      3:50pm – 4:40pmRonald Ming Lui“TEMPO: Feature-endowed Teichmuller extremal mappings of point cloud for shape classification”
      June 30 – Day 4
      9:00amBreakfast
      9:30am – 10:20amJin Keun Seo“Mathematical methods for biomedical impedance imaging”
      10:20am – 10:50amBreak
      10:50am – 11:40amGabriele Steidl, “Iterative Multiplicative Filters for Data Labeling”
      11:40am – 12:30pmRaymond Chan, “Point-spread function reconstruction in ground-based astronomy”
      * This event is sponsored by CMSA Harvard University.

      Organizers: Raymond Chan and Shing-Tung Yau

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA/Tsinghua Math-Science Literature Lecture: Scott Kominers
      9:00 am-10:30 am
      12/01/2024

      CMSA/Tsinghua Math-Science Literature Lecture

      Prof. Scott Kominers will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

      Date: Monday, November 20, 2023

      Time: 9:00 – 10:30 am ET

      Location: Via Zoom Webinar

      Registration is required.

      Title: 60 Years of Matching: From Gale and Shapley to Trading Networks

      Abstract: Gale and Shapley’s 1962 American Mathematical Monthly paper, “College Admissions and the Stability of Marriage,” is by now one of the most cited articles in the journal’s history, having served as the foundation for an entire branch of the field of market design. This success owes in large part to the beautiful, applicable, and surprisingly general theory of matching mechanisms uncovered in Gale and Shapley’s work. This talk traces the history and evolution of matching theory from that paper forward to the present day, along the way touching on real-world applications to everything from medical residency matching to electricity markets.

      Moderator: Sergiy Verstyuk


      Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

       

      CMSA COVID-19 Policies

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      10/19/2021 Combinatorics, Physics and Probability Seminar
      9:00 am-10:00 am
      12/01/2024

      Title: Ising model, total positivity, and criticality

      Abstract: The Ising model, introduced in 1920, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.
      The totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases, and is closely related to cluster algebras and scattering amplitudes.
      I will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian, obtained in our recent work with P. Pylyavskyy. Building on this connection, I will give a new boundary correlation formula for the critical Ising model

    • Workshop
      9:00 am-5:00 pm
      12/01/2024-05/19/2023
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      GRAMSIAcover-600x338

      On May 16 – May 19, 2023 the CMSA hosted a four-day workshop on GRAMSIA: Graphical Models, Statistical Inference, and Algorithms. The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop was organized by David Gamarnik (MIT), Kavita Ramanan (Brown), and Prasad Tetali  (Carnegie Mellon).

      The purpose of this workshop is to highlight various mathematical questions and issues associated with graphical models and message-passing algorithms, and to bring together a group of researchers for discussion of the latest progress and challenges ahead. In addition to the substantial impact of graphical models on applied areas, they are also connected to various branches of the mathematical sciences. Rather than focusing on the applications, the primary goal is to highlight and deepen these mathematical connections.

      Location: Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

       

      Speakers:
      • Jake Abernethy (Georgia Tech)
      • Guy Bresler (MIT)
      • Florent Krzakala (Ecole Polytechnique Federale de Lausanne)
      • Lester Mackey (Microsoft Research New England)
      • Theo McKenzie (Harvard)
      • Andrea Montanari (Stanford)
      • Elchanan Mossel (MIT)
      • Yury Polyanskiy (MIT)
      • Patrick Rebeschini (Oxford)
      • Subhabrata Sen (Harvard)
      • Devavrat Shah (MIT)
      • Pragya Sur (Harvard)
      • Alex Wein (UC Davis)
      • Yihong Wu (Yale)
      • Sarath Yasodharan (Brown)
      • Horng-Tzer Yau (Harvard)
      • Christina Lee Yu (Cornell)
      • Ilias Zadik (MIT)
      Schedule:

      Tuesday, May 16, 2023

      9:00 amBreakfast
      9:15 – 9:30 amIntroductory remarks by organizers
      9:30 – 10:20 amSubhabrata Sen (Harvard)

      Title: Mean-field approximations for high-dimensional Bayesian regression

      Abstract: Variational approximations provide an attractive computational alternative to MCMC-based strategies for approximating the posterior distribution in Bayesian inference. The Naive Mean-Field (NMF) approximation is the simplest version of this strategy—this approach approximates the posterior in KL divergence by a product distribution. There has been considerable progress recently in understanding the accuracy of NMF under structural constraints such as sparsity, but not much is known in the absence of such constraints. Moreover, in some high-dimensional settings, the NMF is expected to be grossly inaccurate, and advanced mean-field techniques (e.g. Bethe approximation) are expected to provide accurate approximations. We will present some recent work in understanding this duality in the context of high-dimensional regression. This is based on joint work with Sumit Mukherjee (Columbia) and Jiaze Qiu (Harvard University).

      10:30 – 11:00 amCoffee break 
      11:00 – 11:50 amElchanan Mossel (MIT)

      Title: Some modern perspectives on the Kesten-Stigum bound for reconstruction on trees.

      Abstract: The Kesten-Stigum bound is a fundamental spectral bound for reconstruction on trees. I will discuss some conjectures and recent progress on understanding when it is tight as well as some conjectures and recent progress on what it signifies even in cases where it is not tight.

      12:00 – 2:00 pmLunch
      2:00 – 2:50 pmChristina Lee Yu (Cornell)

      Title: Exploiting Neighborhood Interference with Low Order Interactions under Unit Randomized Design

      Abstract: Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in many real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we utilize knowledge of the network structure to provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. Central to our contribution is a new framework for balancing between model flexibility and statistical complexity as captured by this low order interactions structure.

      3:00 – 3:30 pmCoffee break
      3:30 – 4:20 pmTheo McKenzie (Harvard)

      Title: Spectral statistics for sparse random graphs

      Abstract: Understanding the eigenvectors and eigenvalues of the adjacency matrix of random graphs is fundamental to many algorithmic questions; moreover, it is related to longstanding questions in quantum physics. In this talk we focus on random models of sparse graphs, giving some properties that are unique to these sparse graphs, as well as some specific obstacles. Based on this, we show some new results on spectral statistics of sparse random graphs, as well as some conjectures.

      4:40 – 6:30 pmLightning talk session + welcome reception

       

      Wednesday, May 17, 2023

      9:00 amBreakfast
      9:30 – 10:20Ilias Zadik (MIT)

      Title: Revisiting Jerrum’s Metropolis Process for the Planted Clique Problem

      Abstract: Jerrum in 1992 (co-)introduced the planted clique model by proving the (worst-case initialization) failure of the Metropolis process to recover any o(sqrt(n))-sized clique planted in the Erdos-Renyi graph G(n,1/2). This result is classically cited in the literature of the problem, as the “first evidence” the o(sqrt(n))-sized planted clique recovery task is “algorithmically hard”.
      In this work, we show that the Metropolis process actually fails to work (under worst-case initialization) for any o(n)-sized planted clique, that is the failure applies well beyond the sqrt(n) “conjectured algorithmic threshold”. Moreover we also prove, for a large number of temperature values, that the Metropolis process fails also under “natural initialization”, resolving an open question posed by Jerrum in 1992.

      10:30 – 11:00Coffee break
      11:00 – 11:50Florent Krzakala (Ecole Polytechnique Federale de Lausanne)

      Title: Are Gaussian data all you need for machine learning theory?

      Abstract: Clearly, no! Nevertheless, the Gaussian assumption remains prevalent among theoreticians, particularly in high-dimensional statistics and physics, less so in traditional statistical learning circles. To what extent are Gaussian features merely a convenient choice for certain theoreticians, or genuinely an effective model for learning? In this talk, I will review recent progress on these questions, achieved using rigorous probabilistic approaches in high-dimension and techniques from mathematical statistical physics. I will demonstrate that, despite its apparent limitations, the Gaussian approach is sometimes much closer to reality than one might expect. In particular, I will discuss key findings from a series of recent papers that showcase the Gaussian equivalence of generative models, the universality of Gaussian mixtures, and the conditions under which a single Gaussian can characterize the error in high-dimensional estimation. These results illuminate the strengths and weaknesses of the Gaussian assumption, shedding light on its applicability and limitations in the realm of theoretical statistical learning.

      12:00 – 2:00 pmLunch
      2:00 – 2:50 pmAndrea Montanari (Stanford)

      Title: Dimension free ridge regression

      Abstract: Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we revisit ridge regression. We allow the feature vector to be high-dimensional, or even infinite-dimensional, in which case it belongs to a separable Hilbert space and assume it to satisfy a certain convex concentration property. Within this setting, we establish non-asymptotic bounds that approximate the bias and variance of ridge regression in terms of the bias and variance of an ‘equivalent’ sequence model (a regression model with diagonal design matrix). Previously, such an approximation result was known only in the proportional regime and only up to additive errors: in particular, it did not allow to characterize the behavior of the excess risk when this converges to 0. Our general theory recovers earlier results in the proportional regime (with better error rates). As a new application, we obtain a completely explicit and sharp characterization of ridge regression for Hilbert covariates with regularly varying spectrum. Finally, we analyze the overparametrized near-interpolation setting and obtain sharp ‘benign overfitting’ guarantees.

      [Based on joint work with Chen Cheng]

      3:00 – 3:50 pmYury Polyanskiy (MIT)

      Title: Recent results on broadcasting on trees and stochastic block model

      Abstract: I will survey recent results and open questions regarding the q-ary stochastic block model and its local version (broadcasting on trees, or BOT). For example, establishing uniqueness of non-trivial solution to distribution recursions (BP fixed point) implies a characterization for the limiting mutual information between the graph and community labels. For q=2 uniqueness holds in all regimes. For q>2 uniqueness is currently only proved above a certain threshold that is asymptotically (for large q) is close to Kesten-Stigum (KS) threshold. At the same time between the BOT reconstruction and KS we show that uniqueness does not hold, at least in the presence of (arbitrary small) vertex-level side information. I will also discuss extension of the robust reconstruction result of Janson-Mossel’2004.

      Based on joint works with Qian Yu (Princeton) and Yuzhou Gu (MIT).

      4:00 – 4:30 pmCoffee break
      4:30 – 5:20 pmAlex Wein (UC Davis)

      Title: Is Planted Coloring Easier than Planted Clique?

      Abstract: The task of finding a planted clique in the random graph G(n,1/2) is perhaps the canonical example of a statistical-computational gap: for some clique sizes, the task is statistically possible but believed to be computationally hard. Really, there are multiple well-studied tasks related to the planted clique model: detection, recovery, and refutation. While these are equally difficult in the case of planted clique, this need not be true in general. In the related planted coloring model, I will discuss the computational complexity of these three tasks and the interplay among them. Our computational hardness results are based on the low-degree polynomial model of computation.By taking the complement of the graph, the planted coloring model is analogous to the planted clique model but with many planted cliques. Here our conclusion is that adding more cliques makes the detection problem easier but not the recovery problem.

       

      Thursday, May 18, 2023

      9:00Breakfast
      9:30 – 10:20Guy Bresler (MIT)

      Title: Algorithmic Decorrelation and Planted Clique in Dependent Random Graphs

      Abstract: There is a growing collection of average-case reductions starting from Planted Clique (or Planted Dense Subgraph) and mapping to a variety of statistics problems, sharply characterizing their computational phase transitions. These reductions transform an instance of Planted Clique, a highly structured problem with its simple clique signal and independent noise, to problems with richer structure. In this talk we aim to make progress in the other direction: to what extent can these problems, which often have complicated dependent noise, be transformed back to Planted Clique? Such a bidirectional reduction between Planted Clique and another problem shows a strong computational equivalence between the two problems.  We develop a new general framework for reasoning about the validity of average-case reductions based on low sensitivity to perturbations. As a concrete instance of our general result, we consider the planted clique (or dense subgraph) problem in an ambient graph that has dependent edges induced by randomly adding triangles to the Erdos-Renyi graph G(n,p), and show how to successfully eliminate dependence by carefully removing the triangles while approximately preserving the clique (or dense subgraph). Joint work with Chenghao Guo and Yury Polyanskiy.

      10:30 – 11:00Coffee break 
      11:00 – 11:50Sarath Yasodharan (Brown)

      Title: A Sanov-type theorem for unimodular marked random graphs and its applications

      Abstract: We prove a Sanov-type large deviation principle for the component empirical measures of certain sequences of unimodular random graphs (including Erdos-Renyi and random regular graphs) whose vertices are marked with i.i.d. random variables. Specifically, we show that the rate function can be expressed in a fairly tractable form involving suitable relative entropy functionals. As a corollary, we establish a variational formula for the annealed pressure (or limiting log partition function) for various statistical physics models on sparse random graphs. This is joint work with I-Hsun Chen and Kavita Ramanan.

      12:00 – 12:15 pm

      12:15 – 2:00 pm

      Group Photo

      Lunch

      2:00 – 2:50 pmPatrick Rebeschini (Oxford)

      Title: Implicit regularization via uniform convergence

      Abstract: Uniform convergence is one of the main tools to analyze the complexity of learning algorithms based on explicit regularization, but it has shown limited applicability in the context of implicit regularization. In this talk, we investigate the statistical guarantees on the excess risk achieved by early-stopped mirror descent run on the unregularized empirical risk with the squared loss for linear models and kernel methods. We establish a direct link between the potential-based analysis of mirror descent from optimization theory and uniform learning. This link allows characterizing the statistical performance of the path traced by mirror descent directly in terms of localized Rademacher complexities of function classes depending on the choice of the mirror map, initialization point, step size, and the number of iterations. We will discuss other results along the way.

      3:00 – 3:50 pmPragya Sur (Harvard)

      Title: A New Central Limit Theorem for the Augmented IPW estimator in high dimensions

      Abstract: Estimating the average treatment effect (ATE) is a central problem in causal inference. Modern advances in the field studied estimation and inference for the ATE in high dimensions through a variety of approaches. Doubly robust estimators such as the augmented inverse probability weighting (AIPW) form a popular approach in this context. However, the high-dimensional literature surrounding these estimators relies on sparsity conditions, either on the outcome regression (OR) or the propensity score (PS) model. This talk will introduce a new central limit theorem for the classical AIPW estimator, that applies agnostic to such sparsity-type assumptions. Specifically, we will study properties of the cross-fit version of the estimator under well-specified OR and PS models, and the proportional asymptotics regime where the number of confounders and sample size diverge proportional to each other. Under assumptions on the covariate distribution, our CLT will uncover two crucial phenomena among others: (i) the cross-fit AIPW exhibits a substantial variance inflation that can be quantified in terms of the signal-to-noise ratio and other problem parameters, (ii) the asymptotic covariance between the estimators used while cross-fitting is non-negligible even on the root-n scale. These findings are strikingly different from their classical counterparts, and open a vista of possibilities for studying similar other high-dimensional effects. On the technical front, our work utilizes a novel interplay between three distinct tools—approximate message passing theory, the theory of deterministic equivalents, and the leave-one-out approach.

      4:00 – 4:30 pmCoffee break
      4:30 – 5:20 pmYihong Wu (Yale)

      Title: Random graph matching at Otter’s threshold via counting chandeliers

      Abstract: We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erdős–Rényi graphs G(n,q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nq\to\infty and the edge correlation coefficient ρ satisfies ρ^2>α≈0.338, where α is Otter’s tree-counting constant. Moreover, this almost exact matching can be made exact under an extra condition that is information-theoretically necessary. This is the first polynomial-time graph matching algorithm that succeeds at an explicit constant correlation and applies to both sparse and dense graphs. In comparison, previous methods either require ρ=1−o(1) or are restricted to sparse graphs. The crux of the algorithm is a carefully curated family of rooted trees called chandeliers, which allows effective extraction of the graph correlation from the counts of the same tree while suppressing the undesirable correlation between those of different trees. This is joint work with Cheng Mao, Jiaming Xu, and Sophie Yu, available at https://arxiv.org/abs/2209.12313

       

      Friday, May 19, 2023

      9:00Breakfast
      9:30 – 10:20Jake Abernethy (Georgia Tech)

      Title: Optimization, Learning, and Margin-maximization via Playing Games

      Abstract: A very popular trick for solving certain types of optimization problems is this: write your objective as the solution of a two-player zero-sum game, endow both players with an appropriate learning algorithm, watch how the opponents compete, and extract an (approximate) solution from the actions/decisions taken by the players throughout the process. This approach is very generic and provides a natural template to produce new and interesting algorithms. I will describe this framework and show how it applies in several scenarios, including optimization, learning, and margin-maximiation problems. Along the way we will encounter a number of novel tools and rediscover some classical ones as well.

      10:30 – 11:00Coffee break 
      11:00 – 11:50Devavrat Shah (MIT)

      Title: On counterfactual inference with unobserved confounding via exponential family

      Abstract: We are interested in the problem of unit-level counterfactual inference with unobserved confounders owing to the increasing importance of personalized decision-making in many domains: consider a recommender system interacting with a user over time where each user is provided recommendations based on observed demographics, prior engagement levels as well as certain unobserved factors. The system adapts its recommendations sequentially and differently for each user. Ideally, at each point in time, the system wants to infer each user’s unknown engagement if it were exposed to a different sequence of recommendations while everything else remained unchanged. This task is challenging since: (a) the unobserved factors could give rise to spurious associations, (b) the users could be heterogeneous, and (c) only a single trajectory per user is available.

      We model the underlying joint distribution through an exponential family. This reduces the task of unit-level counterfactual inference to simultaneously learning a collection of distributions of a given exponential family with different unknown parameters with single observation per distribution. We discuss a computationally efficient method for learning all of these parameters with estimation error scaling linearly with the metric entropy of the space of unknown parameters – if the parameters are an s-sparse linear combination of k known vectors in p dimension, the error scales as O(s log k/p).  En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality.

      Based on a joint work with Raaz Dwivedi, Abhin Shah and Greg Wornell (all at MIT) with manuscript available here: https://arxiv.org/abs/2211.08209

      12:00 – 2:00 pmLunch 
      2:00 – 2:50 pmLester Mackey  (Microsoft Research New England)

      Title: Advances in Distribution Compression

      Abstract: This talk will introduce two new tools for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning:
      1. Given an initial n-point summary (for example, from independent sampling or a Markov chain), kernel thinning finds a subset of only square-root n-points with comparable worst-case integration error across a reproducing kernel Hilbert space.
      2. If the initial summary suffers from biases due to off-target sampling, tempering, or burn-in, Stein thinning simultaneously compresses the summary and improves the accuracy by correcting for these biases.
      These tools are especially well-suited for tasks that incur substantial downstream computation costs per summary point like organ and tissue modeling in which each simulation consumes 1000s of CPU hours.
      Based on joint work with Raaz Dwivedi, Marina Riabiz, Wilson Ye Chen, Jon Cockayne, Pawel Swietach, Steven A. Niederer, Chris. J. Oates, Abhishek Shetty, and Carles Domingo-Enrich.

      3:00 – 3:30 pmCoffee break
      3:30 – 4:20 pmHorng-Tzer Yau (Harvard)

      Title: On the spectral gap of mean-field spin glass models.

      Abstract: We will discuss recent progress regarding spectral gaps for the Glauber dynamics of spin glasses at high temperature. In addition, we will also report on estimating the operator norm  of the covariance matrix for the SK model.

       

      Moderators: Benjamin McKenna, Harvard CMSA & Changji Xu, Harvard CMSA


       

      CMSA COVID-19 Policies

       

    • CMSA EVENT: Mini-school on Nonlinear Equations, December 3-4, 2016
      9:00 am-5:00 pm
      12/01/2024-12/04/2016

      The Center of Mathematical Sciences and Applications will be hosting a Mini-school on Nonlinear Equations on December 3-4, 2016. The conference will have speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138.

      The mini-school will consist of lectures by experts in geometry and analysis detailing important developments in the theory of nonlinear equations and their applications from the last 20-30 years.  The mini-school is aimed at graduate students and young researchers working in geometry, analysis, physics and related fields.

      Please click here to register for this event.

      Speakers:

      1. Cliff Taubes (Harvard University)
      2. Valentino Tosatti (Northwestern University)
      3. Pengfei Guan (McGill University)
      4. Jared Speck (MIT)

      Schedule:

      December 3rd – Day 1
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”
      December 4th – Day 2
      9:00am – 10:30amCliff Taubes, “Compactness theorems in gauge theories”
      10:45am – 12:15pmValentino Tosatti, “Complex Monge-Ampère Equations”
      12:15pm – 1:45pmLUNCH
      1:45pm – 3:15pmPengfei Guan, “Monge-Ampère type equations and related geometric problems”
      3:30pm – 5:00pmJared Speck, “Finite-time degeneration of hyperbolicity without blowup for solutions to quasilinear wave equations”

      Please click Mini-School Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • CMSA EVENT: Mirror symmetry, gauged linear sigma models, matrix factorizations, and related topics
      9:00 am-4:30 pm
      12/01/2024-03/06/2020
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Mirror-Symmetry-poster-1

      On March 4-6, 2020 the CMSA will be hosting a three-day workshop on Mirror symmetry, Gauged linear sigma models, Matrix factorizations, and related topics as part of the Simons Collaboration on Homological Mirror Symmetry. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      Speakers: 

      Schedule

      Videos from the workshop are available in the Youtube playlist.

    • CMSA EVENT: Quantum Matter Workshop
      9:00 am-5:00 pm
      12/01/2024-12/04/2019
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Quantum Matter Workshop

      On December 2-4, 2019 the CMSA will be hosting a workshop on Quantum Matter as part of our program on Quantum Matter in Mathematics and Physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Pictures can be found here.

      Organizers: Juven Wang (CMSA), Xiao-Gang Wen (MIT), and Shing-Tung Yau (Harvard)

      Confirmed Speakers: 

       

    • CMSA EVENT: Workshop on Coding and Information Theory
      9:00 am-3:30 pm
      12/01/2024-04/13/2018

      The workshop on coding and information theory will take place April 9-13, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      This workshop will focus on new developments in coding and information theory that sit at the intersection of combinatorics and complexity, and will bring together researchers from several communities — coding theory, information theory, combinatorics, and complexity theory — to exchange ideas and form collaborations to attack these problems.

      Squarely in this intersection of combinatorics and complexity, locally testable/correctable codes and list-decodable codes both have deep connections to (and in some cases, direct motivation from) complexity theory and pseudorandomness, and recent progress in these areas has directly exploited and explored connections to combinatorics and graph theory.  One goal of this workshop is to push ahead on these and other topics that are in the purview of the year-long program.  Another goal is to highlight (a subset of) topics in coding and information theory which are especially ripe for collaboration between these communities.  Examples of such topics include polar codes; new results on Reed-Muller codes and their thresholds; coding for distributed storage and for DNA memories; coding for deletions and synchronization errors; storage capacity of graphs; zero-error information theory; bounds on codes using semidefinite programming; tensorization in distributed source and channel coding; and applications of information-theoretic methods in probability and combinatorics.  All these topics have attracted a great deal of recent interest in the coding and information theory communities, and have rich connections to combinatorics and complexity which could benefit from further exploration and collaboration.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      Click here for a list of registrants. 

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

    • Workshop
      9:00 am-6:00 pm
      12/01/2024-05/12/2023
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      The CMSA will be hosting a Workshop on Global Categorical Symmetries from May 7 – 12, 2023

      Participation in the workshop is by invitation.

      Public Lectures

      There will be three lectures on Thursday, May 11, 2023, which are open to the public.
      Location:  Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
      Note: The public lectures will be held in-person only.

      2:00 – 2:50 pm
      Speaker: Kantaro Ohmori (U Tokyo )
      Title: Fusion Surface Models: 2+1d Lattice Models from Higher Categories
      Abstract: Generalized symmetry in general dimensions is expected to be described by higher categories. Conversely, one might expect that, given a higher category with appropriate structures, there exist models that admit the category as its symmetry. In this talk I will explain a construction of such 2+1d lattice models for fusion 2-categories defined by Douglas and Reutter, generalizing the work of Aasen, Fendley and Mong on anyon chains. The construction is by decorating a boundary of a topological Freed-Teleman-Moore sandwich into a non-topological boundary. In particular we can construct a family of candidate lattice systems for chiral topological orders.

       

      3:00 – 3:50 pm
      Speaker: David Jordan (Edinburgh)
      Title: Langlands duality for 3-manifolds
      Abstract: Originating in number theory, and permeating representation theory, algebraic geometry, and quantum field theory, Langlands duality is a pattern of predictions relating pairs of mathematical objects which have no clear a priori mathematical relation. In this talk I’ll explain a new conjectural appearance of Langlands duality in the setting of 3-manifold topology, I’ll give some evidence in the form of special cases, and I’ll survey how the conjecture relates to both the arithmetic and geometric Langlands duality conjectures.

      3:50 – 4:30 pm
      Tea/Snack Break

      4:30 – 5:30 pm
      Speaker: Ken Intriligator (UCSD)
      Colloquium
      Title: QFT Aspects of Symmetry
      Abstract: Everything in the Universe, including the photons that we see and the quarks and electrons in our bodies, are actually ripples of quantum fields. Quantum field theory (QFT) is the underlying mathematical framework of Nature, and in the case of electrons and photons it is the most precisely tested theory in science. Strongly coupled aspects, e.g. the confinement of quarks and gluons at long distances, remain challenging. QFT also describes condensed matter systems, connects to string theory and quantum gravity, and describes cosmology. Symmetry has deep and powerful realizations and implications throughout physics, and this is especially so for the study of QFT. Symmetries play a helpful role in characterizing the phases of theories and their behavior under renormalization group flows (zooming out). Quantum field theory has also been an idea generating machine for mathematics, and there has been increasingly fruitful synergy in both directions. We are currently exploring the symmetry-based interconnections between QFT and mathematics in our Simons Collaboration on Global Categorical Symmetry, which is meeting here this week. I will try to provide an accessible, colloquium-level introduction to aspects of symmetries and QFT, both old and new.


    • CMSA EVENT: Big Data Conference 2023
      9:00 am-5:00 pm
      12/01/2024-09/01/2023
      1 Oxford Street, Cambridge MA 02138

      On August 31-Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

      Location: Harvard University Science Center Hall D & via Zoom.

      Directions and Recommended Lodging

      Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

      Registration is required.

      Note: In-person registration is at capacity. Please sign up for the Zoom Webinar (registration link).

       

      Speakers:

       

      Organizers:

      • Michael Douglas, CMSA, Harvard University
      • Yannai Gonczarowski, Economics and Computer Science, Harvard University
      • Lucas Janson, Statistics and Computer Science, Harvard University
      • Tracy Ke, Statistics, Harvard University
      • Horng-Tzer Yau, Mathematics and CMSA, Harvard University
      • Yue Lu, Electrical Engineering and Applied Mathematics, Harvard University

      Schedule

      (PDF download)

      Thursday, August 31, 2023

      9:00 AMBreakfast
      9:30 AMIntroductions
      9:45–10:45 AMAlbert-László Barabási (Northeastern, Harvard)

      Title: From Network Medicine to the Foodome: The Dark Matter of Nutrition

      Abstract: A disease is rarely a consequence of an abnormality in a single gene but reflects perturbations to the complex intracellular network. Network medicine offer a platform to explore systematically not only the molecular complexity of a particular disease, leading to the identification of disease modules and pathways, but also the molecular relationships between apparently distinct (patho) phenotypes. As an application, I will explore how we use network medicine to uncover the role individual food molecules in our health. Indeed, our current understanding of how diet affects our health is limited to the role of 150 key nutritional components systematically tracked by the USDA and other national databases in all foods. Yet, these nutritional components represent only a tiny fraction of the over 135,000 distinct, definable biochemicals present in our food. While many of these biochemicals have documented effects on health, they remain unquantified in any systematic fashion across different individual foods. Their invisibility to experimental, clinical, and epidemiological studies defines them as the ‘Dark Matter of Nutrition.’ I will speak about our efforts to develop a high-resolution library of this nutritional dark matter, and efforts to understand the role of these molecules on health, opening novel avenues by which to understand, avoid, and control disease.

      https://youtu.be/UmgzUwi6K3E

      10:45–11:00 AMBreak
      11:00 AM–12:00 PMRachel Cummings (Columbia)

      Title: Differentially Private Algorithms for Statistical Estimation Problems

      Abstract: Differential privacy (DP) is widely regarded as a gold standard for privacy-preserving computation over users’ data.  It is a parameterized notion of database privacy that gives a rigorous worst-case bound on the information that can be learned about any one individual from the result of a data analysis task. Algorithmically it is achieved by injecting carefully calibrated randomness into the analysis to balance privacy protections with accuracy of the results.
      In this talk, we will survey recent developments in the development of DP algorithms for three important statistical problems, namely online learning with bandit feedback, causal interference, and learning from imbalanced data. For the first problem, we will show that Thompson sampling — a standard bandit algorithm developed in the 1930s — already satisfies DP due to the inherent randomness of the algorithm. For the second problem of causal inference and counterfactual estimation, we develop the first DP algorithms for synthetic control, which has been used non-privately for this task for decades. Finally, for the problem of imbalanced learning, where one class is severely underrepresented in the training data, we show that combining existing techniques such as minority oversampling perform very poorly when applied as pre-processing before a DP learning algorithm; instead we propose novel approaches for privately generating synthetic minority points.

      Based on joint works with Marco Avella Medina, Vishal Misra, Yuliia Lut, Tingting Ou, Saeyoung Rho, and Ethan Turok.

      https://youtu.be/0cPE6rb1Roo

      12:00–1:30 PMLunch
      1:30–2:30 PMMorgane Austern (Harvard)

      Title: To split or not to split that is the question: From cross validation to debiased machine learning

      Abstract: Data splitting is a ubiquitous method in statistics with examples ranging from cross-validation to cross-fitting. However, despite its prevalence, theoretical guidance regarding its use is still lacking. In this talk, we will explore two examples and establish an asymptotic theory for it. In the first part of this talk, we study the cross-validation method, a ubiquitous method for risk estimation, and establish its asymptotic properties for a large class of models and with an arbitrary number of folds. Under stability conditions, we establish a central limit theorem and Berry-Esseen bounds for the cross-validated risk, which enable us to compute asymptotically accurate confidence intervals. Using our results, we study the statistical speed-up offered by cross-validation compared to a train-test split procedure. We reveal some surprising behavior of the cross-validated risk and establish the statistically optimal choice for the number of folds. In the second part of this talk, we study the role of cross-fitting in the generalized method of moments with moments that also depend on some auxiliary functions. Recent lines of work show how one can use generic machine learning estimators for these auxiliary problems, while maintaining asymptotic normality and root-n consistency of the target parameter of interest. The literature typically requires that these auxiliary problems are fitted on a separate sample or in a cross-fitting manner. We show that when these auxiliary estimation algorithms satisfy natural leave-one-out stability properties, then sample splitting is not required. This allows for sample reuse, which can be beneficial in moderately sized sample regimes.

      https://youtu.be/L_pHxgoQSgU

      2:30–2:45 PMBreak
      2:45–3:45 PMAnkur Moitra (MIT)

      Title: Learning from Dynamics

      Abstract: Linear dynamical systems are the canonical model for time series data. They have wide-ranging applications and there is a vast literature on learning their parameters from input-output sequences. Moreover they have received renewed interest because of their connections to recurrent neural networks.
      But there are wide gaps in our understanding. Existing works have only asymptotic guarantees or else make restrictive assumptions, e.g. that preclude having any long-range correlations. In this work, we give a new algorithm based on the method of moments that is computationally efficient and works under essentially minimal assumptions. Our work points to several missed connections, whereby tools from theoretical machine learning including tensor methods, can be used in non-stationary settings.

      https://youtu.be/UmgzUwi6K3E

      3:45–4:00 PMBreak
      4:00–5:00 PMMark Sellke (Harvard)

      Title: Algorithmic Thresholds for Spherical Spin Glasses

      Abstract: High-dimensional optimization plays a crucial role in modern statistics and machine learning. I will present recent progress on non-convex optimization problems with random objectives, focusing on the spherical p-spin glass. This model is related to spiked tensor estimation and has been studied in probability and physics for decades. We will see that a natural class of “stable” optimization algorithms gets stuck at an algorithmic threshold related to geometric properties of the landscape. The algorithmic threshold value is efficiently attained via Langevin dynamics or by a second-order ascent method of Subag. Much of this picture extends to other models, such as random constraint satisfaction problems at high clause density.

      https://youtu.be/JoghiwiIbT8

      6:00 – 8:00 PMBanquet for organizers and speakers

       

      Friday, September 1, 2023

      9:00 AMBreakfast
      9:30 AMIntroductions
      9:45–10:45 AMJacob Andreas (MIT)

      Title: What Learning Algorithm is In-Context Learning?

      Abstract: Neural sequence models, especially transformers, exhibit a remarkable capacity for “in-context” learning. They can construct new predictors from sequences of labeled examples (x,f(x)) presented in the input without further parameter updates. I’ll present recent findings suggesting that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context, using in-context linear regression as a model problem. First, I’ll show by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, I’ll show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Finally, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners’ late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. This work is joint with Ekin Akyürek at MIT, and Dale Schuurmans, Tengyu Ma and Denny Zhou at Stanford.

      https://youtu.be/UNVl64G3BzA

      10:45–11:00 AMBreak
      11:00 AM–12:00 PMTommi Jaakkola (MIT)

      Title: Generative modeling and physical processes

      Abstract: Rapidly advancing deep distributional modeling techniques offer a number of opportunities for complex generative tasks, from natural sciences such as molecules and materials to engineering. I will discuss generative approaches inspired from physical processes including diffusion models and more recent electrostatic models (Poisson flow), and how they relate to each other in terms of embedding dimension. From the point of view of applications, I will highlight our recent work on SE(3) invariant distributional modeling over backbone 3D structures with ability to generate designable monomers without relying on pre-trained protein structure prediction methods as well as state of the art image generation capabilities (Poisson flow). Time permitting, I will also discuss recent analysis of efficiency of sample generation in such models.

      https://youtu.be/GLEwQAWQ85E

      12:00–1:30 PMLunch
      1:30–2:30 PMMarinka Zitnik (Harvard Medical School)

      Title: Multimodal Learning on Graphs

      Abstract: Understanding biological and natural systems requires modeling data with underlying geometric relationships across scales and modalities such as biological sequences, chemical constraints, and graphs of 3D spatial or biological interactions. I will discuss unique challenges for learning from multimodal datasets that are due to varying inductive biases across modalities and the potential absence of explicit graphs in the input. I will describe a framework for structure-inducing pretraining that allows for a comprehensive study of how relational structure can be induced in pretrained language models. We use the framework to explore new graph pretraining objectives that impose relational structure in the induced latent spaces—i.e., pretraining objectives that explicitly impose structural constraints on the distance or geometry of pretrained models. Applications in genomic medicine and therapeutic science will be discussed. These include TxGNN, an AI model enabling zero-shot prediction of therapeutic use across over 17,000 diseases, and PINNACLE, a contextual graph AI model dynamically adjusting its outputs to contexts in which it operates. PINNACLE enhances 3D protein structure representations and predicts the effects of drugs at single-cell resolution.

      https://youtu.be/hjt4nsN_8iM

      2:30–2:45 PMBreak
      2:45–3:45 PMJianqing Fan (Princeton)

      Title: UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

      Abstract: Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts. Numerous methods are available for constructing prediction intervals, such as quantile regression and conformal predictions, among others. Nevertheless, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this work, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions.  Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics. (Joint work Jiawei Ge and Debarghya Mukherjee).

      https://youtu.be/WY6dr1oEOrk

      3:45–4:00 PMBreak
      4:00–5:00 PMMelissa Dell (Harvard)

      Title: Efficient OCR for Building a Diverse Digital History

      Abstract: Many users consult digital archives daily, but the information they can access is unrepresentative of the diversity of documentary history. The sequence-to-sequence architecture typically used for optical character recognition (OCR) – which jointly learns a vision and language model – is poorly extensible to low-resource document collections, as learning a language-vision model requires extensive labeled sequences and compute. This study models OCR as a character-level image retrieval problem, using a contrastively trained vision encoder. Because the model only learns characters’ visual features, it is more sample-efficient and extensible than existing architectures, enabling accurate OCR in settings where existing solutions fail. Crucially, it opens new avenues for community engagement in making digital history more representative of documentary history.

      https://youtu.be/u0JY9vURUAs

       


      Information about the 2022 Big Data Conference can be found here.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Invariant theory for maximum likelihood estimation
      9:00 am-10:00 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-2.8.2022

      Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach.

    • CMSA EVENT: Workshop on Probabilistic and Extremal Combinatorics
      9:00 am-1:30 pm
      12/01/2024-02/09/2018

      The workshop on Probabilistic and Extremal Combinatorics will take place February 5-9, 2018 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Extremal and Probabilistic Combinatorics are two of the most central branches of modern combinatorial theory. Extremal Combinatorics deals with problems of determining or estimating the maximum or minimum possible cardinality of a collection of finite objects satisfying certain requirements. Such problems are often related to other areas including Computer Science, Information Theory, Number Theory and Geometry. This branch of Combinatorics has developed spectacularly over the last few decades. Probabilistic Combinatorics can be described informally as a (very successful) hybrid between Combinatorics and Probability, whose main object of study is probability distributions on discrete structures.

      There are many points of interaction between these fields. There are deep similarities in methodology. Both subjects are mostly asymptotic in nature. Quite a few important results from Extremal Combinatorics have been proven applying probabilistic methods, and vice versa. Such emerging subjects as Extremal Problems in Random Graphs or the theory of graph limits stand explicitly at the intersection of the two fields and indicate their natural symbiosis.

      The symposia will focus on the interactions between the above areas. These topics include Extremal Problems for Graphs and Set Systems, Ramsey Theory, Combinatorial Number Theory, Combinatorial Geometry, Random Graphs, Probabilistic Methods and Graph Limits.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Benny Sudakov and David Conlon.  More details about this event, including participants, will be updated soon.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The n-queens problem
      9:00 am-10:00 am
      12/01/2024

      Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n).

      In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption.

      This is joint work with Peter Keevash.

    • CMSA EVENT: Workshop on Geometry, Imaging, and Computing
      9:00 am-6:15 pm
      12/01/2024-03/26/2018
      GIC-Poster-2-e1520002551865

      On March 24-26, The Center of Mathematical Sciences and Applications will be hosting a workshop on Geometry, Imaging, and Computing, based off  the journal of the same name. The workshop will take place in CMSA building, G10.

      The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and Shing-Tung Yau (Harvard).

      Please click here to register for the event.

      Confirmed Speakers:

    • CMSA EVENT: Machine Learning for Multiscale Model Reduction Workshop
      9:00 am-11:55 am
      12/01/2024-03/29/2019
      Machine-Learning-Poster

      The Machine Learning for Multiscale Model Reduction Workshop will take place on March 27-29, 2019. This is the second of two workshops organized by Michael BrennerShmuel Rubinstein, and Tom Hou.  The first, Fluid turbulence and Singularities of the Euler/ Navier Stokes equations, will take place on March 13-15, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Speakers:

    • CMSA EVENT: The 2017 Charles River Lectures
      9:15 am-5:30 pm
      12/01/2024

      The 2017 Charles River Lectures

      Charles River with Bench at Sunset

      Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community.

      The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University  in the Harvard Science Center.


      ***************************************************

      UPDATED LOCATION

      Harvard University

      Harvard Science Center (Halls C & E)

      1 Oxford Street, Cambridge, MA 02138 (Map)

      Monday, October 2, 2017

      9:15 AM – 5:30 PM

      **************************************************

      Please note that registration has closed.

      Speakers:

      Agenda:

      In Harvard Science Center Hall C:

      8:45 am – 9:15 amCoffee/light breakfast

      9:15 am – 10:15 am: Ofer Zeitouni

      Title: Noise stability of the spectrum of large matrices

      Abstract: The spectrum of large non-normal matrices is notoriously sensitive to perturbations, as the example of nilpotent matrices shows. Remarkably, the spectrum of these matrices perturbed by polynomially (in the dimension) vanishing additive noise is remarkably stable. I will describe some results and the beginning of a theory.

      The talk is based on joint work with Anirban Basak and Elliot Paquette, and earlier works with Feldheim, Guionnet, Paquette and Wood.

      10:20 am – 11:20 am: Andrea Montanari

      Title: Algorithms for estimating low-rank matrices 

      Abstract: Many interesting problems in statistics can be formulated as follows. The signal of interest is a large low-rank matrix with additional structure, and we are given a single noisy view of this matrix. We would like to estimate the low rank signal by taking into account optimally the signal structure. I will discuss two types of efficient estimation procedures based on message-passing algorithms and semidefinite programming relaxations, with an emphasis on asymptotically exact results.

      11:20 am – 11:45 amBreak

      11:45 am – 12:45 pm: Paul Bourgade

      Title: Random matrices, the Riemann zeta function and trees

      Abstract: Fyodorov, Hiary & Keating have conjectured that the maximum of the characteristic polynomial of random unitary matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the typical size of local maxima of the Riemann zeta function along the critical axis. I will first explain the origins of this conjecture, and then outline the proof for the leading order of the maximum, for unitary matrices and the zeta function. This talk is based on joint works with Arguin, Belius, Radziwill and Soundararajan.

      1:00 pm – 2:30 pm: Lunch

      In Harvard Science Center Hall E:

      2:45 pm – 3:45 pm: Roman Vershynin

      Title: Deviations of random matrices and applications

      Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.

      3:45 pm – 4:15 pm: Break

      4:15 pm – 5:15 pm: Massimiliano Gubinelli

      Title: Weak universality and Singular SPDEs

      Abstract: Mesoscopic fluctuations of microscopic (discrete or continuous) dynamics can be described in terms of nonlinear stochastic partial differential equations which are universal: they depend on very few details of the microscopic model. This universality comes at a price: due to the extreme irregular nature of the random field sample paths, these equations turn out to not be well-posed in any classical analytic sense. I will review recent progress in the mathematical understanding of such singular equations and of their (weak) universality and their relation with the Wilsonian renormalisation group framework of theoretical physics.

      Poster:

      2017 Charles River Lectures Poster

      Organizers:

       Alexei BorodinHenry CohnVadim GorinElchanan MosselPhilippe RigolletScott Sheffield, and H.T. Yau

    • CMSA EVENT: Topology and Dynamics in Quantum Matter Workshop
      9:15 am-3:25 pm
      12/01/2024-09/11/2019
      Topology-Poster

      On September 10-11, 2019, the CMSA will be hosting a second workshop on Topological Aspects of Condensed Matter.

      New ideas rooted in topology have recently had a major impact on condensed matter physics, and have led to new connections with high energy physics, mathematics and quantum information theory.  The aim of this program will be to deepen these connections and spark new progress by fostering discussion and new collaborations within and across disciplines.

      Topics include i) the classification of topological states  ii) topological orders in two and three dimensions including quantum spin liquids, quantum Hall states and fracton phases and iii)  interplay of symmetry and topology in quantum many body systems, including symmetry protected topological phases, symmetry fractionalization and anomalies iv) topological phenomena in quantum systems  driven far from equlibrium v) quantum field theory approaches to topological matter.

      This workshop is part of the CMSA’s program on Program on Topological Aspects of Condensed Matterand is the second of two workshops, in addition to a visitor program and seminars.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Click here for a list of restaurants in the area. 

      Organizers: Michael Hermele (CU Boulder) and Ashvin Vishwanath (Harvard)

      Partial list of speakers:

      Videos of the lectures can be found in the Youtube playlist below. Links to talks are also available on the schedule below.

    • CMSA EVENT: Workshop on Invariance and Geometry in Sensation, Action and Cognition
      9:15 am-10:00 am
      12/01/2024-04/17/2019

      As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

      Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.

      This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.

      In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Videos

      Tentative Speaker List:

      Schedule:

      Monday, April 15

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:15amWelcome and Introduction
      9:15 – 10:00amVivek JayaramanTitle: Insect cognition: Small tales of geometry & invariance

      Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

      10:00 – 10:45amElizabeth TorresTitle: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability

      Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.

      In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.

      I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

      10:45 – 11:15amCoffee Break
      11:15 – 12:00pmPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical prerequisites will be kept to a bare minimum.

      12:00 – 12:45pmStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      12:45 – 2:00pmLunch
      2:00 – 2:45pmAnitha PasupathyTitle: Invariant and non-invariant representations in mid-level ventral visual cortex

      My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

      2:45 – 3:30pmJacob FeldmanTitle: Bayesian skeleton estimation for shape representation and perceptual organization

      Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmMoira DillonTitle: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

      Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

      4:45 – 5:30pmMichael McCloskeyTitle: Axes and Coordinate Systems in Representing Object Shape and Orientation

      Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame.  I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

      5:30 – 6:30pmReception

       

      Tuesday, April 16

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amPeter OlverTitle: Symmetry and invariance in cognition — a mathematical perspective”

      Abstract: Symmetry recognition and appreciation is fundamental in human cognition.  (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance.  Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones.  Mathematical pre

      9:45 – 10:30amStefano Soatto/Alessandro AchilleTitle: Information in the Weights and Emergent Properties of Deep Neural Networks

      Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network  and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.

      While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amJeannette BohgTitle: On perceptual representations and how they interact with actions and physical representations

      Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

      11:45 – 12:30pmDagmar SternadTitle: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise

      Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

      12:30 – 2:00pmLunch
      2:00 – 2:45pmSam OckoTitle: Emergent Elasticity in the Neural Code for Space

      Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

      2:45 – 3:30pmTatyana SharpeeTitle: Hyperbolic geometry of the olfactory space

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      3:30 – 4:00pmTea Break
      4:00 – 4:45pmEd ConnorTitle: Representation of solid geometry in object vision cortex

      Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

      4:45 – 5:30pmL. MahadevanTitle: Simple aspects of geometry and probability in perception

      Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.


      Wednesday, April 17

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 9:45amGily GinosarTitle: The 3D geometry of grid cells in flying bats

      Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.

      Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1

      (1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel

      (2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK

      (3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew

      University of Jerusalem, Jerusalem, 91904, Israel

      9:45 – 10:30amSandro RomaniTitle: Neural networks for 3D rotations

      Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.

      This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

      10:30 – 11:00amCoffee Break
      11:00 – 11:45amSam GershmanTitle: The hippocampus as a predictive map

      Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

      11:45 – 12:30pmLucia JacobsTitle: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose

      Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

      12:30 – 1:30pmLunch
      1:30 – 2:15pmTalia KonkleTitle: The shape of things and the organization of object-selective cortex

      Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

      2:15 – 3:00pmVijay BalasubramanianTitle: Becoming what you smell: adaptive sensing in the olfactory system

      Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors.  In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors.  The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules.  I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors.  The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain.  The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans.   It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

      3:00 – 3:45pmIla FeiteTitle: Invariance, stability, geometry, and flexibility in spatial navigation circuits

      Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

      3:45 – 4:00pmL Mahadevan – summary
    • CMSA EVENT: Kickoff Workshop on Topology and Quantum Phases of Matter
      9:20 am-3:15 pm
      12/01/2024-08/28/2018
      Topological-1

      Screen-Shot-2018-08-13-at-2.28.22-PM

      On August 27-28, 2018, the CMSA will be hosting a Kickoff workshop on Topology and Quantum Phases of Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by fostering discussion and seeding new collaborations within and across disciplines.

      This workshop is a part of the CMSA’s program on Program on Topological Aspects of Condensed Matter,  and will be the first of two workshops, in addition to a visitor program and seminars.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please register here

      Speakers: 

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Max Wiesner

      Title: Light strings, strong coupling, and the Swampland

      Abstract: In this talk, I will start by reviewing central ideas of the so-called Swampland Program. The Swampland Program aims to identify criteria that distinguish low-energy effective field theories, that can be consistently coupled to quantum gravity, from those theories that become inconsistent in the presence of quantum gravity.

      In my talk I will specialize to four-dimensional effective field theories with N=2 and N=1 supersymmetry. In weakly-coupled regions of the scalar field space of such theories, it has been shown that light strings are crucial to realize certain Swampland criteria. Complementary to that, the focus of this talk will be on the role of such light strings away from these weak-coupling regimes. In this context, I will first discuss a relation between light perturbative strings and strong coupling singularities in the Kähler moduli space of 4d N=1 compactifications of F-theory. More precisely, in regions of moduli space, in which a critical string classically becomes light, I will show that non-perturbative corrections yield to strong coupling singularities for D7-brane gauge theories which obstruct weak-coupling limits. Moreover, I will demonstrate that in the vicinity of this strong coupling singularity, the critical, light string in fact leaves the spectrum of BPS strings thereby providing an explanation for the obstruction of the weak coupling limit.

      I will then move on and discuss the backreaction of perturbative strings in 4d EFTs. Away from the string core, the backreaction of such strings necessarily leads to strong coupling regions where naively the energy stored in the backreaction diverges. I will show how the introduction of additional non-critical strings can regulate this backreaction and how this can be used to study the spectrum of BPS strings and their tensions even beyond weak coupling regions. In this context, I will demonstrate how the requirement, that the total string tension should not exceed the Planck scale, constrains the possible BPS string charges.

    • Special Seminar
      Special Seminar
      3/30/2018 Special Seminar
      9:30 am-11:00 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Speaker: Bong Lian

      Title: Singular Calabi-Yau mirror symmetry

      Abstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors, including Matsumoto, Sasaki, Yoshida and others, mainly from the viewpoint of their moduli spaces and their comparisons.  I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono, Tsung-Ju Lee, Hiromichi Takagi, Shing-Tung Yau.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Tsung-Ju Lee

      Title: Periods for singular CY families and Riemann–Hilbert correspondence

      Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and mirror symmetry. In this talk, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.

    • Member Seminar
      9:30 am-11:30 am
      12/01/2024

      Member Seminar

      Speaker: Chuck Doran

      Title: The Greene-Plesser Construction Revisited

      Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The threshold for stacked triangulations
      9:30 am-10:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10
      CMSA-Combinatorics-Physics-and-Probability-Seminar-05.03.22

      Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{[n]}3$, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle.
      Suppose that every triangle is initially infected independently with probability p=p(n), what is the threshold probability for percolation — the event that all triangles get infected? How many new triangles do get infected in the subcritical regime?

      This notion of percolation can be viewed as a simplification of simple-connectivity. Namely, a stacked triangulation of a triangle is obtained by repeatedly subdividing an inner face into three faces.
      We ask: for which $p$ does the random simplicial complex Y_2(n,p) contain, for every triple $xyz$, the faces of a stacked triangulation of $xyz$ whose internal vertices are arbitrarily labeled in [n].

      We consider this problem in every dimension d>=2, and our main result identifies a sharp probability threshold for percolation, showing it is asymptotically (c_d*n)^(-1/d), where c_d is the growth rate of the Fuss–Catalan numbers of order d.

      The proof hinges on a second moment argument in the supercritical regime, and on Kalai’s algebraic shifting in the subcritical regime.

      Joint work with Eyal Lubetzky.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-Seminar-09.13.22

      Quantum Matter in Mathematics and Physics

      Speaker: Yichul Cho (SUNY Stony Brook)

      Title: Non-invertible Symmetries in Nature

      Abstract: In this talk, I will discuss non-invertible symmetries in
      familiar 3+1d quantum field theories describing our Nature. In
      massless QED, the classical U(1) axial symmetry is not completely
      broken by the ABJ anomaly. Instead, it turns into a discrete,
      non-invertible symmetry. The non-invertible symmetry operator is
      obtained by dressing the naïve U(1) axial symmetry operator with a
      fractional quantum Hall state. We also find a similar non-invertible
      symmetry in the massless limit of QCD, which provides an alternative
      explanation for the neutral pion decay. In the latter part of the
      talk, I will discuss non-invertible time-reversal symmetries in 3+1d
      gauge theories. In particular, I will show that in free Maxwell
      theory, there exists a non-invertible time-reversal symmetry at every
      rational value of the theta angle.

      Based on https://arxiv.org/abs/2205.05086 and https://arxiv.org/abs/2208.04331.

       

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Mathlit_WOODIN

      CMSA/Tsinghua Math-Science Literature Lecture

      woodin_portait_books

      Prof. Hugh Woodin will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.

      Date: Wednesday, November 9, 2022

      Time: 9:30 – 11:00 am ET

      Location: Via Zoom Webinar and Room G10, CMSA, 20 Garden Street, Cambridge MA 02138

      Directions and Recommended Lodging

      Registration is required.

       

      Title: Large cardinals and small sets: The AD+ Duality Program

      Abstract: The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers.  The modern view is that determinacy axioms concern generalizations of the borel sets, and deep connections with large cardinal axioms have emerged.

      The study of determinacy axioms has led to a specific technical refinement of AD, this is the axiom AD+. The further connections with large axioms have in turn implicitly led to a duality program, this is the AD+ Duality Program.

      The main open problems here are intertwined with those of the Inner Model Program, which is the central program in the study of large cardinal axioms.

      This has now all been distilled into a series of specific conjectures.

       

      Talk chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)

      Moderator: Alejandro Poveda Ruzafa (Harvard CMSA)

       

      Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

       

      CMSA COVID-19 Policies

    • Member Seminar
      9:30 am-11:00 am
      12/01/2024

      Member Seminar

      Speaker: Sergiy Verstyuk

      Title: Machine Learning the Gravity Equation for International Trade

      Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 11.10.22

      General Relativity Seminar

      Speaker: Pierre Heidmann (Johns Hopkins)

      Title: Schwarzschild-like Topological Solitons in Gravity

      Abstract: We present large classes of non-extremal solitons in gravity that are asymptotic to four-dimensional Minkowski spacetime plus extra compact dimensions. They correspond to smooth horizonless geometries induced by topology in spacetime and supported by electromagnetic flux, which characterize coherent states of quantum gravity. We discuss a new approach to deal with Einstein-Maxwell equations in more than four dimensions, such that they decompose into a set of Ernst equations. We generate the solitons by applying different techniques associated with the Ernst formalism. We focus on solitons with zero net charge yet supported by flux, and compare them to Schwarzschild black holes. These are also ultra-compact geometries with very high redshift but differ in many aspects. At the end of the talk, we discuss the stability properties of the solitons and their gravitational signatures.

    • Algebraic Geometry in String Theory Seminar
    • CMSA EVENT: Math-Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024
      Math-Science Literature Lecture Series

      Mathematics & Literature Lecture Series

      Beginning in Spring 2020, the CMSA will be hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars. Talks will take place throughout the semester. All talks will take place virtually. You must register to attend. Recordings will be posted to this page.

      Written articles will accompany each lecture in this series and be available as part of the publication “The Literature and History of Mathematical Science

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry, transforming Calabi-Yau 3-folds between A- and B-models. In this talk, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X, detail the change of derived categories from its smoothing to its small resolution.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Pok Man Tam (University of Pennsylvania)

      Title: Topology of the Fermi sea: Ordinary metals as topological materials

      Abstract: It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F  to experimental observables, namely: (i) equal-time density/number correlations [1], and (ii) Andreev state transport along a planar Josephson junction [2]. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.

      [1] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)

      [2] P. M. Tam and C. L. Kane, arXiv:2210.08048

       

      https://www.youtube.com/watch?v=AXHLAo8kMHQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=25

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Title: Asymptotic localization, massive fields, and gravitational singularities

      Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-03.09.2022

      Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Prague dimension of random graphs
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-11.23.21

      Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      General Relativity Seminar

      Speaker: Semyon Dyatlov (MIT)

      Title: Ringdown and geometry of trapping for black holes

      Abstract: Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of a black hole merger when the dynamics is expected to be driven by linear effects. In this talk I give an overview of various results in pure mathematics which relate asymptotic behavior of quasi-normal modes at high frequency to the geometry of the set of trapped null geodesics, such as the photon sphere in Schwarzschild (-de Sitter). These trapped geodesics have two kinds of behavior: the geodesic flow is hyperbolic in directions normal to the trapped set (a feature stable under perturbations) and it is completely integrable on the trapped set. It turns out that normal hyperbolicity gives information about the rate of decay of quasi-normal modes, while complete integrability gives rise to a quantization condition.

    • Colloquium
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Elliptic chiral homology and chiral index
      9:30 am-10:30 am
      12/01/2024
      20220330_Si-LI_poster

      Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture - Karen Uhlenbeck
      9:30 am-2:26 pm
      12/01/2024
      Lecture_Uhlenbeck_12921

      Karen Uhlenbeck (Institute for Advanced Study)

      Title: The Noether Theorems in Geometry: Then and Now

      Abstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature.

      Talk Chair: Laura DeMarco

      VIDEO

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Gabriel Wong (Harvard CMSA)

      Title: 3D gravity and gravitational entanglement entropy

      Abstract: Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime. Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge modes.

       

      https://www.youtube.com/watch?v=xD0hWdS-OAc&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=24

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Changji Xu

      Title: On the solution space of the Ising perceptron model

      Abstract:  Consider the discrete cube $\{-1,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk, we will talk about its sharp threshold phenomenon, the frozen structure of the solution space, and the Gardner formula.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Counting invariant curves on a Calabi-Yau threefold with an involution
      9:30 am-10:30 am
      12/01/2024
      Jim-Bryan_poster_3Nov2021

      Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g,h) which are conjectured to be equivalent, one in terms of a version of PT theory, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface, the specialization of n_beta(g,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-04.27.22

      Speaker: Venkatesan Guruswami, UC Berkeley

      Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

      Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.
      We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

      Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

      This is joint work with Xiaoyu He and Ray Li.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Michael Simkin

      Title: Threshold phenomena in random graphs and hypergraphs

      Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields.

      The model is defined as follows: Given a natural number $n$ and a parameter $p \in [0,1]$, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$, independent of all others. Despite their apparent simplicity, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena.

      A central feature is the appearance of threshold phenomena: For all monotone properties (e.g., connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e., with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Speaker: Freid Tong

      Title: The complex Monge-Ampere equation in Kahler geometry

      Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry, with a particular focus on the a priori C^0 estimates and their various applications. In the end, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.

    • Colloquium
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Gradient flows on totally nonnegative flag varieties
      9:30 am-10:30 am
      12/01/2024

      Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications, we show how the classical Toda flow fits into this framework, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Kan Lin

      Title: China’s financial regulatory reform, financial opening-up, and Central Bank Digital Currency (CBDC)

      Abstract: In this talk, I will explain the overall situation of China’s financial industry and review the development of China’s financial regulatory system reform from 1949 to 2021. Then, I will explain the policies of the 3 stages of financial opening-up, 2001–08, 2008–18, 2018≠present. In particular, the latest round of opening-up from 2018 has brought great opportunities for foreign institutions. China has the world’s largest banking industry with assets totaling $53 trillion, and accounts for 1/3 of the growth in global insurance premiums over the next 10 years. I will also introduce the progress of research & development of China’s Central Bank Digital Currency (CBDC, or E-CNY). By October 2021, 140 million people had opened E-CNY wallets, and 1.6 million merchants could accept payments using eCNY wallets, including utilities, catering services, transportation, retail, and government services.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-03.24.2022-1583x2048

      Youtube Video

       

      Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.16.21-1-1

      Abstract: I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine (arxiv:2109.13323).

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 09.30.2022

      Algebraic Geometry in String Theory Seminar

      Speaker:  Mauricio Romo, Tsinghua University

      Title: GLSM, Homological projective duality and nc resolutions
      Abstract: Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.
    • Algebraic Geometry in String Theory Seminar
    • CMSA EVENT: Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations
      9:30 am-5:00 pm
      12/01/2024-03/01/2019

      From February 25 to March 1, the CMSA will be hosting a workshop on Growth and zero sets of eigenfunctions and of solutions to elliptic partial differential equations. 

      Key participants of this workshop include David Jerison (MIT), Alexander Logunov (IAS), and Eugenia Malinnikova (IAS).  This workshop will have morning sessions on Monday-Friday of this week from 9:30-11:30am, and afternoon sessions on Monday, Tuesday, and Thursday from 3:00-5:00pm.
      The sessions will be held in  \(G02\) (downstairs) at 20 Garden, except for Tuesday afternoon, when the talk will be in \(G10\).

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-05.18.22

      Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.07.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Sam Bardwell-Evans, Boston University
      Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
      Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.
    • Algebraic Geometry in String Theory Seminar
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Flip processes
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1

      Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1,\ldots,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1,\ldots,v_k]$ by  $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process.

      Given a flip process with a rule $\mathcal{R}$, we construct time-indexed trajectories $\Phi:\Gra\times [0,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph).

      These graphon trajectories are then studied from the perspective of dynamical systems. Among others, we study continuity properties of these trajectories with respect to time and the initial graphon, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272).

      We also study several specific families flip processes. This is joint work with Pedro Ara\’ujo, Eng Keat Hng and Matas \v{S}ileikis (in preparation).
      A brief introduction to the necessary bits of the theory of graph limits will be given in the talk.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Gabriel Wong 

      Title: Universal relations between entanglement, symmetries, and entropy

      Abstract: Entanglement is an essential property of quantum systems that distinguishes them from classical ones.   It is responsible for the nonlocal character of quantum information and provides a resource for quantum teleportation and quantum computation. In this talk I will provide an introduction to quantum entanglement and explain the essential role it plays in two seemingly unrelated subjects: implementation of measurement-based quantum computation and microstate counting of black holes in quantum gravity.   Time permitting, I will also discuss attempts to characterize entanglement in string theory. A unifying theme that illuminates the entanglement structure of these diverse systems is the role of surface symmetries and (entanglement) edge modes. We will explain how these universal aspects of entanglement are captured in the framework of extended topological quantum field theory.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Hypergraph Matchings Avoiding Forbidden Submatchings
      9:30 am-10:30 am
      12/01/2024

      Abstract:  In 1973, Erdős conjectured the existence of high girth (n,3,2)-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős’ conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős’ conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth (n,q,r)-Steiner systems. We prove the approximate version of their conjecture.  This result follows from our general main results which concern finding perfect or almost perfect matchings in a hypergraph G avoiding a given set of submatchings (which we view as a hypergraph H where V(H)=E(G)). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when H is a hypergraph with small codegrees (for which high girth designs is a specific instance). Indeed, the coloring version of our result even yields an almost partition of K_n^r into approximate high girth (n,q,r)-Steiner systems.  If time permits, I will explain some of the other applications of our main results such as to rainbow matchings.  This is joint work with Luke Postle.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.14.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Daniel Pomerleano, UMass Boston

      Title: Singularities of the quantum connection on a Fano variety

      Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty.

      I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M, D).

    • Member Seminar
      9:30 am-11:00 am
      12/01/2024

      Member Seminar

      Speaker: Juven Wang

      Title: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass

      Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1,2,3,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765arXiv:2204.08393arXiv:2202.13498 and references therein.

    • Colloquium
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Daniel Junghans

      Title: AdS with Scale Separation

      Abstract: I will talk about Anti-de Sitter solutions in string theory with a parametric separation between the AdS curvature scale and the Kaluza-Klein scale. In particular, I will discuss recent progress on computing backreaction corrections in such solutions, and I will explain how to construct solutions without Romans mass that can be lifted to M-theory.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.28.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Ahsan Khan, IAS

      Title: 2-Categories and the Massive 3d A-Model

      Abstract: I will outline the construction of a 2-category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two, and three dimensions combined with a three-dimensional version of the Gaiotto-Moore-Witten web formalism.

       

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-GR-Seminar-03.24.22

      Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Vitor Cardoso, IST, Lisbon and The Niels Bohr Institute, Copenhagen

      Title: Testing GR with GWs

      Abstract: One of the most remarkable possibilities of General Relativity concerns gravitational collapse to black holes, leaving behind a geometry with light rings, ergoregions and horizons. These peculiarities are responsible for uniqueness properties and energy extraction mechanisms that turn black holes into ideal laboratories of strong gravity, of particle physics (yes!) and of possible quantum-gravity effects. I will discuss some of the latest progress in tests of General Relativity with black holes.

    • Colloquium
    • Seminars
      Seminars Colloquia & Seminar
      4/18/2019 General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)
      3/2/2022Richard Kenyon (Yale University)
      3/9/2022Richard Tsai (UT Austin)
      3/23/2022Joel Cohen (University of Maryland)
      3/30/2022Rob Leigh (UIUC)
      4/6/2022Johannes Kleiner (LMU München)
      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
      4/20/2022TBA
      4/27/2022TBA
      5/4/2022Melody Chan (Brown University)
      5/11/2022TBA
      5/18/2022TBA
      5/25/2022Heeyeon Kim (Rutgers University)

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-03.17.2022-1-1544x2048-1

      Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)Title: Learning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

      3/2/2022Richard Kenyon (Yale University)Title: Dimers and webs

      Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

      This is joint work with Dan Douglas and Haolin Shi.

      3/9/2022Yen-Hsi Richard Tsai (UT Austin)Title: Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space

      Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

      3/23/2022Joel Cohen (University of Maryland)Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths

      Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics, as Taylor’s law in ecology, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas, motivations, recent theoretical results, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown, Richard A. Davis, Victor de la Peña, Gennady Samorodnitsky, Chuan-Fa Tang, and Sheung Chi Phillip Yam.

      3/30/2022Rob Leigh (UIUC)Title: Edge Modes and Gravity

      Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

      4/6/2022Johannes Kleiner (LMU München)Title: What is Mathematical Consciousness Science?

      Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)Title: Quantisation in monoidal categories and quantum operads

      Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure.  But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups.

      The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

      In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts

      4/27/2022Venkatesan Guruswami (UC Berkeley)Title: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

      Abstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.

      We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

      Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

      This is joint work with Xiaoyu He and Ray Li.

      5/18/2022 David Nelson (Harvard)TitleStatistical Mechanics of Mutilated Sheets and Shells

      Abstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons, as well as an anomalous coefficient of thermal expansion.  Finally, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature, even in the absence of an external pressure.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-01.26.2022

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Yingying Wu

      Title: Moduli Space of Metric SUSY Graphs

      Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties, followed by a discussion on the connection with the classical case.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Dan Kapec

      Title: Black Holes, 2D Gravity, and Random Matrices

      Abstract: I will discuss old and new connections between black hole physics, 2D quantum gravity, and random matrix theory. Black holes are believed to be very complicated, strongly interacting quantum mechanical systems, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model, but this result raises more questions than it answers. If time permits, I will discuss some extensions of these results and possible future directions.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Cohomology of the moduli of Higgs bundles via positive characteristic
      9:30 am-8:30 pm
      12/01/2024

      Abstract: In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the character variety of the curve.  I will then explain how certain symmetries of this cohomology, which are predictions of this conjecture, can be constructed using techniques from non-abelian Hodge theory in positive characteristic.  Based on joint work with Mark de Cataldo, Junliang Shen, and Siqing Zhang.

    • Colloquium
    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Algebraic Geometry in String Theory 10.21.2022

      Algebraic Geometry in String Theory Seminar

      Speaker: Nicolo Piazzalunga, Rutgers

      Title: The index of M-theory

      Abstract: I’ll introduce the higher-rank Donaldson-Thomas theory for toric Calabi-Yau threefolds, within the setting of equivariant K-theory. I’ll present a factorization conjecture motivated by Physics. As a byproduct, I’ll discuss some novel properties of equivariant volumes, as well as their generalizations to the genus-zero Gromov-Witten theory of non-compact toric varieties.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The singularity probability of random symmetric matrices
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-12.07.2021

      Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-03.30.2022

      Abstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes, paying attention to relevant symmetries, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 12.08.22

      General Relativity Seminar

      Speaker: Allen Fang (Princeton)

      Title: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

      Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vector field techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-04.26.2022

      Abstract:   In “Mirror symmetry for log Calabi–Yau surfaces I,” given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y,D) with at worst du Val singularities. As a corollary, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 03.30.23

      General Relativity Seminar

      Speaker: Alejandra Castro (University of Cambridge)

      Title: Gravitational perturbations near to extreme Kerr

      Abstract: Gravitational perturbations of a black hole illustrate the invaluable synergy between theory, experiment, and numerical simulations in general relativity. A recent development in the theory side has been the identification of the relevant degrees of freedom describing the low energy physics driving a black hole away from extremality.  For simple cases, this low energy sector determines important aspects of the gravitational backreaction, and several properties that are key to our microscopic (quantum) understanding of black hole physics.
      In this talk I will discuss these developments in the context of the (near-)extreme Kerr black hole. In particular, I will revisit the spectrum of linear axisymmetric gravitational perturbations of this black hole. The aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. I will show that for Kerr the low-lying mode sector is subtle and intricate—features that their charged spherical symmetric cousins do not display. This unveils new clues on how to decode a microscopic, and holographic, understanding of the Kerr black hole.
    • Seminars
      Seminars Colloquia & Seminar
      8/4/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Sifan Yu, Vanderbilt University

      Title: Rough solutions of the relativistic Euler equations

      Abstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.

    • Seminars
      Seminars Colloquia & Seminar
      8/11/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/18/2020 Geometry and Physics Seminar
      9:30 am-11:30 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/19/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Conference
      9:30 am-5:00 pm
      12/01/2024-04/08/2022

      General Relativity Conference

      This conference will be held virtually on Zoom. Registration is required.
      Webinar Registration

      A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
      In-Person Registration

      Schedule | April 4–8, 2022

      Schedule (PDF)

      Monday, April 4, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amPieter Blue, University of Edinburgh, UK
      (virtual)
      Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge

      Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of the Einstein equation in this gauge, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975, Chrzanowski introduced the “outgoing radiation gauge”, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently, using a flow along null geodesics, we have constructed a new gauge such that, in this gauge, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge.

      This is joint work with Lars Andersson, Thomas Backdahl, and Siyuan Ma.

      10:30 am–11:30 amPeter Hintz, ETH Zürich
      (virtual)
      Title: Mode stability and shallow quasinormal modes of Kerr-de Sitter
      black holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe, such as our own, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question), mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which, depending on the scaling, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.
      11:30 am–12:30 pmLars Andersson, Albert Einstein Institute, Germany
      (virtual)
      Title: Gravitational instantons and special geometry

      Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

      12:30 pm–1:30 pmbreak
      1:30 pm–2:30 pmMartin Taylor, Imperial College London
      (virtual)
      Title: The nonlinear stability of the Schwarzschild family of black holes

      Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

      2:30 pm–3:30 pmPo-Ning Chen, University of California, Riverside
      (virtual)
      Title: Angular momentum in general relativity

      Abstract:
      The definition of angular momentum in general relativity has been a subtle issue since the 1960s, due to the ‘supertranslation ambiguity’. In this talk, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.
      3:30 pm–4:00 pmbreak
      4:00 pm–5:00 pmDan Lee, Queens College (CUNY)
      (hybrid: in person & virtual)
      Title: Stability of the positive mass theorem

      Abstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem, focusing on recent work with Kazaras and Khuri, in which we proved that if one assumes a lower Ricci curvature bound, then stability holds with respect to pointed Gromov-Hausdorff convergence.

       

      Tuesday, April 5, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amXinliang An, National University of Singapore
      (virtual)
      Title: Anisotropic dynamical horizons arising in gravitational collapse

      Abstract: Black holes are predicted by Einstein’s theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk, we will present several results in these directions. First, in a joint work with Qing Han, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second, in joint works with Dejan Gajic and Ruixiang Zhang, for the spherically symmetric Einstein-scalar field system, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism. If time permits, some results on fluid dynamics will also be addressed.

      10:30 am–11:30 amSergiu Klainerman, Princeton
      (virtual)
      Title: Nonlinear stability of slowly rotating Kerr solutions

      Abstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.

      11:30 am–12:30 pmSiyuan Ma, Sorbonne University
      (virtual)
      Title: Sharp decay for Teukolsky master equation

      Abstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmJonathan Luk, Stanford
      (virtual)
      Title: A tale of two tails

      Abstract: Motivated by the strong cosmic censorship conjecture, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).

      2:30 pm–3:30 pmGary Horowitz, University of California Santa Barbara
      (virtual)
      Title: A new type of extremal black hole

      Abstract: I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero, if quantum matter is added, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmLydia Bieri, University of Michigan
      (virtual)
      Title: Gravitational radiation in general spacetimes

      Abstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

       

      Wednesday, April 6, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amGerhard Huisken, Mathematisches Forschungsinstitut Oberwolfach
      (virtual)
      Title: Space-time versions of inverse mean curvature flow

      Abstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.

      10:30 am–11:30 amCarla Cederbaum, Universität Tübingen, Germany
      (virtual)
      Title: Coordinates are messy

      Abstract: Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M,g,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.

      11:30 am–12:30 pmStefanos Aretakis, University of Toronto
      (virtual)
      Title: Observational signatures for extremal black holes

      Abstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmJared Speck, Vanderbilt University
      (virtual)
      Title: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow

      Abstract: In the last two decades, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia, M. Disconzi, and J. Luk.

      2:30 pm–3:30 pmLan-Hsuan Huang, University of Connecticut
      (virtual)
      Title: Null perfect fluids, improvability of dominant energy scalar, and Bartnik mass minimizers

      Abstract: We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture.

      Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmDemetre Kazaras, Duke University
      (virtual)
      Title: Comparison geometry for scalar curvature and spacetime harmonic functions

      Abstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

       

      Thursday, April 7, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amPiotr Chrusciel, Universitat Wien
      (virtual)
      Title: Maskit gluing and hyperbolic mass

      Abstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.

      10:30 am–11:30 amGreg Galloway, University of Miami (virtual)Title:  Initial data rigidity and applications

      Abstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP, 2021), and look at some consequences.  In a note with Piotr Chruściel (CQG 2021), we showed how to use this result, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.

      11:30 am–12:30 pmPengzi Miao, University of Miami
      (virtual)
      Title: Some remarks on mass and quasi-local mass

      Abstract: In the first part of this talk, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello, and with H.C. Jang.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmYakov Shlapentokh Rothman, Princeton
      (hybrid: in person & virtual)
      Title: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations

      Abstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.

      2:30 pm–3:30 pmMarcelo Disconzi, Vanderbilt University
      (virtual)
      Title: General-relativistic viscous fluids.

      Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmMaxime van de Moortel, Princeton
      (hybrid: in person & virtual)
      Title: Black holes: the inside story of gravitational collapse

      Abstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models, the global structure of the black hole interior has largely remained unexplored.
      These questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.
      I will present my recent resolution of these problems in spherical gravitational collapse, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.

       

      Friday, April 8, 2022

      Time (ET)SpeakerTitle/Abstract
      9:30 am–10:30 amYe-Kai Wang, National Cheng Kun University, Taiwan
      (virtual)
      Title: Supertranslation invariance of angular momentum at null infinity in double null gauge

      Abstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing
      how Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen, Jordan Keller, Mu-Tao Wang, and Shing-Tung Yau.

      10:30 am–11:30 amZoe Wyatt, King’s College London
      (virtual)
      Title: Global Stability of Spacetimes with Supersymmetric Compactifications

      Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in
      supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.

      11:30 am–12:30 pmElena Giorgi, Columbia University
      (hybrid: in person & virtual)
      Title: The stability of charged black holes

      Abstract: Black hole solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

      12:30 pm–1:30 pmBreak
      1:30 pm–2:30 pmMarcus Khuri, Stony Brook University
      (virtual)
      Title: The mass-angular momentum inequality for multiple black holes

      Abstract
      : Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected, axisymmetric, maximal, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain, Chrusciel-Li-Weinstein, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from
      R^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han, G. Weinstein, and J. Xiong.
      2:30 pm–3:30 pmMartin Lesourd, Harvard
      (hybrid: in person & virtual)
      Title:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature

      Abstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau, Prof. D. A. Lee, and R. Unger.

      3:30 pm–4:00 pmBreak
      4:00 pm–5:00 pmGeorgios Moschidis, Princeton
      (virtual)
      Title: Weak turbulence for the Einstein–scalar field system.

      Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
      In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams.

    • Seminars
      Seminars Colloquia & Seminar
      8/20/2020 Quantum Matter
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/23/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      BCFW recursion relations and non-planar positive geometry
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-04.12.22-1583x2048-1

      Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.

      **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

      All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

      LINK TO FORM

    • Seminars
      Seminars Colloquia & Seminar
      8/25/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/26/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      8/27/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Special Seminar
      9:30 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Michael Douglas

      Title: Knowledge Graph Embeddings and Inference

      Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.
      A popular KG representation method is graph embedding, which facilitates question answering, inferring missing edges, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning, network learning, and unstructured statistical inference, and describe experiments to measure the contributions of each mechanism.

      Joint work with M. Simkin, O. Ben-Eliezer, T. Wu, S. P. Chin, T. V. Dang and A. Wood.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/30/2020 Condensed Matters Seminar
      9:30 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/22/2020 Quantum Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker:An Huang

      Title: Quadratic reciprocity from a family of adelic conformal field theories

      Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories, and ensures that these Green’s functions satisfy an adelic product formula. In particular, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place, the desired holomorphic factorization follows from the global conformal symmetry.

    • Seminars
      Seminars Colloquia & Seminar
      6/24/2020 Quantum Matter Seminar
      9:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-02.10.2022-1544x2048-1

      Speaker: Mohamed Anber (Durham University)

      Title: The global structure of the Standard Model and new nonperturbative processes

      Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Matteo Parisi

      Title: Amplituhedra, Scattering Amplitudes and Triangulations

      Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

    • Geometry and Physics Seminar
      Geometry and Physics Seminar
      Geometry and Physics Seminar
      9:30 am-9:30 pm
      12/01/2024-12/22/2020
      unnamed-537x338

      During the summer of 2020, the CMSA will be hosting a new Geometry Seminar. Talks will be scheduled on Mondays at 9:30pm or Tuesdays at 9:30am, depending on the location of the speaker. This seminar is organized by Tsung-Ju Lee, Yoosik Kim, and Du Pei.

      To learn how to attend this seminar, please contact Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu).

      DateSpeakerTitle/Abstract
      6/2/2020
      9:30am ET
      Siu-Cheong Lau
      Boston University
      This meeting will be taking place virtually on Zoom.

      Speaker: Equivariant Floer theory and SYZ mirror symmetry

      Abstract: In this talk, we will first review a symplectic realization of the SYZ program and some of its applications. Then I will explain some recent works on equivariant Lagrangian Floer theory and disc potentials of immersed SYZ fibers. They are joint works with Hansol Hong, Yoosik Kim and Xiao Zheng.

      6/8/2020
      9:30pm ET
      Youngjin Bae (KIAS)This meeting will be taking place virtually on Zoom.

      TitleLegendrian graphs and their invariants

      Abstract: Legendrian graphs naturally appear in the study of Weinstein manifolds with a singular Lagrangian skeleton, and a tangle decomposition of Legendrian submanifolds. I will introduce various invariant of Legendrian graphs including DGA type, polynomial type, sheaf theoretic one, and their relationship. This is joint work with Byunghee An, and partially with Tamas Kalman and Tao Su.

      6/16/2020
      9:30am ET
      Michael McBreen (CMSA)This meeting will be taking place virtually on Zoom.

      Title: Loops in hypertoric varieties and symplectic duality

      Abstract: Hypertoric varieties are algebraic symplectic varieties associated to graphs, or more generally certain hyperplane arrangements. They make many appearances in modern geometric representation theory. I will discuss certain infinite dimensional or infinite type generalizations of hypertoric varieties which occur in the study of enumerative invariants, focusing on some elementary examples. Joint work with Artan Sheshmani and Shing-Tung Yau.

      6/22/2020
      9:30pm ET
      Ziming Ma (CUHK)This meeting will be taking place virtually on Zoom.

      Title: The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties

      Abstract: In this talk, we construct a \(dgBV algebra PV*(X)\) associated to a possibly degenerate Calabi–Yau variety X equipped with local thickening data. This gives a version of the Kodaira–Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi–Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi–Yau varieties X satisfying Hodge–deRham degeneracy property for cohomology of X, in the spirit of Kontsevich–Katzarkov–Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.

      6/30/2020
      9:30pm ET
      Sunghyuk Park (Caltech)This meeting will be taking place virtually on Zoom.

      Title: 3-manifolds, q-series, and topological strings

      Abstract: \(\hat{Z}\) is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients), which has interesting modular properties. While originally from physics, this invariant has been mathematically constructed for a big class of 3-manifolds, and conjecturally it can be extended to all 3-manifolds. In this talk, I will give a gentle introduction to \(\hat{Z}\) and what is known about it, as well as highlighting some recent developments, including the use of R-matrix, generalization to higher rank, large N-limit and interpretation as open topological string partition functions.

      7/7/2020
      9:30am ET
      Jeremy Lane  (McMaster University)This meeting will be taking place virtually on Zoom.

      TitleCollective integrable systems and global action-angle coordinates

      Abstract: A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates.  Moreover, the image of the moment map is a (non-simple) convex polytope.

      7/13/2020
      9:30pm ET
      Po-Shen Hsin (Caltech)This meeting will be taking place virtually on Zoom.

      TitleBerry phase in quantum field theory

      Abstract: We will discuss Berry phase in family of quantum field theories using effective field theory. The family is labelled by parameters which we promote to be spacetime-dependent sigma model background fields. The Berry phase is equivalent to Wess-Zumino-Witten action for the sigma model. We use Berry phase to study diabolic points in the phase diagram of the quantum field theory and discuss applications to deconfined quantum criticality and new tests for boson/fermion dualities in \((2+1)d\).

      7/20/2020
      9:30pm ET
      Sangwook Lee (KIAS)This meeting will be taking place virtually on Zoom.

      Title: A geometric construction of orbifold Jacobian algebras

      Abstract: We review the definition of a twisted Jacobian algebra of a Landau-Ginzburg orbifold due to Kaufmann et al. Then we construct an A-infinity algebra of a weakly unobstructed Lagrangian submanifold in a symplectic orbifold. We work on an elliptic orbifold sphere and see that above two algebras are isomorphic, and furthermore their structure constants are related by a modular identity which was used to prove the mirror symmetry of closed string pairings. This is a joint work with Cheol-Hyun Cho.

      7/27/2020 9:30pm ETMao Sheng (USTC)This meeting will be taking place virtually on Zoom.

      Title: Parabolic de Rham bundles: motivic vs periodic

      Abstract: Let \($C$\) be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over \($C$\) (with rational weights in parabolic structure). Many examples arise from geometry: let \($f: X\to U$\) be a smooth projective morphism over some nonempty Zariski open subset \($U\subset C$\). Then the Deligne–Iyer–Simpson canonical parabolic extension of the Gauss–Manin systems associated to \($f$\) provides such examples. We call a parabolic de Rham bundle \emph{motivic}, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory, to get a characterization of motivic parabolic de Rham bundles. In this talk, I introduce another subcategory of parabolic de Rham bundles, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan–Sheng–Zuo on Higgs-de Rham flows, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus–Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck–Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz’s work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture, we would like to single out the conjectural arithmetic Simpson correspondence, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.

      8/4/2020
      9:30am Et
      Pavel Safronov (University of Zurich)This meeting will be taking place virtually on Zoom.

      TitleKapustin–Witten TFT on 3-manifolds and skein modules

      Abstract: Kapustin and Witten have studied a one-parameter family of topological twists of \(4d N=4\) super Yang–Mills. They have shown that the categories of boundary conditions on a surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid–Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.

      8/11/2020
      9:30am
      Xujia Chen (Stonybrook)This meeting will be taking place virtually on Zoom.

      TitleLifting cobordisms and Kontsevich-type recursions for counts of real curves

      Abstract: Kontsevich’s recursion, proved in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger’s invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon’s recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon’s approach).

      8/18/2020
      9:30am ET
      Dongmin Gang (Asia Pacific Center for Theoretical Physics)This meeting will be taking place virtually on Zoom.

      Title: M-theoretic genesis of topological phases

      Abstract:  I will talk about a novel way of constructing \((2+1)d\) topological phases using M-theory. They emerge as macroscopic world-volume theories of M5-branes wrapped on non-hyperbolic 3-manifolds. After explaining the algorithm of extracting modular structures of the topological phase  from topological data of the 3-manifold, I will discuss the possibility of full classification of topological orders via the geometrical construction.

      8/25/2020
      9:30pm ET
      Mykola Dedushenko (Caltech)This meeting will be taking place virtually on Zoom.

      TitleAlgebras and traces at the boundary of \(4d N=4\) SYM

      Abstract: I will describe how the structure of supersymmetric boundary correlators in \(4d N=4\) SYM can be encoded in a class of associative algebras equipped with twisted traces. In the case of interfaces, this yields a new connection to integrability.

    • Seminars
      Seminars Colloquia & Seminar
      6/2/2020 Geometry Seminar
      9:30 am-10:30 am
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: In this talk, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian, over the torus fixed points, this representation is a Verma module. The vertex function, a K-theoretic enumerative invariant introduced by A. Okounkov, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application, this gives a proof of the invariance of the quantum q-difference module under variation of GIT.

    • Colloquium
      9:30 am-10:00 am
      12/01/2024

      Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Juven Wang

      Title: C-P-T Fractionalization, and Quantum Criticality Beyond the Standard Model

      Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT), or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320.

      In the second part of my talk, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-02.17.2022-1544x2048

      Speaker: Andrea Grigoletto (SISSA & INFN)

      Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

      Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

    • Seminars
      Seminars Colloquia & Seminar
      6/25/2020 Condensed Matter Seminar
      9:30 am-11:00 am
      12/01/2024
    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-04.06.2022

      Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

    • Seminars
      Seminars Colloquia & Seminar
      7/7/2020 Geometry and Physics Seminar
      9:30 am-10:30 am
      12/01/2024
    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-04.07.2022-1583x2048-1

      Youtube Video

       

      Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.

      References:
      [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021)
      [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022)
      [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation.
      [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Shahar Hadar (University of Haifa)

      Title: Resolving the photon ring

      Abstract: In the past few years, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes, M87* and SgrA*. It is believed that within these images is embedded a fine, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of strong lensing by the black hole and thereby conveys information on its spacetime geometry, potentially providing a new independent avenue for tests of general relativity in the strong-field regime. In the talk I will briefly review the theory of the photon ring and its corresponding spacetime region, the photon shell, which governs the universal lensing structure. I will then describe some current efforts and future prospects for resolving the ring, which include both the construction of transformative new instruments and the development of novel analysis methods. Focusing on the latter, I will present an upcoming proposal to use spectro-temporal autocorrelations in signals emitted from black hole environs as a probe of strong lensing effects.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024

      This is the Fall 2020 – Spring 2022 Quantum Matter in Mathematics and Physics Archive page.

      To view current seminars, please visit the Fall 2022-Spring 2023 Quantum Matter Seminar Page

      As part of the program on Quantum Matter in Mathematics and Physics, the CMSA hosted two weekly seminars. The Quantum Matter/Quantum Field Theory seminar took place on Wednesdays from 10:30 – 12:00pm on Zoom.

      The Condensed Matter/Math Seminar took place on  Thursdays from 10:30 – 12:00pm on Zoom.  In addition to the Quantum Matter seminar, the CMSA  also hosted a related seminar series on  Strongly Correlated Quantum Materials and High-Temperature Superconductors.

      Videos are available at the Quantum Matter in Mathematics and Physics  Youtube Playlist

      Spring 2022

      DateSpeakerTitle/Abstract
      1/18/2022
      2:30–4:00 pm ET
      Aavishkar Patel (UC Berkeley)Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

      Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

      Video

      1/28/2022 2:30–4:00 pm ETMaria Tikhanovskaya (Harvard)Title: Maximal quantum chaos of the critical Fermi surface

      Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

      2/2/2022
      8:00 -9:30 pm ET
      Yunqin Zheng (IPMU & ISSP, U Tokyo)Title: Kramers-Wannier-like duality defects in higher dimensions

      Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

      2/3/2022
      11:30 – 1:00 pm ET
      Lu Li (U Michigan)Title:  Quantum Oscillations of Electrical Resistivity in an Insulator

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

      2/9/2022
      8:00 –9:30 pm ET
      Yuji Tachikawa (Kavli IPMU, U Tokyo)Title: On the absence of global anomalies of heterotic string theories

      Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
      2/10/2022Mohamed Anber (Durham University)Title: The global structure of the Standard Model and new nonperturbative processes

      Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.

      2/16/2022
      10:30 am–12:00 pm ET
      Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part I

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

      2/17/2022
      9:30–11:00 am ET
      Andrea Grigoletto (SISSA & INFN)Title: Spin-cobordisms, surgeries and fermionic modular bootstrap

      Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.

      2/23/2022
      10:30 am–12:00 pm ET
      Petr Hořava (UC Berkeley)Title: Topological Quantum Gravity and the Ricci Flow – Part II

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

      2/24/2022
      8:00–9:30 pm ET
      Yohei Fuji (U Tokyo)Title: Bridging three-dimensional coupled-wire models and cellular topological states

      Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/1/2021Keisuke HarigayaTitle: Naturalness and muon anomalous magnetic moment

      Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

      Watch Video on Youtube

      9/2/2021Joseph Maciejko (University of Alberta)Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

      Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

      Watch Video on Youtube

      9/8/2021William Witczak-Krempa (U Montreal)Title: Cornering the universal shape of fluctuations and entanglement

      Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

      Ref: arXiv:2102.06223

      Watch Video on Youtube

      9/9/2021Sung-Sik Lee (McMaster University, Perimeter Institute)Title: Quantum gravity from quantum matter

      Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

      Watch Video on Youtube

      9/10/2021

      *special time: 3:30pm – 5:00pm ET*

      Ofri Telem (UC Berkeley)Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

      Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
      Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

      Watch Video on Youtube

      9/15/2021Liang Fu (MIT)Title: Three-particle mechanism for pairing and superconductivity

      Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

      [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
      [2] V. Crepel and L. Fu, arXiv:2103.12060
      [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

      Watch Video on Youtube

      9/16/2021Shiraz Minwalla (Tata Institute of Fundamental Research)Title: The Hilbert Space of large N Chern-Simons matter theories

      Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of  this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to  a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

      Watch Video on Youtube

      9/17/2021

      *special time 3:30 pm- 5 pm ET*

      Eslam Khalaf (Harvard)Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

      Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

      Watch Video on Youtube

      9/22/2021Daniel S Freed (U Texas)Title: Symmetry types in QFT and the CRT theorem

      Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

      Watch Video on Youtube

      9/23/2021Edward Shuryak (Stony Brook University)Title: Applications of instantons, sphalerons and instanton-dyons in QCD

      Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

      Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

      Watch Video on Youtube

      9/29/2021

      *special time 11:30 am- 1 pm ET*

      Nai Phuan Ong (Princeton University)Title: Oscillations in the thermal conductivity of a spin liquid*

      Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

      *Czajka et al., Nature Physics 17, 915 (2021).

      Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

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      10/06/2021Gabriel Cuomo (SCGP)Title: Line defects in CFTs: renormalization group flows and semiclassical limits

      Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

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      10/07/2021Ryan Thorngren (Harvard CMSA)Title: A tour of categorical symmetry

      Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

      Watch Video on Youtube

      10/07/2021

      *special time 8:30 pm- 10 pm ET*

      Nima Arkani-Hamed (IAS Princeton)Title: UV/IR and Effective Field Theory

      Watch Video on Youtube

      10/21/2021

      *special time 13:30 – 15:00 ET*

      Anton Kapustin (Caltech)Title: Electric-magnetic duality and the Geometric Langlands duality

      Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

      Watch Video on Youtube

      10/22/2021

      *special time 10:30am – 12:00 noon ET*

      Netta Engelhardt (MIT)Title:  Recent Holographic Developments on the Black Hole Information Problem

      Watch Video on Youtube

      10/29/2021

      *special time 2:15pm – 3:45pm ET*

      Eric Sharpe (Virginia Tech)Title: Anomaly resolution via decomposition

      Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

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      10/29/2021

      *special time 4:00pm – 5:30pm*

      Biao Lian (Princeton)Title: Integrability and chaos of 1+1d chiral edge states

      Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

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      11/03/2021
      *special time 2:00pm – 3:30pm ET*
      Clay Cordova (U Chicago)Title: Non-Invertible Duality Defects in 3+1 Dimensions

      Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

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      11/04/2021Yifan Wang (NYU)Title: Fusion Category Symmetries in Quantum Field Theory

      Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

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      11/10/21
      *special time 10–11:30 am ET*
      Michael Stone (UIUC)Title: Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT

      Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature.  I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.

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      11/12/21
      *special time 2:30–4:00 pm ET*
      Jeongwan Haah (Microsoft)Title: A degeneracy bound for homogeneous topological order

      Watch Video on Youtube

      11/16/21
      *special time 3–4:30 pm ET*
      Jie Wang
      (Center for Computational Quantum Physics, Flatiron Institute, Simons Foundation)
      Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

      Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

      [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
      [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
      [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

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      11/18/2021 2:30–4:00 pm ETB. Andrei Bernevig (Princeton University)Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

      Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

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      11/24/21Shinsei Ryu (Princeton University)Title: Multipartitioning topological phases and quantum entanglement

      Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

      Watch Video on Youtube

      12/1/21
      10:00–11:30 am ET
      Daniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 1

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
      12/2/21 10:30–12:00 pm ETDaniel Harlow (MIT)Title: Symmetry in quantum field theory and quantum gravity 2

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

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      12/8/21 10:30–12:00 pm ETFei Yan (Rutgers)Title: Defects, link invariants and exact WKB

      Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

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      12/10/21 2:30–4:00 pm ETLukasz Fidkowski (U Washington)Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

      Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

      Watch Video on Youtube

      Summer 2021:

      DateSpeakerTitle/Abstract
      6/2/2021Juven Wang (Harvard CMSA)

      Video

      TitleUltra Unification:
      Quantum Fields Beyond the Standard Model
      Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
      6/3/2021Tian Lan (CUHK & U Waterloo)

      Video

      TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

      Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
      6/9/2021Yizhi You (Princeton U)

      Video

      TitleFracton critical point and Topological phase transition beyond renormalization

      Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
      6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)

      Video

      TitleMinimal nondegenerate extensions and an anomaly indicator

      Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

      6/16/2021Arkady Vainshtein (UMN)

      Video

      TitleUses of Wilson Operator Expansion in Gauge Theories

      Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

      It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

      6/17/2021Mikhail Shifman (UMN)

      Video

      TitleWhat can supersymmetry do that other field theory cannot
      7/7/2021Dung Nguyen (Brown)

      Video

      TitleFrom Fractional Quantum Hall to higher rank symmetry

      Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of  W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems.  Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
      7/8/2021

      8:00 – 9:30pm

      Jing-Yuan Chen (Tsinghua)

      Video

      TitleSolvable Lattice Hamiltonians with Fractional Hall Conductivity

      Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]

      7/14/2021Liujun Zou (Perimeter Institute)

      Video

      TitleStiefel liquids: Possible non-Lagrangian quantum criticality from intertwined orders

      Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.

      Ref: arXiv: 2101.07805.

      7/15/2021Nathanan Tantivasadakarn (Harvard)

      Video

      TitleHybrid Fracton Orders

      Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

      Based on 2102.09555 and 2106.03842

      7/21/2021Daniel Bulmash (UMD)TitleAnomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs

      Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.

      Ref: arXiv:2104.14567

      7/22/2021
      8:00pm ET
      Hong Yao (Tsinghua)TitleEmergent spacetime supersymmetry in topological phases of matter

      Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators.
      References:
      [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015)
      [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017)
      [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017)
      [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)

      7/28/2021Max Metlitski (MIT)Title: Boundary criticality of the O(N) model in d = 3 critically revisited.

      Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry.
      Based on arXiv:2009.05119.

      7/29/2021Ady Stern & David Mross (Weizmann)TitleThe nu=5/2 enigma: Recent insights from theory and experiment

      Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

      8/4/2021Nathan Benjamin (Princeton & Caltech)Title: Harmonic analysis of 2d CFT partition functions

      Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.

      8/5/2021Hans-Werner Hammer (TU Darmstadt)Title: Un-nuclear physics: conformal symmetry in nuclear reactions

      Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.

      8/11/2021Piers Coleman (Rutgers)Title: Order Fractionalization*

      Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

      8/12/2012Beni Yoshida (Perimeter Institute)Title: On the firewall puzzle

      Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.

      8/18/2021Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics
      Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
      8/19/2021Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)Title: “Probing the Standard Model of Particle Physics Using the Muon
      Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
      8/25/2021Hitoshi Murayama  (UC Berkely & IPMU)Title: Some Exact Results in QCD-like and Chiral Gauge Theories

      Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/20/2021Thomas Peter Devereaux (Stanford University)

      Video

      Title:  Numerical investigations of models of the cuprates

      Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

      I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

      1/21/2021
      8:30-10:00pm ET
      Masahito Yamazaki (IPMU)

      Video

      TitleConfinement as Analytic Continuation Beyond Infinity
      1/27/2021Luigi Tizzano  (SCGP)

      Video

      TitleInstantons, symmetries and anomalies in five dimensions

      Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

      1/28/2021Simon Catterall (Syracuse University)

      Video

      TitleChiral Fermions from Staggered Fields

      Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.

      2/3/2020Philip Phillips (University of Illinois Urbana-Champaign)

      Video

      TitleBeyond BCS: An Exact Model for Superconductivity and Mottness

      Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
      [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

      2/4/2021Diego Delmastro (Perimeter PI)

      Video

      Title: Domain Walls in 4d N=1 Supersymmetric Yang-Mills

      Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).

      2/10/2021Senthil Todadri (MIT)

      Video

      TitleStrange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

      Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.

      [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789
      [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

      2/11/2021Michael Hermele (University of Colorado Boulder)

      Video

      TitleFamilies of gapped systems and quantum pumps

      Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.

      2/17/2021Jaume Gomis (Perimeter PI)

      Video

      TitleGlobal Anomalies on the Hilbert Space

      Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

      2/18/2021Xiao-Gang Wen (MIT)

      Video

      TitleA solution to the chiral fermion problem

      Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

      2/24/2021Zhenghan Wang (Microsoft Station Q)

      Video

      Title:  A Riemann sum of quantum field theory:  lattice Hamiltonian realization of TQFTs

      Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics.  I will start with the conceptual origin of this model as requested by the organizer.  Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds.  In the end, I will mention lattice models that generalize the Haah codes in two directions:  general three manifolds and more than two qubits per site.

      If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum.  New lattice models in fracton physics raise an interesting question:  what kinds of quantum field theories are they approximating if their continuous limits exist?  Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.

      2/25/2021Justin Kaidi (SCGP)

      Video

      TitleExploring Non-Supersymmetric String Theory

      Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.

      3/3/2021Tim Hsieh (Perimeter PI)

      Video

      Title: Symmetry-protected sign problem and magic in quantum phases of matter

      Abstract:  We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
      3/4/2021Mohamed Anber (Clark University)

      Video

      TitleGeneralized ‘t Hooft anomalies in vector-like theories

      Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories.  Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics.  In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls.  This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.

      3/10/2021

      7:30pm ET

      Satoshi Yamaguchi (Osaka U)

      Video

      TitleSupersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases

      Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.

      3/11/2021Chao-Ming Jian (Cornell)

      Video

      Title: Entanglement Criticality in Random Gaussian Quantum Circuits

      Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.

      3/17/2021Silviu S. Pufu (Princeton)

      Video

      Title:  Exact symmetries and threshold states in two-dimensional models for QCD

      Abstract:  Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

      3/18/2021
      12:00 – 1:30pm ET
      Thomas Dumitrescu (UCLA)

      Video

      Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD

      Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint

      3/24/2021Emily Nardoni (UCLA)

      Video

      Title: From SU(N) Seiberg-Witten Theory to Adjoint QCD: Part 2

      Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.

      3/25/2021Michael Levin (U Chicago)

      Video

      TitleAn introduction to string-net models

      Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.

      3/31/2021Dam Thanh Son (U Chicago)

      Video

      TitleSpin of the fractional quantum Hall magnetoroton through polarized Raman scattering

      Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.

      4/1/2021

      9:00am ET

      Naoto Nagaosa (Tokyo U.)

      Video

      Title: Applied physics of high-Tc theories

      Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

      4/7/2021Sakura Schafer-Nameki (University of Oxford)

      Video

      Title: Higher Form Symmetries in string/M-theory

      Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.

      4/8/2020

      1:00pm ET

      Anton Kapustin (Caltech)

      Video

      TitleChiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics
      Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
      4/14/2021Lakshya Bhardwaj (University of Oxford)

      Video

      TitleConfinement and 1-form Symmetries in 4d from 6d (2,0)

      Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
      4/15/2021Michael Creutz (Brookhaven National Laboratory)

      Video

      TitleQCD without diagrams

      Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.

      4/21/2021Sergei Gukov (Caltech)

      Video

      TitleExotic new animals in the CFT zoo: quasiparticles and anisotropic scaling
      4/22/2021Dung-Hai Lee (UC Berkeley)

      Video

      Title Non-abelian bosonization in two and three spatial dimensions and some applications
      Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
      4/28/2021Dominic Williamson (Stanford)

      Video

      Title1-form symmetry-protected topological phases and measurement-based quantum computation

      Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
      4/29/2021Fiona Burnell (University of Minnesota)

      Video

      TitleSubsystem-Symmetry protected phases of matter

      Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter.  These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states.  After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries.  I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.

      5/5/2021

      8:00pm ET

      Ioannis Papadimitriou (KIAS)

      Video

      TitleAnomalies and Supersymmetry

      Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.

      5/6/2021Weslei Bernardino Fontana (Boston University & Estadual)

      Video

      TitleChern-Simons-like theories for fracton phases

      Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.

      5/12/2021André-Marie Tremblay (University of Sherbrooke)

      Video

      Title: A unified theoretical perspective on the cuprate phase diagram

      Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

      5/13/2021Masataka Watanabe (Weizmann Institute of Science)

      Video

      TitleQuantum Information Theory of the Gravitational Anomaly

      Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].

      5/19/2021Herbert Neuberger (Rutgers)

      Video

      Title:  Construction of Lattice Chiral Gauge Theory

      Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided.
      The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.

      5/20/2021Steven Weinberg (UT Austin)

      Video

      TitleMassless Particles
      6/2/2021Juven Wang (Harvard CMSA)

      Video

      TitleUltra Unification:
      Quantum Fields Beyond the Standard Model
      Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
      6/3/2021Tian Lan (CUHK & U Waterloo)TitleHigher Dimensional Topological Order, Higher Category and A Classification in 3+1D

      Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
      6/9/2021Yizhi You (Princeton U)TitleFracton critical point and Topological phase transition beyond renormalization

      Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
      6/10/2021Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)TitleMinimal nondegenerate extensions and an anomaly indicator

      Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

      6/16/2021Arkady Vainshtein (UMN)TitleUses of Wilson Operator Expansion in Gauge Theories

      Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

      It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

      6/17/2021Mikhail Shifman (UMN)TitleWhat can supersymmetry do that other field theory cannot
      8/11/2021Piers Coleman (Rutgers)TBA
      8/26/2021Daniel Harlow (MIT)Title: Symmetries in quantum field theory and quantum gravity
      TBAAdy Stern & David Mross (Weizmann)TBA

      Fall 2020:

      DateSpeakerTitle/Abstract
      9/2/2020Subir Sachdev (Harvard University)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

      Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
      describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

      9/3/2020
      9:30 – 11:00am
      Janet Ling Yan Hung (Fudan University)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleGapped Boundaries, Junctions via (fermionic) anyon condensation

      Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.

      9/9/2020Ying-Hsuan Lin (Caltech)

      Video

      This meeting will be taking place virtually on Zoom.

      Title:  Exotic Consistent (1+1)d Anomalies: A Ghost Story

      Abstract:  We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions.  On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm.  For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection.  Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines.  The holomorphic bc ghost system realizes all the exotic consistent anomalies.

      9/10/2020Maissam Barkeshli (Maryland)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleAbsolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions

      Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553

      9/16/2020Andreas Karch (UT Austin)

      Video

      This meeting will be taking place virtually on Zoom.

      TitleBranes, Black Holes and Islands

      Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.

      9/17/2020Roger Mong (University of Pittsburgh)

      Video

      TitleUniversal multipartite entanglement in quantum spin chains

      Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems.  Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations.  Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment.  The measures are based off of the entanglement of purification and the reflected entropy popular among holography.  For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases.  We conclude with a few remarks regarding applications to 2D phases.

      9/23/2020Subir Sachdev (Harvard University)

      Video

      TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders II

      Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

      9/24/2020
      12:00 – 2:30pm ET
      Inna Vishik (University of California, Davis)

      Video

      TitleUniversality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201

      Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.

      9/30/2020Jordan Cotler (Harvard)

      Video

      Title: Gravitational Constrained Instantons and Random Matrix Theory

      Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action.  We find these instantons in all spacetime dimensions, for AdS and dS.  Many can be written in closed form and are quadratically stable.  In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes.  We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.

      10/1/2020Omri Golan (Weizmann Institute of Science)

      Video

      Title: Intrinsic sign problems in topological matter

      Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions.  Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.

      10/7/2020Romain Vasseur (UMass Amherst)

      Video

      Title“Symmetry-enriched random critical points and topological phase transitions“

      Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.

      10/8/2020Justin Kulp (Perimeter Institute)

      Video

      TitleOrbifold Groupoids

      Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
      10/14/2020Yin-Chen He (Perimeter Institute)

      Video

      TitleNon-Wilson-Fisher Kinks of Conformal Bootstrap: Deconfined Phase Transition and Beyond

      Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.

      10/15/2020Louis Taillefer (University of Sherbrooke)

      Video

      TitleNew signatures of the pseudogap phase of cuprate superconductors

      Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

      10/21/2020Oleg Dubinkin (University of Illinois at Urbana–Champaign)

      Video

      Title: Multipole Insulators and Higher-Form symmetries

      Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.

      10/22/2020Paul Fendley (University of Oxford)

      Video

      TitleThe uses of lattice topological defects

      Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains.
      These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion.  One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.  I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.

      10/28/2020Patrick Lee (MIT)

      Video

      Title: The not-so-normal normal state of underdoped Cuprate

      Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

      10/29/2020Biao Lian (Princeton University)

      Video

      TitleSymmetry, Insulating States and Excitations of Twisted Bilayer Graphene with Coulomb Interaction

      Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.

      11/5/2020Zohar Ringel (Racah Institute of Physics)TitleThe information bottleneck: A numerical microscope for order parameters.

      Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.

      11/6/2020
      12:30pm
      Zhi-Xun Shen (Stanford University)

      Video

      TitleEssential Ingredients for Superconductivity in Cupper Oxide Superconductors

      Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
      Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
      magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
      (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
      experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

      [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
      [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
      [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
      [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
      [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
      [6] A. Lanzara et al., Nature 412, 510 (2001)
      [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
      [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
      [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
      [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
      [11] A.G. Loeser et al., Science 273, 325 (1996)
      [12] S. Chen et al., Science, 366, 6469 (2019)
      [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
      [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
      [15] Yu He et al., Science, 362, 62 (Oct. 2018)
      [16] Z. Chen, Y. Wang et al., preprint, 2020

      11/11/2020Abhishodh Prakash (ICTS)

      Video

      TitleAspects of fermionic SPT phases: boundary supersymmetry and unwinding

      Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
      11/12/2020Chandra Varma (University of California, Riverside)

      Video

      TitleLoop-Current Order and Quantum-Criticality in Cuprates

      This talk is organized as follows:
      1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
      2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
      3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
      4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.

      Time permitting,
      (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
      (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
      (iii) Problems.

      11/18/2020Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

      Video

      Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

      Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

      11/19/2020Eduardo Fradkin (University of Illinois at Urbana-Champaign)

      Video

      TitlePair Density Waves and Intertwined Orders in High Tc Superconductors

      Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

      11/25/2020Qimiao Si (Rice University)

      Video

      Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

      Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

      12/2/2020Andrey Chubukov (University of Minnesota)

      Video

      TitleInterplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

      Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

      12/3/2020David B. Kaplan  (University of Washington)

      Video

      Title: Domain Wall Fermions and Chiral Gauge theories: Topological Insulators in Particle Physics

      Abstract:  Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics.  I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter.  How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!)  remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
      12/9/2020David Hsieh (Caltech)

      Video

      Title:  Signatures of anomalous symmetry breaking in the cuprates 

      Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
      [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

      [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516
      .

      12/10/2020Xinan Zhou (Princeton PCTS)

      Video

      Title: An analytic bootstrap approach for CFTs on RP^d and CFTs with boundaries

      Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
      12/16/2020Zheng-Yu Weng (Tsinghua University)

      Video

      TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

      Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

      12/17/2020Steven Kivelson (Stanford University)

      Video

      Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

      Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
      12/22/2020David Tong (University of Cambridge)

      Video

      TitleGapped Chiral Fermions

      Abstract: I’ll describe some quantum field theories that gap fermions without breaking chiral symmetries.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      CMSA-Colloquium-04.13.22

      Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure. But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

      In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

      3/2/2022Richard Kenyon (Yale University)
      3/9/2022Richard Tsai (UT Austin)
      3/23/2022Joel Cohen (University of Maryland)
      3/30/2022Rob Leigh (UIUC)
      4/6/2022Johannes Kleiner (LMU München)
      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
      4/20/2022TBA
      4/27/2022TBA
      5/4/2022Melody Chan (Brown University)
      5/11/2022TBA
      5/18/2022TBA
      5/25/2022Heeyeon Kim (Rutgers University)

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024

      Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

      April 20, 2022 | 9:30 – 11:00 am ET

      Title: Mechanism Design

      Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

      Talk chairs: Scott Kominers, Sergiy Verstyuk

      SLIDES | VIDEO

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. Higgs-Coulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wall-crossing results for GLSM and generalizes Landau- Ginzburg/Calabi-Yau correspondence. The talk is based on a joint work in progress with Melissa Liu.

    • Colloquium
      9:30 am-10:30 am
      12/01/2024
      02CMSA-Colloquium-03.02.2022

      Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).

      This is joint work with Dan Douglas and Haolin Shi.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Title: Stable Big Bang formation for the Einstein equations

      Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Itamar Shamir

      Title: Geometry, Entanglement and Quasi Local Data

      Abstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Tropical Lagrangian multi-sections and locally free sheaves
      9:30 am-10:30 am
      12/01/2024

      Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-03.03.2022-1544x2048-1

      Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138

      Member Seminar

      Speaker: Martin Lesourd

      Title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds

      Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, and Prof. D. A. Lee.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      Some combinatorics of Wilson loop diagrams
      9:30 am-10:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands.

      **This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10.

      All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival.

      LINK TO FORM

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 02.03.23

      General Relativity Seminar

      Speaker: Chiara Toldo (Harvard)

      Title: Near extremal de Sitter black holes and JT gravity

      Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

    • Quantum Matter
      9:30 am-10:30 am
      12/01/2024
      CMSA QMMP 1.30.23

      Quantum Matter Seminar

      Title: Group Invariant States as Many-Body Scars

      Speaker: Igor R. Klebanov (Princeton University)

      Abstract: Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies.  The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

       

      https://www.youtube.com/watch?v=O4xizOTzpL4&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=18

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024

      Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

      April 22, 2022 | 9:30 – 11:00 am ET

      Title: Auction Theory

      Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

      Talk chairs: Scott Kominers, Sergiy Verstyuk

      SLIDES | VIDEO Answers to Questions from Talks 2 and 3

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Prashant Kocherlakota (BHI)

      Title: Testing spacetime geometry with images of supermassive compact objects: Current status and the future

      Abstract: Astrophysical black holes (BHs) are expected to be described by the Kerr solution of the Einstein equations. Several frameworks have recently been developed to parametrically deform the Kerr metric in significantly different ways, to enable formulations of tests of the no-hair theorems. Testing the viability status of alternative models – such as non-Kerr BHs from general relativity, BHs from alternative theories, wormholes, and other exotic objects – as descriptors of astrophysical objects has been of longstanding interest. The Event Horizon Telescope (EHT) recently imaged Sagittarius A* (Sgr A*), the supermassive compact object at the center of the Galaxy, making such tests possible. In such tests, the shadow critical curve (or simply shadow boundary), defined on the observer’s image plane, has gained prominence as the observable of interest. We will discuss how the EHT is able to extract information regarding the shadow of Sgr A* and the status of associated tests of the spacetime geometry in the strong-field regime. Future imaging measurements expect to detect the so-called photon ring, a strong-gravitational lensing feature that appears in the close vicinity of the critical curve, which houses higher-order images of the emission source. Time permitting, we will also discuss how these can be used to set up more stringent tests of the spacetime metric and gravity in the future.

       

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: Strominger-Yau-Zaslow conjecture is one of the guiding principles in mirror symmetry, which not only predicts the geometric structures of Calabi-Yau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricci-flat metrics. In this talk, we will explain how SYZ fibrations on log Calabi-Yau surfaces detect the non-standard semi-flat metric which generalized the semi-flat metrics of Greene-Shapere-Vafa-Yau. Furthermore, we will use the SYZ fibration on log Calabi-Yau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Dan Lee

      Title: Survey on stability of the positive mass theorem

      Abstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk, I will discuss various results related to this question.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      The longest induced path in a sparse random graph
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-12.14.2021

      Abstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size, which seems to be a barrier for certain natural approaches. Recently, in joint work with Draganic and Krivelevich, we solved this problem. In the talk, I will discuss the history of the problem and give an overview of the proof.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Speaker: Du Pei

      Title: Wall-crossing from Higgs bundles to vortices

      Abstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks.  In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.

    • Combinatorics Physics and Probability
      9:30 am-10:30 am
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-11.30.2021

      Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
      In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
      Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
      This work was done in collaboration with Renaud Lambiotte.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-04.19.2022

      Abstract:  In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong.

      In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

    • Combinatorics Physics and Probability
      9:30 am-10:30 am
      12/01/2024

      Speaker: Nima Arkani-Hamed, IAS

      Title: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes

    • Colloquium
      9:30 am-10:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/26/2022Samir Mathur (Ohio State University)Title: The black hole information paradox

      Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with a postulate that information would leak out through wormholes. Recently, it was shown that this wormhole idea had some basic flaws, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle.

      Video

      2/2/2022Adam Smith (Boston University)TitleLearning and inference from sensitive data

      Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records.

      I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics, and lay out directions for future investigation.

      2/8/2022Wenbin Yan (Tsinghua University)
      (special time: 9:30 pm ET)
      Title: Tetrahedron instantons and M-theory indices

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

      Video

      2/16/2022Takuro Mochizuki (Kyoto University)Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles

      Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence
      between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles
      and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied.

      In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

      2/23/2022Bartek Czech (Tsinghua University)Title: Holographic Cone of Average Entropies and Universality of Black Holes

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

      3/2/2022Richard Kenyon (Yale University)
      3/9/2022Richard Tsai (UT Austin)
      3/23/2022Joel Cohen (University of Maryland)
      3/30/2022Rob Leigh (UIUC)
      4/6/2022Johannes Kleiner (LMU München)
      4/13/2022Yuri Manin (Max-Planck-Institut für Mathematik)
      4/20/2022TBA
      4/27/2022TBA
      5/4/2022Melody Chan (Brown University)
      5/11/2022TBA
      5/18/2022TBA
      5/25/2022Heeyeon Kim (Rutgers University)

      Fall 2021

      DateSpeakerTitle/Abstract
      9/15/2021Tian Yang, Texas A&MTitle: Hyperbolic Geometry and Quantum Invariants

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

      9/29/2021David Jordan, University of EdinburghTitle: Langlands duality for 3 manifolds

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

      10/06/2021Piotr Sulkowski, U WarsawTitle: Strings, knots and quivers

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

      10/13/2021Alexei Oblomkov, University of MassachusettsTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane.

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

      10/20/2021Peng Shan, Tsinghua UTitle: Categorification and applications

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

      10/27/2021Karim Adiprasito, Hebrew University and University of CopenhagenTitle: Anisotropy, biased pairing theory and applications

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

      11/03/2021Tamas Hausel, IST AustriaTitle: Hitchin map as spectrum of equivariant cohomology

      Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.

      11/10/2021Peter Keevash, OxfordTitle: Hypergraph decompositions and their applications

      Abstract: Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.
      11/17/2021Andrea Brini, U SheffieldTitle: Curve counting on surfaces and topological strings

      Abstract: Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physics-motivated toolkit to tackle several traditionally hard questions in the field.
      I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X, D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X, D), including the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

      12/01/2021Richard Wentworth, University of MarylandTitle: The Hitchin connection for parabolic G-bundles

      Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.

      12/08/2021Maria Chudnovsky, PrincetonTitle: Induced subgraphs and tree decompositions

      Abstract: Tree decompositions are a powerful tool in both structural
      graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph.

      Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

      12/15/21Constantin Teleman (UC Berkeley)Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system

      Abstract: I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with applications (some conjectural, some rigorous) to gauged Gromov-Witten theory. Time permitting, we will review applications to Coulomb branches and the categorified Weyl character formula.

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures.

      The talk is partially based on joint works with Si Li.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Puskar Mondal

      Title: Stability and convergence issues in mathematical cosmology

      Abstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized, one needs to study its stability properties. Therefore, I will briefly discuss the stability issue and its consequences (e.g., structure formation, etc).

    • Algebraic Geometry in String Theory Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA-Algebraic-Geometry-in-String-Theory-02.01.2022

      Abstract: We will consider the following problem: if (C,x_1,…,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,…,y_n, then how many maps f:C -> X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory, the answer may be expressed in terms of the quantum cohomology of X, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle, though in the presence of sufficient positivity, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem, including joint work with Farkas, Pandharipande, and Cela, as well as work of other authors.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 03.09.23

      General Relativity Seminar

      Speaker: Jose Luis Jaramillo (Bourgogne U.)

      Title: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture

      Abstract: Can we measure the ‘effective regularity’ of spacetime from the perturbation of quasi-normal mode (QNM) overtones? Black hole (BH) QNMs encode the resonant response of black holes under linear perturbations, their associated complex frequencies providing an invariant probe into the background spacetime geometry. In the late nineties, Nollert and Price found evidence of a BH QNM instability phenomenon, according to which perturbed QNMs of Schwarzschild spacetime migrate to new perturbed branches of different qualitative behaviour and asymptotics. Here we revisit this BH QNM instability issue by adopting a pseudospectrum approach. Specifically, we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator by adopting a hyperboloidal formulation of spacetime. Non-selfadjoint (more generally non-normal) operators suffer potentially of spectral instabilities, the notion of pseudospectrum providing a tool suitable for their study. We find evidence that perturbed Nollert & Price BH QNMs track the pseudospectrum contour lines, therefore probing the analytic structure of the resolvent, showing the following (in)stability behaviour: i) the slowest decaying (fundamental) mode is stable, whereas ii) (all) QNM overtones are ultraviolet unstable (for sufficiently high frequency). Building on recent work characterizing Burnett’s conjecture as a low-regularity problem in general relativity, we conjecture that (in the infinite-frequency limit) generic ultraviolet spacetime perturbations make BH QNMs migrate to ‘Regge QNM branches’ with a precise universal logarithmic pattern. This is a classical general relativity (effective) low-regularity phenomenon, agnostic to possible detailed (quantum) descriptions of gravity at higher-energies and potentially observationally accessible.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

    • Member Seminar
      9:30 am-10:30 am
      12/01/2024

      Member Seminar

      Speaker: Jue Liu

      Title: Instability of naked singularities in general relativity

      Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, which are called by naked singularities, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method, and it is this wild method that helps us to extend some results to the asymmetric cases.

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024
      CMSA GR Seminar 02.23.23

      General Relativity Seminar

      Speaker: Nikolaos Athanasiou (University of Crete, Greece)

      Title: Formation of trapped surfaces in the Einstein-Yang-Mills system

      Abstract: The purpose of this talk is to give an overview of a semi-global existence result and a trapped surface formation results in the context of the Einstein-Yang-Mills system. Adopting a “signature for decay rates” approach first introduced by An, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yield the desired semi-global existence result. Once semi-global existence has been established, we will explain how the formation of a trapped surface follows from a standard ODE argument. This is joint work with Puskar Mondal and Shing-Tung Yau.

    • Math Science Literature Lecture Series
      9:30 am-11:00 am
      12/01/2024

      Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians

      April 18, 2022 | 9:30 – 11:00 am ET

      Title: Game Theory Basics and Classical Existence Theorems

      Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

      Talk chairs: Scott Kominers, Sergiy Verstyuk

      SLIDES | VIDEO

       

    • Quantum Matter
      9:30 am-11:00 am
      12/01/2024
      CMSA-QMMP-Seminar-04.14.22-1583x2048-1

      Youtube video

       

      Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields.  Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos.  Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).

      As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role.  Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times.  Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime.  This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole).  It also makes a number of testable predictions.

      (Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

    • General Relativity Seminar
      9:30 am-10:30 am
      12/01/2024

      Title: On the Observable Shape of Black Hole Photon Rings

      Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

    • Special Seminar
      9:50 am-10:50 am
      12/01/2024-04/26/2016

      The seminar on geometric analysis will be held on Tuesdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule can be found below. Titles will be added as they are provided.

      DayNameTitle
      09-08-2015Binglong ChenOn the geometry of complete positively curved Kahler manifolds
      09-15-2015Hongwei XuMean Curvature Flow and Sphere Theorem
      09-22-2015Teng FeiSome new solutions to the Strominger system
      09-29-2015Xuqian FanThe Steklov eigenvalues on annuli
      10-06-2015Binglong ChenRicci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds
      10-13-2015Pengfei GuanIsometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$.
      10-20-2015Ovidiu SavinSmoothness of the eigenfunction for the Monge-Ampere equation
      10-27-2015Tom IlmanenFlow of curves by curvature in R^n
      11-03-2015Tom Hou (Caltech)Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations
      11-10-2015Jerome Darbon (9:30am-10:30am) Adam Jacob (10:30am-11:30am)On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations(1,1) forms with specified Lagrangian phase
      11-17-2015Ovidiu SavinExamples of singular minimizers in the calculus of variations
      11-24-2015Hongwei XuMean curvature flow meets Ricci flow:  Convergence and sphere theorems of sub manifolds arising from Yau rigidity theory
      12-01-2015Tom Ilmanen
      01-26-2016Mao ShengUniformization of p-adic curves
      02-02-2016Yi ZhangHodge Bundles on Smooth Compactifications of Siegel Varieties
      02-09-2016Valentino TosattiNon-Kahler Calabi-Yau manifolds
      02-16-2016Camillo De LellisApproaching Plateau’s problem with minimizing sequences of sets
      02-23-2016Junbin LiConstruction of black hole formation spacetimes
      03-01-2016Ben WeinkoveMonge-Ampere equations and metrics on complex manifolds
      03-08-2016Albert ChauSurvey on Kahler Ricci flow on non-negatively curved non-compact manifolds
      03-15-2016Spring Break 
      03-22-2016Richard Schoen (Standford)The geometry of eigenvalue extremal problems
      03-29-2016Piotr ChruscielMass of characteristic surfaces
      04-05-2016 (Room 232, Science Center)Niky Kamran, McGill UniversityNon-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
      04-12-2016Connor Mooney, UT AustinFinite time blowup for parabolic systems in the plane
      04-19-2016 (Room 232, Science Center)Xu-Jia WangBoundary behaviour of solutions to singular elliptic equations
      04-26-2016Andre NevesA path to Yau’s conjecture
    • Seminars
      9:50 am-10:50 am
      12/01/2024

      The seminar for evolution equations, hyperbolic equations, and fluid dynamics will be held on Thursdays from 9:50am to 10:50am with time for questions afterwards in CMSA Building, 20 Garden Street, Room G10. The tentative schedule of speakers is below. Titles for the talks will be added as they are received.

      DateNameTitle
      09-03-2015Long JinScattering Resonances for Convex Obstacles
      09-10-2015Chunjing XieWell/ill-posedness for the rotating shallow water system
      09-17-2015Xiangdi HuangGlobal classical and weak Solutions to the 3D fully compressible Navier-Stokes-Fourier system
      09-24-2015Felix FinsterCausal fermion systems and the causal action principle
      10-01-2015Pin YuConstruction of Cauchy data of vacuum Einstein field equations evolving to black holes
      10-08-2015Chunjing XieSteady Euler flows past a wall or through a nozzle
      10-15-2015Zhou Ping XinOn Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations
      10-22-2015Xiangdi HuangOn Nash’s problem for compressible flows
      10-29-2015Pin YuShock formations for 3 dimensional wave equations
      11-05-2015No talk 
      11-12-2015Zhou Ping Xin (9:30am-10:30am) Nicolai Krylov (10:30am-11:30am)Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star ProblemOn the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions
      11-19-2015Nicolai KrylovTo the theory of viscosity solutions for uniformly parabolic Isaacs equations
      11-26-2015ThanksgivingNo seminar
      12-4-2015John Loftin (@11:00am)Moduli of Equivariant Minimal Surfaces in CH^2$
      01-28-2016Xiaoli HanThe symplecitic and Lagrangian mean curvature flow 
      02-04-2016Pranav PanditCategorical Kähler Geometry
      02-11-2016Lydia BieriEinstein’s Equations, Energy and Gravitational Radiation
      02-18-2016Zuoqiang ShiLow dimensional manifold model for image processing
      02-25-2016Chun Peng WangSmooth Transonic Flows of Meyer Type in De Laval Nozzles
      03-03-2016Piotr ChruscielSingularities in general relativity
      03-10-2016Feimin HuangIsometric immersion of complete surface with slowly decaying negative Gauss curvature
      03-17-2016Spring BreakNo Talk
      03-24-2016Michael EichmairMinimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds
      03-31-2016Felix FinsterLorentzian spectral geometry and the fermionic signature operator
      04-07-2016(Room 232, Science Center)Stefano Bianchini, SISSAConcentration of entropy dissipation for scalar conservation laws
      04-14-2016Tai-peng TsaiStability of periodic waves of the 1D nonlinear Schr\”odinger equations
      04-21-2016Stefano Bianchini, SISSAQuadratic interaction functional for system of conservation laws
      04-28-2016Mihalis Dafermos, PrincetonThe linear stability of the Schwarzschild solution to gravitational perturbations
      05-05-2016Xu-Jia WangMonge-Ampere equations arising in geometric optics
      05-12-2016Stefano Bianchini
    • General Relativity Seminar
      10:00 am-11:00 am
      12/01/2024

      Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

    • Workshop
      10:00 am-5:00 pm
      12/01/2024-05/08/2022

      On May 6–8, 2022, the CMSA  hosted a second NSF FRG Workshop.

      This project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology), Computer Science (Scientific Computing and Complexity Theory), and domain sciences, from Data Sciences to Computational Biology.

      Scientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time, however, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing, searching, simulating, analyzing, and comparing shapes. These methods and tools can be applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition, and satellite image analysis.

      This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

      The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.


      Workshop on Discrete Shapes
      May 6–8, 2022

      Organizers:

      • David Glickenstein (University of Arizona)
      • Joel Hass (University of California, Davis)
      • Patrice Koehl (University of California, Davis)
      • Feng Luo (Rutgers University, New Brunswick)
      • Maria Trnkova (University of California, Davis)
      • Shing-Tung Yau (Harvard)

      Speakers:

      • Miri Ben-Chen (Technion)
      • Alexander Bobenko (TU Berlin)
      • John Bowers (James Madison)
      • Steven Gortler (Harvard)
      • David Gu (Stony Brook)
      • Anil Hirani (UIUC)
      • Yanwen Luo (Rutgers)
      • Peter Schroeder (Caltech)
      • Justin Solomon (MIT)
      • Tianqi Wu (Clark University)

      Contributed Talk Speakers:

      • Oded Stein (MIT)
      • Bohan Zhou (Dartmouth)

      Schedule
      Schedule (PDF)

      Friday, May 6, 2022

      10:00–10:05 amWelcome Opening
      10:05–10:55 amAnil N. HiraniTitle: Discrete vector bundles with connection

      Abstract: We have recently initiated a generalization of discrete exterior calculus to differential forms with values in a vector bundle. A discrete vector bundle with connection over a simplicial complex has fibers at vertices and transport maps on edges, just as in lattice gauge theory. The first part of this work involves defining and examining properties of a combinatorial exterior covariant derivative and wedge product. We find that these operators commute with pullback under simplicial maps of the base space. From these definitions emerges a combinatorial curvature. In the second part of this work we showed that the curvature behaves as one expects: it measures failure of parallel transport to be independent of the path, and is the local obstruction to a trivialization. For a bundle with metric, metric compatibility of the discrete connection is equivalent to a Leibniz rule.  Vanishing curvature is indeed equivalent to an appropriately defined discrete flat connection, and curvature obstructs trivializability. In this talk I will focus on just the first part, and talk about naturality of the discrete exterior covariant derivative and discrete wedge product using simple examples. Joint work with Daniel Berwick-Evans (UIUC) and Mark Schubel (Apple, Inc.).

      11:10–12:00 pmDavid GuTitle: Surface Quadrilateral Meshing Based on Abel-Jacobi Theory

      Abstract: Surface quadrilateral meshing plays an important role in many fields. For example, in CAD (computer-aided design), all shapes are represented as Spline surfaces, which requires structured quad-meshing; in CAE (computer-aided engineering), the surface tessellation greatly affects the accuracy and efficiency of numerical simulations. Although the research on mesh generation has a long history, it remains a great challenge to automatically generate structured quad-meshes with high qualities. The key is to find the governing equation for the singularities of the global structured quad-meshes.

      In this talk, we introduce our recent discovery:  the singularities of a quad-mesh are governed by the Abel theorem. We show that each quad-mesh determines a conformal structure and a meromorphic quadratic differential, the configuration of the mesh singularities can be described as the divisor of the differential. The quad-mesh divisor minus four times of the divisor of a holomorphic one-form is principal and satisfies the Abel theorem: its image under the Jacobi map is zero in the Jacobi variety.

      This leads to a rigorous and efficient algorithm for surface structured quadrilateral meshing. After determining the singularities, the metric induced by the quad-mesh can be computed using the discrete Yambe flow, and the meromorphic quartic differential can be constructed, the trajectories of the differentials give the quad-mesh. The method can be applied directly for geometric modeling and computational mechanics.

      12:00–2:00 pmLunch Break
      2:00–2:50 pm Justin SolomonTitle:  Geometry Processing with Volumes

      Abstract:  Many algorithms in geometry processing are restricted to two-dimensional surfaces represented as triangle meshes.  Drawing inspiration from simulation, medical imaging, and other application domains, however, there is a substantial demand for geometry processing algorithms targeted to volumes represented as tetrahedral meshes or grids.  In this talk, I will summarize some efforts in our group to develop a geometry processing toolkit specifically for volumes.  Specifically, I will cover our recent work on hexahedral remeshing via cuboid decomposition, volumetric correspondence, and minimal surface computation via geometric measure theory.

      3:00–3:20 pmOded SteinTitle: Optimization for flip-free parametrization

      Abstract: Parametrizations without flipped elements are desirable in a variety of applications such as UV mapping and surface/volume correspondence. Computing flip-free parametrizations can be challenging, and there are many different approaches to the problem. In this talk we will look at multiple strategies for flip-free parametrizations that are based on the optimization of continuous energies. Due to the nature of the problem, these energies are often nonconvex and unbounded, which is a challenge for optimization methods. We will also take a closer look at our recently developed method for computing flip-free parametrizations using the Alternating Direction Method of Multipliers (ADMM).

      3:20–4:00 pmBreak
      4:00–4:50 pmJohn BowersTitle: Koebe-Andre’ev-Thurston Packings via Flow

      Abstract: Recently, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation, flip-and-flow, that allows two tangency packings whose contact graphs differ by a combinatorial edge flip to be continuously deformed from one to the other while maintaining tangencies across all of their common edges. Starting from a canonical tangency circle packing with the desired number of circles a finite sequence of flip-and-flow operations may be applied to obtain a circle packing for any desired (proper) contact graph with the same number of circles.

      The full Koebe-Andre’ev-Thurston theorem generalizes the circle packing theorem to allow for neighboring circles to overlap by angles up to $\pi/2$. In this talk I will show that the Connelly-Gortler method can be extended to allow for circles to overlap to angles up to $\pi/2$. This results in a new proof of the general Koebe-Andre’ev-Thurston theorem for disk patterns on $\mathbb{S}^2$ as well as a numerical algorithm for computing them. The proof involves generalizing a notion of convexity for circle polyhedra that was recently used to prove the global rigidity of certain circle packings, which is then used to show that all convex circle polyhedra are infinitesimally rigid, a result of independent interest.

      5:00–5:30 pmMovies “conform!” & ”Koebe polyhedra”

       

      Saturday, May 7, 2022

      9:30–10:20 amAlexander BobenkoTitle: The Bonnet problem: Is a surface characterized by its metric and curvatures?

      Abstract: We consider a classical problem in differential geometry, known as the Bonnet problem, whether a surface is characterized by a metric and mean curvature function. Generically, the answer is yes. Special cases when it is not the case are classified. In particular, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas

      10:20–11:00 amBreak
      11:00–11:50 amMiri Ben ChenTitle: Surface Multigrid via Intrinsic Prolongation

      Abstract: The solution of a linear system is a required ingredient in many geometry processing applications, and multigrid methods are among the most efficient solution techniques. However, due to the unstructured nature of triangle meshes, mapping functions between different multigrid levels is challenging. In this talk I will present our recent work that uses an intrinsic prolongation operator as the main building block in a multigrid solver for curved triangle meshes. Our solver can be used as a black-box in any triangle-mesh based system that requires a linear solve, and leads to order of magnitude time-efficiency improvement compared to direct solvers.

      12:00–2:00 pmLunch Break
      2:00–2:50 pmSteven GortlerTitle: Reconstructing configurations and graphs from unlabeled distance measurements

      Abstract: Place a configuration of n  points (vertices) generically in R^d. Measure the Euclidean lengths of m point-pairs (edges). When is the underlying graph determined by these $m$ numbers (up to isomorphism)? When is the point configuration determined by these $m$ numbers (up to congruence)? This question is motivated by a number of inverse problem applications. In this talk, I will review what is known about this question.

      3:00–3:20 pmBohan ZhouTitle: Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs

      Abstract: Optimal transport has profound and wide applications since its introduction in 1781 by Monge. Thanks to the Benamou-Brenier formulation, it provides a meaningful functional in the image science like image and shape registrations. However, exact computation through LP or PDE is in general not practical in large scale, while the popular entropy-regularized method introduces additional diffusion noise, deteriorating shapes and boundaries. Until the recent work [Jacobs and Leger, A Fast Approach to Optimal Transport: the back-and-forth method, Numerische Mathematik, 2020], solving OT in a both accurate and fast fashion finally becomes possible. Multiple marginal optimal transport is a natural extension from OT but has its own interest and is in general more computationally expensive. The entropy method suffers from both diffusion noise and high dimensional computational issues. In this work with Matthew Parno, we extend from two marginals to multiple marginals, on a wide class of cost functions when those marginals have a graph structure. This new method is fast and does not introduce diffusion. As a result, the new proposed method can be used in many fields those require sharp boundaries. If time allows, we will illustrate by examples the faithful joint recover via MMOT of images with sharp boundaries, with applications on sea ice prediction.

      3:20–4:00 pmBreak
      4:00–4:50 pmPeter SchroederTitle: Constrained Willmore Surfaces

      Abstract: The Willmore energy of a surface is a canonical example of a squared curvature bending energy. Its minimizers are therefore of interest both in the theory of surfaces and in practical applications from physical and geometric modeling. Minimizing the bending energy alone however is insufficient. Taking a cue from univariate splines which incorporate an isometry constraint we consider Willmore minimizers subject to a conformality constraint. In this talk I will report on a numerical algorithm to find such constrained minimizers for triangle meshes.

      Joint work with Yousuf Soliman (Caltech), Olga Diamanti (UGraz), Albert Chern (UCSD), Felix Knöppel (TU Berlin), Ulrich Pinkall (TU Berlin).

      5:00–5:50 pmProblems and Application discussions

       

      Sunday, May 8, 2022

      9:00–9:50 amTianqi WuTitle: Convergence of discrete uniformizations

      Abstract: The theory of discrete conformality, based on the notion of vertex scaling, has been implemented in computing conformal maps or uniformizations of surfaces. We will show that if a Delaunay triangle mesh approximates a smooth surface, then the related discrete uniformization will converge to the smooth uniformization, with an error bounded linearly by the size of the triangles in the mesh.

      10:10–11:00 amYanwen LuoTitle:  Recent Progress in Spaces of Geodesic Triangulations of Surfaces

      Abstract:
      Spaces of geodesic triangulations of surfaces are natural discretization of the groups of surface diffeomorphisms isotopy to the identity. It has been conjectured that these spaces have the same homotopy type as their smooth counterparts. In this talk, we will report the recent progress in this problem. The key ingredient is the idea in Tutte’s embedding theorem. We will explain how to use it to identify the homotopy types of spaces of geodesic triangulations. This is joint work with Tianqi Wu and Xiaoping Zhu.
      11:10–12:00 pmProblems and Application discussions
      12:00–1:00 pmMovie“The Discrete Charm of Geometry”

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Meng Cheng (Yale)

      Title: Symmetry and many-body topology in mixed states

      Abstract: It is by now well-understood that gapped ground states of local Hamiltonians can be classified topologically, and the nontrivial states exhibit many interesting topological phenomena. In this talk I’ll discuss recent developments in generalizing the topological classification to mixed states. Global symmetry plays a key role in understanding phases in pure states. For mixed states, certain “weak” symmetries may hold “on average” for the entire ensemble, in contrast to “strong” symmetries respected by each state in the ensemble. I will show that the interplay between these two kinds of symmetries lead to a rich landscape of symmetry-protected mixed states, and can also be used to characterize mixed state topological order.

       

    • CMSA EVENT: Computational Biology Symposium
      10:00 am-4:00 pm
      12/01/2024
      Compbiotextlessfeature-600x338

      On May 3, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo.

      The symposium will begin at 10:00am ET. There will be a morning and afternoon session, with an hour break for lunch.

      Videos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.

      Confirmed participants:

      Schedule:

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/19/2021 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Swampland Seminar
      10:00 am-11:00 am
      12/01/2024

      Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Aleksey Cherman (UMN)

      Title: Exact lattice chiral symmetry in 2d gauge theory

      Abstract: Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory.  I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

    • Swampland Seminar
      10:00 am-11:00 am
      12/01/2024

      Swampland Seminar

      Speakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech)

      Title: Causality constraints on corrections to Einstein gravity

      Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

    • Quantum Matter
    • Seminars
      Seminars Colloquia & Seminar
      13/3/2018 Topology Seminar
      10:00 am-11:30 am
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/26/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/22/2018 Topology Seminar
      10:00 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 05.05.23 (2)

      Quantum Matter Seminar

      Speaker: Sona Najafi (IBM Quantum)

      Title: Detecting central charge in a superconducting quantum processor

      Abstract: Physical systems at the continuous phase transition point exhibit conformal symmetry rendering local scaling invariance. In two dimensions, the conformal group possesses infinite generators described by Virasoro algebra with an essential parameter known as a central charge. While the central charge manifests itself in a variety of quantities, its detection in experimental setup remains elusive. In this work, we utilize Shannon-Renyi entropy on a local basis of a one-dimensional quantum spin chain at a critical point. We first use a simulated variational quantum eigen solver to prepare the ground state of the critical transfer field Ising model and XXZ model with open and periodic boundary conditions and perform local Pauli X and Z basis measurements. Using error mitigation such as probabilistic error cancellation, we extract an estimation of the local Pauli observables needed to determine the Shannon-Renyi entropy with respect to subsystem size. Finally, we obtain the central charge in the sub-leading term of Shannon-Renyi entropy.

      https://www.youtube.com/watch?v=Os26XRahD0c&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=5

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024

      Speaker: Haoyu Guo (Harvard)

      Title: Transport in large-N critical Fermi surface

      Abstract:
       A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermion-scalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and show that a previously proposed mega^{-2/3} contribution to the optical conductivity at frequency mega has vanishing co-efficient. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity behaves like a Fermi liquid. Arxiv references: 2203.04990, 2207.08841

    • Topological Quantum Matter Seminar
      10:00 am-11:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 12.07.22

      Topological Quantum Matter Seminar

      Speaker: Vasil Rokaj (Harvard)

      Title: Controlling Quantum Matter with Quantum Cavity Fields

      Abstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free electron gas [5]. The exact analytic solution of the Sommerfeld model in the cavity will be presented as well as its fundamental properties. Then, in the second part of the talk, I will focus on a many-particle system of cold ions in a harmonic trap coupled to the cavity field. I will show how this system couples collectively to the cavity and that hybrid states between light and matter, known as polaritons, emerge. The formation of polaritons leads to the modification of the properties of the cold ions and enhances the localization of the many-body wave function [6]. Connections to experiments will be discussed as well.

      [1] F. Garcia-Vidal, C. Ciuti, T. W. Ebbesen, Science, 373, 178 (2021)

      [2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)

      [3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)

      [4] T. W. Ebbesen, Acc. Chem. Res. 49, 11, 2403–2412 (2016)

      [5] V. Rokaj, M. Ruggenthaler, F. G. Eich, A. Rubio, Phys. Rev. Research 4, 013012 (2022)

      [6] V. Rokaj, S.I. Mistakidis, H.R. Sadeghpour, arXiv:2207.03436 (2022)

    • Algebraic Geometry in String Theory Seminar
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Pre-talk Speaker: David Wu (Harvard Physics): 10:00-10:30 am

      Speaker: Damian van de Heisteeg, CMSA

      Title: Species Scale across String Moduli Spaces

      Abstract: String theories feature a wide array of moduli spaces. We propose that the energy cutoff scale of these theories – the so-called species scale – can be determined through higher-curvature corrections. This species scale varies with the moduli; we use it both asymptotically to bound the diameter of the field space, as well as in the interior to determine a “desert point” where it is maximized.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      10:00 am-11:00 am
      12/01/2024

      Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or, Neumann) eigenvalues. Using the results on the Birkhoff conjecture, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks, which Kac proved to be uniquely determined, these are the only domains for which it is known that one can hear their shape.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Andreas Bauer  (Freie Universität Berlin)

      Title: Tensorial TQFT and disentangling modular Walker-Wang models

      Abstract: I will introduce simple “tensorial” definitions for many algebraic and categorical structures appearing in the classification of topological phases of matter. Such “tensorial TQFTs” will be defined as maps that associate tensors to geometric/topological objects of some type, subject to gluing axioms. Tensorial TQFTs are very directly related to microscopic physical models in terms of discrete path integrals. I will use those tensorial definitions to construct invertible boundaries which disentangle modular Walker-Wang models.

       

      https://www.youtube.com/watch?v=MJ8NRSrvihQ&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=12

    • Topological Quantum Matter Seminar
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Topological Seminar 11.16.22

      Topological Quantum Matter Seminar

      Speaker: Jérôme Faist  (ETH Zurich)

      Title: Vacuum fluctuations in cavities: breakdown of the topological protection in the integer Quantum Hall effect

      Abstract: When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling ΩR is such that the coupling energy becomes close to the one of the bare matter resonance ω0. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian.

      In a microcavity, the strength of the electric field caused by the vacuum fluctuations, to which the strength of the light-matter coupling ΩR is proportional, scales inversely with the cavity volume. One very interesting feature of the circuit-based metamaterials is the fact that this volume can be scaled down to deep subwavelength values in all three dimension of space.1 Using metamaterial coupled to two-dimensional electron gases under a strong applied magnetic field, we have now explored to which extend this volume can be scaled down and reached a regime where the stability of the polariton is limited by diffraction into a continuum of plasmon modes2.

      We have also used transport to probe the ultra-strong light-matter coupling3, and show now that the latter can induce a breakdown of the integer quantum Hall effect4. The phenomenon is explained in terms of cavity-assisted hopping, an anti-resonant process where an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity5. We are also evaluating a proposal suggesting that the value of the quantization voltage can be renormalized by the cavity6.

       

      1. Scalari, G. et al. Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial. Science 335, 1323–1326 (2012).
      2. Rajabali, S. et al. Polaritonic Nonlocality in Light Matter Interaction. Nat Photon 15, 690–695 (2021).
      3. Paravicini-Bagliani, G. L. et al. Magneto-Transport Controlled by Landau Polariton States. Nat. Phys. 15, 186–190 (2019).
      4. Appugliese, F. et al. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science 375, 1030–1034 (2022).
      5. Ciuti, C. Cavity-mediated electron hopping in disordered quantum Hall systems. Phys. Rev. B 104, 155307 (2021).
      6. Rokaj, V., Penz, M., Sentef, M. A., Ruggenthaler, M. & Rubio, A. Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance. Phys. Rev. B 105, 205424 (2022).

       

    • Quantum Matter
      10:00 am-11:00 am
      12/01/2024
      CMSA QMMP 03.10.23

      Quantum Matter Seminar

      Speaker: Yichen Huang (Harvard)

      Title: Quantum entropy thermalization

      Abstract: In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization.

      References: arXiv:2302.10165, 2209.09826; Joint work with Aram W. Harrow

       

      https://www.youtube.com/watch?v=8b4g9SEFn_Y&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=13

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Scalable Dynamic Graph Algorithms
      10:00 am-10:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      CMSA Interdisciplinary Science Seminar

      Speaker: Quanquan Liu, Northwestern University

      Title: Scalable Dynamic Graph Algorithms

      Abstract: The field of dynamic graph algorithms seeks to understand and compute statistics on real-world networks that undergo changes with time. Some of these networks could have up to millions of edge insertions and deletions per second. In light of these highly dynamic networks, we propose various scalable and accurate graph algorithms for a variety of problems. In this talk, I will discuss new algorithms for various graph problems in the batch-dynamic model in shared-memory architectures where updates to the graph arrive in multiple batches of one or more updates. I’ll also briefly discuss my work in other dynamic models such as distributed dynamic models where the communication topology of the network also changes with time (ITCS 2022). In these models, I will present efficient algorithms for graph problems including k-core decomposition, low out-degree orientation, matching, triangle counting, and coloring.

      Specifically, in the batch-dynamic model where we are given a batch of B updates, I’ll discuss an efficient O(B log^2 n) amortized work and O(log^2 n log log n) depth algorithm that gives a (2+\epsilon)-approximation on the k-core decomposition after each batch of updates (SPAA 2022). We also obtain new batch-dynamic algorithms for matching, triangle counting, and coloring using techniques and data structures developed in our k-core decomposition algorithm. In addition to our theoretical results, we implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyper-threading on 11 graphs of varying densities and sizes. Our experiments show improvements over state-of-the-art algorithms even on machines with only 4 cores (your standard laptop). I’ll conclude with a discussion of some open questions and potential future work that these lines of research inspire.

      Bio: Quanquan C. Liu is a postdoctoral scholar at Northwestern University under the mentorship of Prof. Samir Khuller. She completed her PhD in Computer Science at MIT where she was advised by Prof. Erik Demaine and Prof. Julian Shun. Before that, she obtained her dual bachelor’s degree in computer science and math also at MIT. She has worked on a number of problems in algorithms and the intersection between theory and practice. Her most recent work focuses on scalable dynamic and static graph algorithms as well as differentially private graph algorithms for problems including k-core decomposition, densest subgraphs, subgraph counting, matching, maximal independent set and coloring. She has earned the Best Paper Award at SPAA 2022, a NSF Graduate Research Fellowship, and participated in the 2021 EECS Rising Stars workshop. Outside of research, she is extensively involved in programming outreach as a coach for the USA Computing Olympiad (USACO) and as a trainer for the North America Programming Camp (NAPC).

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Margarita Davydova (MIT)

      Title: Floquet codes, automorphisms, and quantum computation

      Abstract: In this talk, I will introduce a new kind of measurement-based quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of low-weight measurements which simultaneously encode logical information and enable error correction.  We introduce a new class of quantum error-correcting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes.

      As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of time-like domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model.  This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes.

      The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two- and, rarely three-body measurements. Using adaptive two-body measurements, we can achieve a non-Clifford gate in 3+1d, making the first step towards universal quantum computation in this model.

      The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].

    • CMSA EVENT: Frontiers in Applied Mathematics and Computation
      10:00 am-2:00 pm
      12/01/2024-04/29/2020
      Frontiers In Applied Mathematics And Computation

      Together with the School of Engineering and Applied Sciences, the CMSA will be hosting a lecture series on the Frontiers in Applied Mathematics and Computation. Talks in this series will aim to highlight current research trends at the interface of applied math and computation and will explore the application of these trends to challenging scientific, engineering, and societal problems.

      Lectures will take place on March 25, April 1, and April 29, 2021.

      Speakers:

      • George Biros (U.T. Austin)
      • Laura Grigori (INRIA Paris)
      • Samory K. Kpotufe (Columbia)
      • Jonas Martin Peters (University of Copenhagen)
      • Joseph M. Teran (UCLA)

      The schedule below will be updated as talks are confirmed.

       

      Date/TimeSpeakerTitle/Abstract
      3/25/2021
      10:00 – 11:00am ET
      Joseph M. TeranTitle: Affine-Particle-In-Cell with Conservative Resampling and Implicit Time Stepping for Surface Tension Forces

      Abstract: The Particle-In-Cell (PIC) method of Harlow is one of the first and most widely used numerical methods for Partial Differential Equations (PDE) in computational physics. Its relative efficiency, versatility and intuitive implementation have made it particularly popular in computational incompressible flow, plasma physics and large strain elastoplasticity. PIC is characterized by its dual particle/grid (Lagrangian/Eulerian) representation of material where particles are generally used to track material transport in a Lagrangian way and a structured Eulerian grid is used to discretize remaining spatial derivatives in the PDE. I will discuss the importance of conserving linear and angular momentum when switching between these two representations and the recent Affine-Particle-In-Cell (APIC) extension to PIC designed for this conservation. I will also discuss a recent APIC technique for discretizing surface tension forces and their linearizations needed for implicit time stepping. This technique is characterized by a novel surface resampling strategy and I will discuss a generalization of the APIC conservation to this setting.

      4/1/2021
      9:00 – 10:00am ET
      George BirosTitle: Inverse biophysical modeling and its application to neurooncology

      Abstract: A predictive, patient-specific, biophysical model of tumor growth would be an invaluable tool for causally connecting diagnostics with predictive medicine. For example, it could be used for tumor grading, characterization of the tumor microenvironment, recurrence prediction, and treatment planning,  e.g., chemotherapy protocol or enrollment eligibility for clinical trials. Such a model also would provide an important bridge between molecular drivers of tumor growth and imaging-based phenotypic signatures, and thus,  help identify and quantify mechanism-based associations between these two. Unfortunately, such a predictive biophysical model does not exist. Existing models undergoing clinical evaluation are too simple–they do not even capture the MRI phenotype. Although many highly complex models have been proposed, the major hurdle in deploying them clinically is their calibration and validation.

      In this talk, I will discuss the challenges related to the calibration and validation of biophysical models, and in particular the mathematical structure of the underlying inverse problems. I will also present a new algorithm that localizes the tumor origin within a few millimeters.

      4/1/2021
      10:00 – 11:00am ET
      Samory K. KpotufeTitle: From Theory to Clustering

      Abstract: Clustering is a basic problem in data analysis, consisting of partitioning data into meaningful groups called clusters. Practical clustering procedures tend to meet two criteria: flexibility in the shapes and number of clusters estimated, and efficient processing. While many practical procedures might meet either of these criteria in different applications, general guarantees often only hold for theoretical procedures that are hard if not impossible to implement. A main aim is to address this gap.
      We will discuss two recent approaches that compete with state-of-the-art procedures, while at the same time relying on rigorous analysis of clustering. The first approach fits within the framework of density-based clustering, a family of flexible clustering approaches. It builds primarily on theoretical insights on nearest-neighbor graphs, a geometric data structure shown to encode local information on the data density. The second approach speeds up kernel k-means, a popular Hilbert space embedding and clustering method. This more efficient approach relies on a new interpretation – and alternative use – of kernel-sketching as a geometry-preserving random projection in Hilbert space.
      Finally, we will present recent experimental results combining the benefits of both approaches in the IoT application domain.
      The talk is based on various works with collaborators Sanjoy Dasgupta, Kamalika Chaudhuri, Ulrike von Luxburg, Heinrich Jiang, Bharath Sriperumbudur, Kun Yang, and Nick Feamster.

      4/29/2021
      12:00 – 1:00pm ET
      Jonas Martin PetersTitle: Causality and Distribution Generalization

      Abstract: Purely predictive methods do not perform well when the test distribution changes too much from the training distribution. Causal models are known to be stable with respect to distributional shifts such as arbitrarily strong interventions on the covariates, but do not perform well when the test distribution differs only mildly from the training distribution. We discuss anchor regression, a framework that provides a trade-off between causal and predictive models. The method poses different (convex and non-convex) optimization problems and relates to methods that are tailored for instrumental variable settings. We show how similar principles can be used for inferring metabolic networks. If time allows, we discuss extensions to nonlinear models and theoretical limitations of such methodology.

      4/29/2021
      1:00 – 2:00pm ET
      Laura GrigoriTitle: Randomization and communication avoiding techniques for large scale linear algebra

      Abstract: In this talk we will discuss recent developments of randomization and communication avoiding techniques for solving large scale linear algebra operations. We will focus in particular on solving linear systems of equations and we will discuss a randomized process for orthogonalizing a set of vectors and its usage in GMRES, while also exploiting mixed precision.  We will also discuss a robust multilevel preconditioner that allows to further accelerate solving large scale linear systems on parallel computers.

    • Math Science Literature Lecture Series
      10:00 am-11:30 am
      12/01/2024

      Zhengwei Liu (Tsinghua University)

      Title: Subfactors–in Memory of Vaughan Jones

      Abstract: Jones initiated modern subfactor theory in early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial, for which Jones won the Fields Metal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed.

      Talk chair: Arthur Jaffe

      Slides | Video 

    • Swampland Seminar
      10:00 am-11:30 am
      12/01/2024

      Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

    • Quantum Matter
      10:00 am
      12/01/2024
      CMSA QMMP 03.03.23

      Quantum Matter Seminar

      Speaker: Anna Hasenfratz (University of Colorado)

      Title: Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions
      Abstract: 4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the conformal phase is well established, very little is known about the nature of the phase transition or the strong coupling phase.
      Lattice QCD methods can predict the RG $\beta$ function, but the calculations are often limited by non-physical bulk phase transition that prevent exploring the strong coupling region of the phase diagram. Even the critical flavor number is controversial, estimates vary between $N_f=8$ and 14 for fundamental fermions.
      Using an improved lattice actions that include heavy Pauli-Villars (PV) type bosons to reduce ultraviolet fluctuations, I was able to simulate an SU(3) system with 8 fundamental flavors at much stronger renormalized coupling than previously possibly. The numerical results indicate a smooth phase transition from weak coupling to a strongly coupled phase.
      I investigate the critical behavior of the transition using finite size scaling. The result of the scaling analysis is not consistent with a first order phase transition, but it is well described by   Berezinsky-Kosterlitz-Thouless or BKT scaling. BKT scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that warrants further investigations.
      The strongly coupled phase appear to be chirally symmetric but gapped, suggesting symmetric mass generation (SMG). This could be the consequence of the lattice fermions used in this study. Staggered fermions in the massless limit are known to be anomaly free, allowing an SMG phase in the continuum limit.

       


      References:
      Phys.Rev.D 106 (2022) 1, 014513 • e-Print: 2204.04801
      Phys.Rev.D 104 (2021) 7, 074509 • e-Print: 2109.02790
      For anomalies and staggered fermion, see
      Phys.Rev.D 104 (2021) 9, 094504 • e-Print: 2101.01026
      https://www.youtube.com/watch?v=3jtNsFGszjE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=14
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Xiao-Gang Wen (MIT)

      Title: A 6-year journey: from gravitational anomaly to a unified theory of generalized symmetry

      Abstract: Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topological-order correspondence. I will also discuss some applications of emergent generalized symmetry.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/16/2020 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Swampland Seminar
      10:00 am-11:30 am
      12/01/2024
      Speakers: Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)
      Title4d strings at strong coupling
      As usual, the format will be 45 min talk + 30 min discussion, to encourage participation from the audience.
      Looking forward to seeing you there!
    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      General Relativity Program Minicourses
      10:00 am-1:00 pm
      12/01/2024-05/17/2022
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Minicourses

      General Relativity Program Minicourses

      During the Spring 2022 semester, the CMSA hosted a program on General Relativity.

      This semester-long program included four minicourses running in March, April, and May;  a conference April 4–8, 2022;  and a workshop from May 2–5, 2022.

       

      ScheduleSpeakerTitleAbstract
      March 1 – 3, 2022
      10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
      Dr. Stefan CzimekCharacteristic Gluing for the Einstein EquationsAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).
      March 22 – 25, 2022
      22nd & 23rd, 10:00 am – 11:30am ET
      24th & 25th, 11:00 am – 12:30pm ET
      Location: Hybrid. CMSA main seminar room, G-10.
      Prof. Lan-Hsuan HuangExistence of Static Metrics with Prescribed Bartnik Boundary DataAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is

      1. The conjecture and an overview of the results
      2. Static regular: a sufficient condition for existence and local uniqueness
      3. Convex boundary, isometric embedding, and static regular
      4. Perturbations of any hypersurface are static regular

      Video on Youtube: March 22, 2022

      March 29 – April 1, 2022 10:00am – 12:00pm ET, each day

      Location: Hybrid. CMSA main seminar room, G-10.

      Prof. Martin TaylorThe nonlinear stability of the Schwarzschild family of black holesAbstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.
      April 19 & 21, 2022
      10 am – 12 pm ET, each dayZoom only
      Prof. Håkan AndréassonTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.

      Video 4/19/2022

      Video 4/22/2022

      May 16 – 17, 2022
      10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
      Prof. Marcelo DisconziA brief overview of recent developments in relativistic fluidsAbstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.

      1. Set-up, review of standard results, physical motivation.
      2. The relativistic Euler equations: null structures and the problem of shocks.
      3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
      4. Relativistic viscous fluids.

      Video 5/16/2022

      Video 5/17/2022

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: John Baez (University of California, Riverside)

      Title: Two of my favorite numbers: 8 and 24

      Abstract: The numbers 8 and 24 play special roles in mathematics. The number 8 is special because of Bott periodicity, the octonions and the E8 lattice, while 24 is special for many reasons, including the binary tetrahedral group, the 3rd stable homotopy group of spheres, and the Leech lattice. The number 8 does for superstring theory what the number 24 does for bosonic string theory. In this talk, which is intended to be entertaining, I will overview these matters and also some connections between the numbers 8 and 24.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 05.12.23

      Quantum Matter Seminar

      Speaker: Carolyn Zhang (U Chicago)

      Title: Anomalies of (1+1)D categorical symmetries

      Abstract: We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $A$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the \emph{electric} Lagrangian algebra, that describes a phase with $A$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $A$. We observe that if there exists a different gapped boundary, given by a \emph{magnetic} Lagrangian algebra, then there exists a gapped phase where $A$ is not spontaneously broken at all, which means that $A$ is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $A$ being anomaly-free. As an application, we consider the Drinfeld centers of $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.

      https://www.youtube.com/watch?v=hSzBMYEY_q8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=4

    • Swampland Seminar
      10:00 am-11:00 am
      12/01/2024

      Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 06.30.23

      Quantum Matter Seminar

      Speaker: Marieke Van Beest (SCGP)

      Title: Monopoles, Scattering, and Generalized Symmetries

      Abstract: In this talk, we will discuss the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle, as they can carry fractional quantum numbers. We argue that such outgoing particles live in the twisted sector of a topological co-dimension 1 surface, which ends topologically on the monopole. This symmetry defect is often non-invertible, and as such the outgoing radiation not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory, which is a new prediction.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 06.26.23

      Quantum Matter Seminar

      Title: Chiral fermionic CFTs of central charge ≤ 16

      Abstract: We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac’s theorem and bosonization/fermionization. This talk will discuss the derivation of this result, its application to the classification of non-supersymmetric heterotic string theories, and along the way we’ll address some oft-overlooked subtleties of bosonization from the point of view of anomalies and topological phases.

    • Quantum Matter
      10:00 am-12:00 pm
      12/01/2024
      CMSA QMMP 06.13.23

      Quantum Matter Seminar

      Speaker: Brandon C. Rayhaun (C. N. Yang ITP, Stony Brook University)

      Title: Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality

      Abstract: Conformal field theories in (1+1)D are key actors in many dramas of physics and mathematics. Their classification has therefore been an important and long-standing problem. In this talk, I will explain the main ideas behind the classification of (most) “small” bosonic CFTs. Here, I use the adjective “small” informally to refer to theories with low central charge (less than 24) and few primary operators (less than 5). Time and attention permitting, I will highlight two applications of this result. First, I will describe how it can be used in tandem with bosonization and fermionization techniques to establish the classification of chiral fermionic CFTs with central charge less than 23. Second, I will showcase how it can be used to bootstrap generalized global symmetries using the concept of “symmetry/subalgebra duality.”

      Talk based on arXiv:2208.05486 [hep-th] (joint work with Sunil Mukhi) and arXiv:2303.16921 [hep-th].

      https://www.youtube.com/watch?v=NrOcsiUmSh0&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=1&t=2s

       

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 03.24.23

      Quantum Matter Seminar

      Speaker: Alexander Zlokapa, MIT

      Title: Traversable wormhole dynamics on a quantum processor

      Abstract: The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

       

      https://www.youtube.com/watch?v=iYkVuju_sP8&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=11

    • CMSA EVENT: 2020 Big Data Conference (Virtual)
      10:00 am-2:05 pm
      12/01/2024-08/25/2020

      On August 24-25, 2020 the CMSA hosted our sixth annual Conference on Big Data. The Conference featured many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. The 2020 Big Data Conference took place virtually.

      Videos of the talks are available in this youtube playlist.

       

      Organizers: 

      • Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University
      • Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
      • Horng-Tzer Yau, Professor of Mathematics, Harvard University
      • Sergiy Verstyuk, CMSA, Harvard University

      Speakers:

      Schedule:
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/1/2021 Math Physics
      10:00 am-11:00 am
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/22/2021 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Cheryne Jonay (Stanford)

      Title: A Physical Theory of Two-stage Thermalization

      Abstract: One indication of thermalization time is subsystem entanglement reaching thermal values. Recent studies on local quantum circuits reveal two exponential stages with decay rates $r_1$ and $r_2$ of the purity before and after thermalization. We provide an entanglement membrane theory interpretation, with $r_1$ corresponding to the domain wall free energy. Circuit geometry can lead to $r_1 < r_2$, producing a “phantom eigenvalue”. Competition between the domain wall and magnon leads to $r_2 < r_1$ when the magnon prevails. However, when the domain wall wins, this mechanism provides a practical approach for measuring entanglement growth through local correlation functions.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 04.28.23

      Quantum Matter Seminar

      Title: Fracton Self-Statistics

      Speaker: Hao Song (ITP-CAS)

      Abstract: Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating other excitations are called fractons. Here we address a fundamental open question — can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged, and show their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of abelian fracton orders. Finally, we show the existence of semionic or fermionic fracton self-statistics in some twisted variants of the checkerboard model and Haah’s code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.

      References: H Song, N Tantivasadakarn, W Shirley, M Hermele, arXiv:2304.00028.

      https://www.youtube.com/watch?v=TBAEif9XVww&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=6

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 04.21.23 (1)

      Quantum Matter Seminar

      Speaker: Prof. Subir Sachdev (Harvard)

      Title: A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order

      Abstract: Soon after the discovery of high-temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low-temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the “pseudogap metal” phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.
      As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.
      This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Mathias S. Scheurer, and S. S., arXiv:2302.07885

      https://www.youtube.com/watch?v=ueT28iMdjzE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=7

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/12/2021 Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4/5/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/5/2021 Interdisciplinary Science Seminar
      10:00 am-11:00 am
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Pre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am

      Pre-talk Title: Introduction to the singularities of the MMP


      Speaker: Dori Bejleri (Harvard Math & CMSA)

      Title: Moduli of boundary polarized Calabi-Yau pairs

      Abstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher, H. Blum, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang.

       

       

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      20 Garden Street, Cambridge MA 02138
      CMSA QMMP 04.14.23

      Quantum Matter Seminar

      Speaker: Guanyu Zhu (IBM Quantum, T. J. Watson Research Center)

      Title: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries

      Abstract: Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects.

      References:
      1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua
      2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O&#39;Connor, Guanyu Zhu
      3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

       

      https://www.youtube.com/watch?v=APcDMMRI9VU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=8

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/8/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Mathematical Physics Seminar, Mondays
      10:00 am-11:00 am
      12/01/2024

      The seminar on mathematical physics will be held on Mondays from 10:00 – 11:00am ET on Zoom. Please email the seminar organizers to learn how toattend. This year’s Seminar will be organized by Yoosik Kim (yoosik@cmsa.fas.harvard.edu), Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu), and Yang Zhou (yangzhou@cmsa.fas.harvard.edu).

      Join the Math-Physics mailing list

      The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

      Spring 2021:

      DateSpeakerTitle/Abstract
      2/1/2021Choa Dongwook
      (KIAS)Video
      TitleFukaya category of Landau-Ginzburg orbifolds.

      Abstract: Landau-Ginzburg orbifold is just another name for a holomorphic function W with its abelian symmetry G. Its Fukaya category can be viewed as a categorification of a homology group of its Milnor fiber. In this introductory talk, we will start with some classical results on the topology of isolated singularities and its Fukaya-Seidel category. Then I will explain a new construction for such category to deal with a non-trivial symmetry group G. The main ingredients are classical variation map and the Reeb dynamics at the contact boundary. If time permits, I will show its application to mirror symmetry of LG orbifolds and its Milnor fiber. This is a joint work with C.-H. Cho and W. Jeong

      2/8/2021Jérémy Guéré (Fourier Institute)TitleCongruences on K-theoretic Gromov-Witten invariants

      Abstract: K-theoretic Gromov-Witten invariants of smooth projective varieties have been introduced by YP Lee, using the Euler characteristic of a virtual structure sheaf. In particular, they are integers. In this talk, I look at these invariants for the quintic threefold and I will explain how to compute them modulo 41, using the virtual localization formula under a finite group action, up to genus 19 and degree 40.

      2/15/2021Zhiwei Zheng (Max Planck Institute)

      Video

      Title: Some new results on automorphisms of hypersurfaces

      Abstract: It is natural to study automorphisms of hypersurfaces in projective spaces. In this talk, I will discuss a new approach to determine all possible orders of automorphisms of smooth hypersurfaces with fixed degree and dimension. Then we consider the specific case of cubic fourfolds, and discuss the relation with Hodge theory.

      2/22/2021Yu-Shen Lin (Boston University)

      Video

      TitleFull SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

      Abstract: Strominger–Yau–Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi–Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

      3/1/2021Carlos S. Shahbazi (Hamburg University)

      Video

      TitleMathematical supergravity and its applications to differential geometry.

      Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

      3/8/2021Miguel Moreira (ETH)

      Video

      TitleVirasoro constraints for stable pairs.

      Abstract: The theory of stable pairs (PT) with descendents, defined on a 3-fold X, is a sheaf theoretical curve counting theory. Conjecturally, it is equivalent to the Gromov-Witten (GW) theory of X via a universal (but intricate) transformation, so we can expect that the Virasoro conjecture on the GW side should have a parallel in the PT world. In joint work with A. Oblomkov, A. Okounkov, and R. Pandharipande, we formulated such a conjecture and proved it for toric 3-folds in the stationary case. The Hilbert scheme of points on a surface S might be regarded as a component of the moduli space of stable pairs on S x P1, and the Virasoro conjecture predicts a new set of relations satisfied by tautological classes on S[n] which can be proven by reduction to the toric case.

      3/15/2021Spring break
      3/22/2021Ying Xie (Shanghai Center for Mathematical Sciences)Title: Derived categories for Grassmannian flips

      Abstract: Flip is a fundamental surgery operation for constructing minimal models in higher-dimensional birational geometry. In this talk, I will introduce a series of flips from Lie theory and investigate their derived categories. This is a joint program with Conan Leung.

      3/29/2021Emanuel Scheidegger (Peking University)Title:  On the quantum K-theory of the quintic.

      Abstract: Quantum cohomology is a deformation of the cohomology of a projective variety governed by counts of stable maps from a curve into this variety. Quantum K-theory is in a similar way a deformation of K-theory but also of quantum cohomology, It has recently attracted attention in physics since a realization in a physical theory has been found. Currently, both the structure and examples in quantum K-theory are far less understood than in quantum cohomology.
      We will explain the properties of quantum K-theory in comparison with quantum cohomology, and we will discuss the examples of projective space and the quintic hypersurface in P^4.
      4/5/2021Gaëtan Borot (HU Berlin)

      Video

      TitleTopological recursion in 4d N = 2 supersymmetric gauge theories

      Abstract: According to the Alday-Gaiotto-Tachikawa conjecture (proved in this case by Schiffman and Vasserot), the instanton partition function in 4d N = 2 SU(r) supersymmetric gauge theory on P^2 with equivariant parameters \epsilon_1,\epsilon_2 is the norm of a Whittaker vector for W(gl_r) algebra. I will explain how these Whittaker vectors can be computed (at least perturbatively in the energy scale) by topological recursion for \epsilon_1 +\epsilon_2 = 0, and by a non-commutation version of the topological recursion in the Nekrasov-Shatashvili regime where \epsilon_1/\epsilon_2 is fixed. This is a joint work to appear with Bouchard, Chidambaram and Creutzig.

      4/12/2021Fei Yan (Rutgers)TitleNetworks and quantization

      Abstract: I will describe two quantization scenarios. The first scenario involves the construction of a quantum trace map computing a link “invariant” (with possible wall-crossing behavior) for links L in a 3-manifold M, where M is a Riemann surface C times a real line. This construction unifies the computation of familiar link invariant with the refined counting of framed BPS states for line defects in 4d N=2 theories of class S. Certain networks on C play an important role in the construction. The second scenario concerns the study of Schroedinger equations and their higher order analogues, which could arise in the quantization of Seiberg-Witten curves in 4d N=2 theories. Here similarly certain networks play an important part in the exact WKB analysis for these Schroedinger-like equations. At the end of my talk I will also try to sketch a possibility to bridge these two scenarios.

      4/19/2021Hazel Mak (Brown University)TitleBranching Rules and Young Tableaux Methods: 10D & 11D Supergravity

      Abstract: In this talk, I will review 4D, N = 1 off-shell supergravity. Then I present explorations to construct 10D and 11D supergravity theories in two steps. The first step is to decompose scalar superfield into Lorentz group representations which involves branching rules and related methods. Interpretations of component fields by Young tableaux methods will be presented. The second step is to implement an analogue of Breitenlohner’s approach for 4D supergravity to 10D and 11D theories.

      4/26/2021Owen Gwilliam (UMass. Amherst)

      Video

      TitleTopological-holomorphic field theories and their BV quantizations

      Abstract: Topological field theories and holomorphic field theories have each had a substantial impact in both physics and mathematics, so it is natural to consider theories that are hybrids of the two, which we call topological-holomorphic and denote as THFTs. Examples include Kapustin’s twist of N=2, D=4 supersymmetric Yang-Mills theory and Costello’s 4-dimensional Chern-Simons theory. In this talk about joint work with Rabinovich and Williams, I will define THFTs, describe several examples, and then explain how to quantize them rigorously and explicitly, by building on techniques of Si Li.  Time permitting, I will indicate how these results offer a novel perspective on the Gaudin model via 3-dimensional field theories.


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/14/2020Lino Amorim (Kansas State University)TitleNon-commutative Gromov-Witten invariants

      Abstract:  I will describe an analogue of Saito’s theory of primitive forms for Calabi-Yau A-infinity categories. Under some conditions on the Hochschild cohomology of the category, this construction recovers the (genus zero) Gromov-Witten invariants of a symplectic manifold from its Fukaya category. This includes many compact toric manifolds, in particular projective spaces.

      9/21/2020Yuhan Sun (Rutgers)Title: Displacement energy of Lagrangian 3-spheres

      Abstract:  We study local and global Hamiltonian dynamical behaviors of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that there is a one-parameter family of Lagrangian tori near S, which are nondisplaceable in X. When dim S = 3, we obtain a new estimate of the displacement energy of S, by estimating the displacement energy of a one-parameter family of Lagrangian tori near S.

      9/28/2020Shota Komatsu (CERN)Title: Wilson loops as matrix product states

      Abstract:  In this talk, I will discuss a reformulation of the Wilson loop in large N gauge theories in terms of matrix product states. The construction is motivated by the analysis of supersymmetric Wilson loops in the maximally super Yang–Mills theory in four dimensions, but can be applied to any other large N gauge theories and matrix models, although less effective. For the maximally super Yang–Mills theory, one can further perform the computation exactly as a function of ‘t Hooft coupling by combining our formulation with the relation to integrable spin chains.

      10/5/2020Ming Zhang (UBC)Title: Verlinde/Grassmannian correspondence and applications.

      Abstract: In the 90s’, Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten’s work by relating the $\text{GL}_{n}$ Verlinde numbers to the level $l$ quantum K-invariants of the Grassmannian $\text{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence.

      The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will discuss the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.  At the end of the talk, I will describe some applications of this correspondence.

      10/12/2020Cancelled -Columbus Day
      10/19/2020Ben Gammage (Harvard)Title3d mirror symmetry for abelian gauge groups

      Abstract: 3d mirror symmetry is a proposed duality relating a pair of 3-dimensional supersymmetric gauge theories. Various consequences of this duality have been heavily explored by representation theorists in recent years, under the name of “symplectic duality”. In joint work in progress with Justin Hilburn, for the case of abelian gauge groups, we provide a fully mathematical explanation of this duality in the form of an equivalence of 2-categories of boundary conditions for topological twists of these theories. We will also discuss some applications to homological mirror symmetry and geometric Langlands duality.

      10/26/2020Cancelled
      11/2/2020Haoyu Sun (Berkeley)TitleDouble-Janus linear sigma models and generalized quadratic reciprocity

      Abstract: We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d N=4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T^2 fibered over S^1) times a circle with an SL(2,Z) duality wall inserted on S^1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2,Z), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
      11/9/2020An Huang (Brandeis)Titlep-adic strings, Einstein equations, Green’s functions, and Tate’s thesis

      Abstract: I shall discuss a recent work on how p-adic strings can produce perturbative quantum gravity, and an adelic physics interpretation of Tate’s thesis.
      11/16/2020
      10:00am ET
      Matt Kerr (WUSTL)Title:  Differential equations and mixed Hodge structures

      Abstract: We report on a new development in asymptotic Hodge theory, arising from work of Golyshev–Zagier and Bloch–Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry.  The talk will focus exclusively on the Hodge/period-theoretic aspects through two main examples.
      Given a variation of Hodge structure M on a Zariski open in P^1, the periods of the limiting mixed Hodge structures at the punctures are interesting invariants of M.  More generally, one can try to compute these asymptotic invariants for iterated extensions of M by “Tate objects”, which may arise for example from normal functions associated to algebraic cycles. The main point of the talk will be that (with suitable assumptions on M) these invariants are encoded in an entire function called the motivic Gamma function, which is determined by the Picard-Fuchs operator L underlying M. In particular, when L is hypergeometric, this is easy to compute and we get a closed-form answer (and a limiting motive).  In the non-hypergeometric setting, it yields predictions for special values of normal functions; this part of the story is joint with V. Golyshev and T. Sasaki.

      11/23/2020

      11:30am ET

      Kyoung-Seog Lee (U of Miami)TitleDerived categories and motives of moduli spaces of vector bundles on curves

      Abstract: Derived categories and motives are important invariants of algebraic varieties invented by Grothendieck and his collaborators around 1960s. In 2005, Orlov conjectured that they will be closely related and now there are several evidences supporting his conjecture. On the other hand, moduli spaces of vector bundles on curves provide attractive and important examples of algebraic varieties and there have been intensive works studying them. In this talk, I will discuss derived categories and motives of moduli spaces of vector bundles on curves. This talk is based on joint works with I. Biswas and T. Gomez.

      11/30/2020Zijun Zhou (IPMU)Title: 3d N=2 toric mirror symmetry and quantum K-theory

      Abstract: In this talk, I will introduce a new construction for the K-theoretic mirror symmetry of toric varieties/stacks, based on the 3d N=2 mirror symmetry introduced by Dorey-Tong. Given the toric datum, i.e. a  short exact sequence 0 -> Z^k -> Z^n -> Z^{n-k} -> 0, we consider the toric Artin stack of the form [C^n / (C^*)^k]. Its mirror is constructed by taking the Gale dual of the defining short exact sequence. As an analogue of the 3d N=4 case, we consider the K-theoretic I-function, with a suitable level structure, defined by counting parameterized quasimaps from P^1. Under mirror symmetry, the I-functions of a mirror pair are related to each other under the mirror map, which exchanges the K\”ahler and equivariant parameters, and maps q to q^{-1}. This is joint work with Yongbin Ruan and Yaoxiong Wen.

      12/7/2020Thomas Grimm (Utrecht)TitleModuli Space Holography and the Finiteness of Flux Vacua

      Abstract: In this talk I describe a holographic perspective to study field spaces that arise in string compactifications. The constructions are motivated by a general description of the asymptotic, near-boundary regions in complex structure moduli spaces of Calabi-Yau manifolds using asymptotic Hodge theory. For real two-dimensional field spaces, I introduce an auxiliary bulk theory and describe aspects of an associated sl(2) boundary theory. The bulk reconstruction from the boundary data is provided by the sl(2)-orbit theorem of Schmid and Cattani, Kaplan, Schmid, which is a famous and general result in Hodge theory. I then apply this correspondence to the flux landscape of Calabi-Yau fourfold compactifications and discuss how this allows us, in work with C. Schnell, to prove that the number of self-dual flux vacua is finite

      For a listing of previous Mathematical Physics Seminars, please click here.

    • Seminars
      Seminars Colloquia & Seminar
      Social Science Applications Forum
      10:00 am-11:00 am
      12/01/2024

      During the Summer of 2020, the CMSA will be hosting a periodic Social Science Applications Seminar.

      The list of speakers is below and will be updated as details are confirmed.

      For a list of past Social Science Applications talks, please click here.
      DateSpeakerTitle/Abstract
      7/13/2020 10:00-11:00am ETLudovic Tangpi (Princeton)Please note, this seminar will take place online using Zoom.

      Title: Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls

      Abstract: This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in non-cooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space.
      For security reasons, you will have to show your full name to join the meeting.

      7/27/2020
      10:00pm
      Michael Ewens (Caltech)Please note, this seminar will take place online using Zoom.

      Title: Measuring Intangible Capital with Market Prices

      Abstract: Despite the importance of intangibles in today’s economy, current standards prohibit the capitalization of internally created knowledge and organizational capital, resulting in a downward bias of reported assets. As a result, researchers estimate this value by capitalizing prior flows of R&D and SG&A. In doing so, a set of capitalization parameters, i.e. the R&D depreciation rate and the fraction of SG&A that represents a long-lived asset, must be assumed. Parameters now in use are derived from models with strong assumptions or are ad hoc. We develop a capitalization model that motivates the use of market prices of intangibles to estimate these parameters. Two settings provide intangible asset values: (1) publicly traded equity prices and (2) acquisition prices. We use these parameters to estimate intangible capital stocks and subject them to an extensive set of diagnostic analyses that compare them with stocks estimated using existing parameters. Intangible stocks developed from exit price parameters outperform both stocks developed by publicly traded parameters and those stocks developed with existing estimates. (Joint work with Ryan Peters and Sean Wang.)

    • Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

       

      Speaker: Carlos S. Shahbazi (Hamburg University)

      Title: Mathematical supergravity and its applications to differential geometry

      Abstract: I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of four-dimensional ungauged supergravity and its Killing spinor equations in a differential-geometric framework.  I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA QMMP 04.07.23

      Quantum Matter Seminar

      Speaker: Nishad Maskara (Harvard)

      Title: Enhancing Detection of Topological Order by Local Error Correction

      Abstract: The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator.  Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.

       

      https://www.youtube.com/watch?v=oWIelx6_taU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=9

    • Algebraic Geometry in String Theory Seminar
      10:00 am-11:00 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA AGST Seminar 04.03.2023

      Algebraic Geometry in String Theory Seminar

      Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse

      Title: Kähler-Einstein metrics on families of Fano varieties

      Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.

    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Nat Tantivasadakarn (Caltech)

      Title: From wave-function collapse and Galois solvability to the realization of non-Abelian topological order on a quantum device

      Abstract: I will review our recent set of theoretical works on efficiently preparing long range quantum entanglement with adaptive quantum circuits: the combination of measurements with unitary gates whose choice can depend on previous measurement outcomes. I will show that this additional ingredient can be leveraged to prepare the long sought-after non-Abelian topological phases with a circuit depth that is independent of system size. Using this framework, we uncover a complexity hierarchy of long-range entangled states based on the minimal number of measurement layers required to create the state. Moreover, we find that certain non-Abelian states that cannot be efficiently prepared with adaptive circuits have a surprising connection to the unsolvability of the quintic polynomial.

      Finally, I will describe our recent collaboration with Quantinuum where we present the first unambiguous realization of non-Abelian D4 topological order and demonstrate control of its anyons. In particular, we are able to detect a non-trivial braiding where three non-Abelian anyons trace out the Borromean rings in spacetime, a signature unique to non-Abelian topological order.

    • Mathematical Physics Seminar
      10:00 am-11:00 am
      12/01/2024

      Speaker: Yu-Shen Lin (Boston University)

      Title: Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

      Abstract: Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi-Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/15/2021 Math Physics Seminar
      10:00 am-11:00 am
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Quantum Matter Seminar

      Speaker: Abijith Krishnan (MIT)

      Title: A Plane Defect in the 3d O(N) Model

      Abstract: It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

       

      https://www.youtube.com/watch?v=6cDK3TJ_H8w&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=10

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      2/10/2021 Strongly Correlated Quantum Materials
      10:00 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:00 am-11:30 am
      12/01/2024
      CMSA QMMP 06.09.23

      Quantum Matter Seminar

      Speakers: Gerald Höhn (Kansas State University) & Sven Möller (University of Hamburg)

      Title: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24

      Abstract: We discuss the classfication of self-dual vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely chiral 2-dimensional fermionic conformal field theories with just one primary field.

      There are exactly 969 such SVOAs under suitable regularity assumptions and the assumption that the shorter moonshine module VB^# is the unique self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1 spaces vanish.

      We construct and classify the self-dual SVOAs by determining the 2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central charge 24 and also by realising them as simple-current extensions of a dual pair containing a certain maximal lattice VOA. We show that all SVOAs besides VB^# x F and potential fake copies thereof stem from elements of the Conway group Co_0, the automorphism group of the Leech lattice.

      By splitting off free fermions F, if possible, we obtain the classification for all central charges less than or equal to 24.
      Reference: G. Höhn, S. Möller, arXiv:2303.17190.

      https://www.youtube.com/watch?v=U0alYxX05xU&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=2

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Previous Random Matrix & Probability Theory Seminars
      10:26 am-10:27 am
      12/01/2024

      Spring 2020:

      DateSpeakerTitle/Abstract
      2/26/2020Louigi Addario-Berry (McGill University)Title: Hipster random walks and their ilk 

      Abstract: I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.

      4/1/2020Ian Jauslin (Princeton)This meeting will be taking place virtually on Zoom.

      Title: A simplified approach to interacting Bose gases
      Abstract: I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.

      4/22/2020Martin Gebert (UC Davis)This meeting will be taking place virtually on Zoom.

      TitleLieb-Robinson bounds for a class of continuum many-body fermion systems

      Abstract: We introduce a class of UV-regularized two-body interactions for
      fermions in $\R^d$ and prove a Lieb-Robinson estimate for the dynamics
      of this class of many-body systems. As a step towards this result, we
      also prove a propagation bound of Lieb-Robinson type for continuum
      one-particle Schr\“odinger operators. We apply the propagation bound to
      prove the existence of a strongly continuous infinite-volume dynamics on
      the CAR algebra.

      4/29/2020Marcin Napiórkowski (University of Warsaw)This meeting will be taking place virtually on Zoom.

      TitleFree energy asymptotics of the quantum Heisenberg spin chain

      Abstract: Spin wave theory suggests that low temperature properties of the Heisenberg model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction. Based on joint work with Robert Seiringer.

      5/6/2020Antti Knowles (University of Geneva)TitleField theory as a limit of interacting quantum Bose gases

      Abstract: We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the mean-field limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions d = 1,2,3. For d > 1 the Gibbs measure is supported on distributions of negative regularity and we have to renormalize the interaction. The proof is based on a functional integral representation of the grand canonical Gibbs state, in which convergence to the mean-field limit follows formally from an infinite-dimensional stationary phase argument for ill-defined non-Gaussian measures. We make this argument rigorous by introducing a white-noise-type auxiliary field, through which the functional integral is expressed in terms of propagators of heat equations driven by time-dependent periodic random potentials. Joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.
      5/13/2020Sven Bachmann (University of British Columbia)TitleQuantized quantum transport and Abelian anyons

      Abstract: I’ll discuss recent developments in the study of quantized quantum transport, focussing on the quantum Hall effect. Beyond presenting an index taking rational values, and which is the Hall conductance in the adapted setting, I will explain how the index is intimately paired with the existence of quasi-particle excitations having non-trivial braiding properties.

      5/20/2020Kristina Schubert (TU Dortmund)TitleFluctuation Results for General Ising Models — Block Spin Ising Models and Random Interactions

      Abstract: Starting from the classical Curie-Weiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins in which the vertices are divided into a finite number of blocks and where pair interactions are given according to their blocks. The magnetization is then the vector of magnetizations within each block, and we are interested in its behaviour and in particular in its fluctuations. On the other hand, we consider Ising models on Erdős-Rényi random graphs. Here, I will also present results on the fluctuations of the magnetization.

       

      Fall 2019:

      DateSpeakerTitle/Abstract
      9/11/2019Subhabrata SenTitle: Sampling convergence for random graphs: graphexes and multigraphexes

      Abstract: We will look at structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs, Chayes, Cohn and Veitch ’17). Sam- pling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We will introduce this framework and motivate the components of a graphex. Subsequently, we will discuss the graphex limit for several well-known sparse random (multi)graph models. This is based on joint work with Christian Borgs, Jennifer Chayes, and Souvik Dhara.

      9/25/2019Jeff Schenker (Michigan State)Title: An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states  

      Abstract: Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one — “entanglement breaking’’ – channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh)

      10/3/2019

       

      Thursday

      4:30pm

      Jian Ding (UPenn)Title: Distances associated with Liouville quantum gravity

      Abstract: I will review some recent progresses on distances associated with Liouville quantum gravity, which is a random measure obtained from exponentiating a planar Gaussian free field.

      The talk is based on works with Julien Dubédat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne, Ofer Zeitouni and Fuxi Zhang in various combinations.

      10/9/2019Ruth Williams (UCSD)Title: Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

      Abstract: Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy. It has been a standing problem to prove stability of this general model when the average load on the system is less than the network’s capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and indicate how to prove stability of the fluid model under mild conditions.

      This talk is based on joint work with Yingjia Fu.

      10/11/2019Cancelled
      10/16/2019Wei-Kuo Chen (University of Minnesota)Title: The generalized TAP free energy

      Abstract: Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag.

      10/23/2019Souvik Dhara (MIT)Title: A new universality class for critical percolation on networks with heavy-tailed degrees

      Abstract: The talk concerns critical behavior of percolation on finite random networks with heavy-tailed degree distribution. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdős-Rényi random graph. Subsequently, there has been a surge in the literature identifying two universality classes for the critical behavior depending on whether the asymptotic degree distribution has a finite or infinite third moment.

      In this talk, we will present a completely new universality class that arises in the context of degrees having infinite second moment. Specifically, the scaling limit of the rescaled component sizes is different from the general description of multiplicative coalescent given by Aldous and Limic (1998). Moreover, the study of critical behavior in this regime exhibits several surprising features that have never been observed in any other universality classes so far.

      This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden.

      10/30/2019Aram Harrow (MIT)Title: Random quantum circuits, phase transitions and complexity

      Abstract: Random unitary dynamics are a toy model for chaotic quantum dynamics and also have applications to quantum information theory and computing. Recently, random quantum circuits were the basis of Google’s announcement of “quantum computational supremacy,” meaning performing a task on a programmable quantum computer that would difficult or infeasible for any classical computer. Google’s approach is based on the conjecture that random circuits are as hard to classical computers to simulate as a worst-case quantum computation would be. I will describe evidence in favor of this conjecture for deep random circuits and against this conjecture for shallow random circuits. (Deep/shallow refers to the number of time steps of the quantum circuit.) For deep random circuits in Euclidean geometries, we show that quantum dynamics match the first few moments of the Haar measure after roughly the amount of time needed for a signal to propagate from one side of the system to the other. In non-Euclidean geometries, such as the Schwarzschild metric in the vicinity of a black hole, this turns out not to be always true. I will also explain how shallow quantum circuits are easier to simulate when the gates are randomly chosen than in the worst case. This uses a simulation algorithm based on tensor contraction which is analyzed in terms of an associated stat mech model.

      This is based on joint work with Saeed Mehraban (1809.06957) and with John Napp, Rolando La Placa, Alex Dalzell and Fernando Brandao (to appear).

      11/6/2019Bruno Nachtergaele (UC Davis)TitleThe transmission time and local integrals of motion for disordered spin chains

      Abstract:  We investigate the relationship between zero-velocity Lieb-Robinson bounds and the existence of local integrals of motion (LIOMs) for disordered quantum spin chains. We also study the effect of dilute random perturbations on the dynamics of many-body localized spin chains. Using a notion of transmission time for propagation in quantum lattice systems we demonstrate slow propagation by proving a lower bound for the transmission time. This result can be interpreted as a robustness property of slow transport in one dimension. (Joint work with Jake Reschke)

      11/13/2019Gourab Ray (University of Victoria)Title: Logarithmic variance of height function of square-iceAbstract: A homomorphism height function on a finite graph is a integer-valued function on the set of vertices constrained to have adjacent vertices take adjacent integer values. We consider the uniform distribution over all such functions defined on a finite subgraph of Z^2 with predetermined values at some fixed boundary vertices. This model is equivalent to the height function of the six-vertex model with a = b = c = 1, i.e. to the height function of square-ice. Our main result is that in a subgraph of Z^2 with zero boundary conditions, the variance grows logarithmically in the distance to the boundary. This establishes a strong form of roughness of the planar uniform homomorphisms.

       

      Joint work with: Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran Raoufi.

      11/20/2019Vishesh Jain (MIT)Title: A combinatorial approach to the quantitative invertibility of random matrices.

       

      Abstract: Abstract: Let $s_n(M_n)$ denote the smallest singular value of an $n\times n$ random matrix $M_n$. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood–Offord theory or net arguments) for obtaining upper bounds on the probability that $s_n(M_n)$ is smaller than $\eta \geq 0$ for quite general random matrix models. Such estimates are a fundamental part of the non-asymptotic theory of random matrices and have applications to the strong circular law, numerical linear algebra etc. In several cases of interest, our approach provides stronger bounds than those obtained by Tao and Vu using inverse Littlewood–Offord theory.

       

       

       

      2018-2019

      DateSpeakerTitle/Abstract
      9/28/2018

      *Friday, 10:00am*

      Yash Deshpande (MIT)Title: Estimating low-rank matrices in noise: phase transitions from spin glass theory

      Abstract: Estimating low-rank matrices from noisy observations is a common task in statistical and engineering applications. Following the seminal work of Johnstone, Baik, Ben-Arous and Peche, versions of this problem have been extensively studied using random matrix theory. In this talk, we will consider an alternative viewpoint based on tools from mean field spin glasses. We will present two examples that illustrate how these tools yield information beyond those from classical random matrix theory. The first example is the two-groups stochastic block model (SBM), where we will obtain a full information-theoretic understanding of the estimation phase transition. In the second example, we will augment the SBM with covariate information at nodes, and obtain results on the altered phase transition.

      This is based on joint works with Emmanuel Abbe, Andrea Montanari, Elchanan Mossel and Subhabrata Sen.

      10/3/2018Ian Jauslin (IAS)Title: Liquid Crystals and the Heilmann-Lieb model

      Abstract: In 1979, O.Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb.

      10/10/2018Afonso Bandeira (NYUTitle: Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment

      Abstract: Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions and orientations; Cryo-Electron Microscopy (Cryo-EM) imaging where projections of a molecule density are taken from unknown rotations, and several others.

      One fundamental example of this type of problems is Multi-Reference Alignment: Given a group acting in a space, the goal is to estimate an orbit of the group action from noisy samples. For example, in one of its simplest forms, one is tasked with estimating a signal from noisy cyclically shifted copies. We will show that the number of observations needed by any method has a surprising dependency on the signal-to-noise ratio (SNR), and algebraic properties of the underlying group action. Remarkably, in some important cases, this sample complexity is achieved with computationally efficient methods based on computing invariants under the group of transformations.

      10/17/2018

      3:30pm

      Thomas Chen (UT Austin)Title: Dynamics of a heavy quantum tracer particle in a Bose gas

      Abstract: We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R^3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit where N tends to infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. This is joint work with Avy Soffer (Rutgers University).

      10/24/2018

      *Room G02*

      Tselil Schramm (Harvard/MIT)Title: (Nearly) Efficient Algorithms for the Graph Matching Problem in Correlated Random Graphs

      Abstract: The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known.

      Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng.

      10/30/2018

      *Tuesday

      10:30am

      SC 507*

      Lauren Williams (Harvard)Title: Introduction to the asymmetric simple exclusion process (from a combinatorialist’s point of view)

      Abstract: The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, subject to the condition that there is at most one particle per site. This model was introduced in 1970 by biologists (as a model for translation in protein synthesis) but has since been shown to display a rich mathematical structure. There are many variants of the model — e.g. the lattice could be a ring, or a line with open boundaries. One can also allow multiple species of particles with different “weights.” I will explain how one can give combinatorial formulas for the stationary distribution using various kinds of tableaux. I will also explain how the ASEP is related to interesting families of orthogonal polynomials, including Askey-Wilson polynomials, Koornwinder polynomials, and Macdonald polynomials.

      11/7/2018Willhelm Schlag (Yale)Title: on the Bourgain-Dyatlov fractal uncertainty principle

      Abstract: We will present the Bourgain-Dyatlov theorem on the line, it’s connection with other uncertainty principles in harmonic analysis, and my recent partial progress with Rui Han on the problem of higher dimensions.

      11/14/2018David Gamarnik (MIT)Title: Two Algorithmic Hardness Results in Spin Glasses and Compressive Sensing.

      Abstract: I will discuss two computational problems in the area of random combinatorial structures. The first one is the problem of computing the partition function of a Sherrington-Kirkpatrick spin glass model. While the the problem of computing the partition functions associated with arbitrary instances is known to belong to the #P complexity class, the complexity of the problem for random instances is open. We show that the problem of computing the partition function exactly (in an appropriate sense) for the case of instances involving Gaussian couplings is #P-hard on average. The proof uses Lipton’s trick of computation modulo large prime number, reduction of the average case to the worst case instances, and the near uniformity of the ”stretched” log-normal distribution.

      In the second part we will discuss the problem of explicit construction of matrices satisfying the Restricted Isometry Property (RIP). This challenge arises in the field of compressive sensing. While random matrices are known to satisfy the RIP with high probability, the problem of explicit (deterministic) construction of RIP matrices eluded efforts and hits the so-called ”square root” barrier which I will discuss in the talk. Overcoming this barrier is an open problem explored widely in the literature. We essentially resolve this problem by showing that an explicit construction of RIP matrices implies an explicit construction of graphs satisfying a very strong form of Ramsey property, which has been open since the seminal work of Erdos in 1947.

      11/28/2018Sean O’ Rourke (UC Boulder)Title: Universality and least singular values of random matrix products

      Abstract: We consider the product of m independent iid random matrices as m is fixed and the sizes of the matrices tend to infinity.  In the case when the factor matrices are drawn from the complex Ginibre ensemble, Akemann and Burda computed the limiting microscopic correlation functions.  In particular, away from the origin, they showed that the limiting correlation functions do not depend on m, the number of factor matrices. We show that this behavior is universal for products of iid random matrices under a moment matching hypothesis.  In addition, we establish universality results for the linear statistics for these product models, which show that the limiting variance does not depend on the number of factor matrices either. The proofs of these universality results require a near-optimal lower bound on the least singular value for these product ensembles.

      12/5/2018

      *Room G02*

      Omer Angel (UBC)Title: balanced excited random walks

      Abstract: I will present results on the scaling limit and asymptotics of the balanced excited random walk and related processes. This is a walk the that moves vertically on the first visit to a vertex, and horizontally on every subsequent visit. We also analyze certain versions of “clairvoyant scheduling” of random walks.

      Joint work with Mark Holmes and Alejandro Ramirez.

      2/7/2019

      Science Center 530

      Ramis Movassagh (IMB Research)Title: Generic Gaplessness, and Hamiltonian density of states from free probability theory

      Abstract: Quantum many-body systems usually reside in their lowest energy states. This among other things, motives understanding the gap, which is generally an undecidable problem. Nevertheless, we prove that generically local quantum Hamiltonians are gapless in any dimension and on any graph with bounded maximum degree.

      We then provide an applied and approximate answer to an old problem in pure mathematics. Suppose the eigenvalue distributions of two matrices M_1 and M_2 are known. What is the eigenvalue distribution of the sum M_1+M_2? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions. We will describe FPT and show examples of its powers for approximating physical quantities such as the density of states of the Anderson model, quantum spin chains, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly (provably NP-hard). Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in fresh new contexts.

      2/14/2019Nike Sun (MIT)Title: Capacity lower bound for the Ising perceptron

      Abstract: The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results.

      2/21/2019Michael Loss (Georgia Tech)Title: Some results for functionals of Aharonov-Bohm type

      Abstract: In this talk I present some variational problems of Aharonov-Bohm type, i.e., they include a  magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a  variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.

      3/6/2019

      4:15pm

      Science Center 411

      Ilya Kachkovskiy (Michigan State University)Title: Localization and delocalization for interacting 1D quasiperiodic particles.

      Abstract: We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large coupling localization depends on symmetries of the single-particle potential. If the potential has no cosine-type symmetries, then we are able to show large coupling localization at all energies, even if the interaction is not small (with some assumptions on its complexity). If symmetries are present, we can show localization away from finitely many energies, thus removing a fraction of spectrum from consideration. We also demonstrate that, in the symmetric case, delocalization can indeed happen if the interaction is strong, at the energies away from the bulk spectrum. The result is based on joint works with Jean Bourgain and Svetlana Jitomirskaya.

      3/14/2019

      5:45pm

      Science Center 232

      Anna Vershynina (University of Houston)Title: How fast can entanglement be generated in quantum systems?

      Abstract: We investigate the maximal rate at which entanglement can be generated in bipartite quantum systems. The goal is to upper bound this rate. All previous results in closed systems considered entanglement entropy as a measure of entanglement. I will present recent results, where entanglement measure can be chosen from a large class of measures. The result is derived from a general bound on the trace-norm of a commutator, and can, for example, be applied to bound the entanglement rate for Renyi and Tsallis entanglement entropies.

      3/28/2019

      Room G02

      Xuwen Chen (University of Rochester)Title: The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics

      Abstract: We derive the 3D energy-critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. We develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false sharp trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new HUFL (hierarchical uniform frequency localization) property for the GP hierarchy and use it to prove a new type of uniqueness theorem.

      4/4/2019Paul Bourgade (NYU)Title: Log-correlations and branching structures in analytic number theory

      Abstract: Fyodorov, Hiary and Keating have predicted the size of local maxima of L-function along the critical axis, based on analogous random matrix statistics. I will explain this prediction in the context of the log-correlated universality class and branching structures. In particular I will explain why the Riemann zeta function exhibits log-correlations, and outline the proof for the leading order of the maximum in the Fyodorov, Hiary and Keating prediction. Joint work with Arguin, Belius, Radziwill and Soundararajan.

      4/9/2019

      Tuesday

      12:00pm

      Room G02

      Giulio Biroli (ENS Paris)Title: Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices

      Abstract: I consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. I will show how to obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $\theta>1$, in large deviations characterized by a small value of $u$, i.e. $u<1-1/\theta$, the second-largest eigenvalue pops out from the Wigner semi-circle and the associated eigenvector orients in the direction corresponding to the rank-one perturbation. These results can be generalized to the Wishart Ensemble, and extended to the first $n$ eigenvalues and the associated eigenvectors.

      Finally, I will discuss motivations and applications of these results to the study of the geometric properties of random high-dimensional functions—a topic that is currently attracting a lot of attention in physics and computer science.

      4/11/2019Rui Han (Georgia Tech)Title: Spectral gaps in graphene structures

      Abstract: We present a full analysis of the spectrum of graphene in magnetic fields with constant flux through every hexagonal comb. In particular, we provide a rigorous foundation for self-similarity by showing that for irrational flux, the spectrum of graphene is a zero measure Cantor set. We also show that for vanishing flux, the spectral bands have nontrivial overlap, which proves the discrete Bethe-Sommerfeld conjecture for the graphene structure. This is based on joint works with S. Becker, J. Fillman and S. Jitomirskaya.

      4/25/2019Benjamin Fehrman (Oxford)Title:  Pathwise well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

      Abstract:  We present a pathwise well-posedness theory for stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise.  Such equations arise in the theory of mean field games, approximate the Dean-Kawasaki equation in fluctuating fluid dynamics, describe the fluctuating hydrodynamics of the zero range process, and model the evolution of a thin film in the regime of negligible surface tension.  Motivated by the theory of stochastic viscosity solutions, we pass to the equation’s kinetic formulation, where the noise enters linearly and can be inverted using the theory of rough paths. The talk is based on joint work with Benjamin Gess.

      4/30/2019TBATBA
      5/2/2019Jian Ding (UPenn)TBA

      2017-2018

      Date…………Name…………….Title/Abstract
      2-16-20183:30pm

      G02

      Reza Gheissari (NYU)Dynamics of Critical 2D Potts ModelsAbstract: The Potts model is a generalization of the Ising model to $q\geq 3$ states with inverse temperature $\beta$. The Gibbs measure on $\mathbb Z^2$ has a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the phase transition is continuous while when $q>4$, the phase transition is discontinuous and the disordered and ordered phases coexist.

      We will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat bath/Metropolis) for the 2D Potts model, where the mixing time on an $n \times n$ torus should transition from $O(\log n)$ at high temperatures to $\exp(c_\beta n)$ at low temperatures, via a critical slowdown at $\beta_c(q)$ that is polynomial in $n$ when $q \leq 4$ and exponential in $n$ when $q>4$.

      2-23-20183:30pm

      G02

      Mustazee Rahman (MIT)On shocks in the TASEPAbstract: The TASEP particle system runs into traffic jams when the particle density to the left is smaller than the density to the right. Macroscopically, the particle density solves Burgers’ equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP shock whereby we identify the microscopic fluctuations around the shock by using exact formulas for the correlation functions of TASEP and its KPZ scaling limit. The resulting laws are related to universal laws of random matrix theory.

      For the curious, here is a video of the shock forming in Burgers’ equation:

      4-20-20182:00-3:00pmCarlo Lucibello(Microsoft Research NE)The Random Perceptron Problem: thresholds, phase transitions, and geometryAbstract: The perceptron is the simplest feedforward neural network model, the building block of the deep architectures used in modern machine learning practice. In this talk, I will review some old and new results, mostly focusing on the case of binary weights and random examples. Despite its simplicity, this model provides an extremely rich phenomenology: as the number of examples per synapses is increased, the system undergoes different phase transitions, which can be directly linked to solvers’ performances and to information theoretic bounds. A geometrical analysis of the solution space shows how two different types of solutions, akin to wide and sharp minima, have different generalization capabilities when presented with new examples.  Solutions in dense clusters generalize remarkably better,  partially closing the gap with Bayesian optimal estimators.  Most of the results I will present were first obtained using non rigorous techniques from spin glass theory and many of them haven’t been rigorously established yet,  although some big steps forward have been taken in recent years.
      4-20-20183:00-4:00pmYash Despande(MIT)Phase transitions in estimating low-rank matricesAbstract: Low-rank perturbations of Wigner matrices have been extensively studied in random matrix theory; much information about the corresponding spectral phase transition can be gleaned using these tools. In this talk, I will consider an alternative viewpoint based on tools from spin glass theory, and two examples that illustrate how these they yield information beyond traditional spectral tools. The first example is the stochastic block model,where we obtain a full information-theoretic picture of estimation. The second example demonstrates how side information alters the spectral threshold. It involves a new phase transition that interpolates between the Wigner and Wishart ensembles.
      DateNameTitle/Abstract
      9-27-17Herbert Spohn, Technische Universität MünchenHydrodynamics of integrable classical and quantum systems

      Abstract:  In the cold atoms community there is great interest in developing Euler-type hydrodynamics for one-dimensional integrable quantum systems, in particular with application to domain wall initial states.  I provide some mathematical physics background and also compare with integrable classical systems.

      10-23-17

      *12:00-1:00pm, Science Center 232*

       Madhu Sudan, Harvard SEASGeneral Strong Polarization

      A recent discovery (circa 2008) in information theory called Polar Coding has led to a remarkable construction of error-correcting codes and decoding algorithms, resolving one of the fundamental algorithmic challenges in the field. The underlying phenomenon studies the “polarization” of a “bounded” martingale. A bounded martingale, X_0,…,X_t,…  is one where X_t in [0,1]. This martingale is said to polarize if Pr[lim_{t\to infty} X_t \in {0,1}] = 1. The questions of interest to the results in coding are the rate of convergence and proximity: Specifically, given epsilon and tau > 0 what is the smallest t after which it is the case that Pr[X_t in (tau,1-tau)] < epsilon? For the main theorem, it was crucial that t <= min{O(log(1/epsilon)), o(log(1/tau))}. We say that a martingale polarizes strongly if it satisfies this requirement. We give a simple local criterion on the evolution of the martingale that suffices for strong polarization. A consequence to coding theory is that a broad class of constructions of polar codes can be used to resolve the afore-mentioned algorithmic challenge.

      In this talk I will introduce the concepts of polarization and strong polarization.  Depending on the audience interest I can explain why this concept is useful to construct codes and decoding algorithms, or explain the local criteria that help establish strong polarization (and the proof of why it does so).

      Based on joint work with Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, and Atri Rudra.

      10-25-17

      *2:00-4:00pm*

      Subhabrata Sen (Microsoft and MIT)

      Noga Alon,(Tel Aviv University)

      Subhabrata Sen, “Partitioning sparse random graphs: connections with mean-field spin glasses”

      Abstract: The study of graph-partition problems such as Maxcut, max-bisection and min-bisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cut-sizes on sparse Erd\ ̋{o}s-R\'{e}nyi and random regular graphs.

      Based on joint work with Aukosh Jagannath.

      Noga Alon, “Random Cayley Graphs”

      Abstract: The study of random Cayley graphs of finite groups is related to the  investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given  group with a prescribed number of generators.  Several intriguing questions that remain open will be mentioned as well.

      11-1-17

      *2:00-4:00pm*

      Kay Kirkpatrick (Illinois)

      and

      Wei-Ming Wang (CNRS)

      Kay Kirkpatrick, Quantum groups, Free Araki-Woods Factors, and a Calculus for Moments

       Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to free Araki-Woods factors, and cases where we have surprisingly good rates of convergence. This is joint work with Michael Brannan. Time permitting, we’ll mention another quantum central limit theorem for Bose-Einstein condensation and work in progress.

      Wei-Min Wang, Quasi-periodic solutions to nonlinear PDE’s

      Abstract: We present a new approach to the existence of time quasi-periodic solutions to nonlinear PDE’s. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a Lagrangian approach to KAM theory, as suggested by J. Moser.

      11-8-17Elchanan MosselOptimal Gaussian Partitions.

      Abstract: How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution.

      The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory.

      I will survey the little we know about this problem and the major open problems in the area.

      11-10-17

      *12pm SC 232*

      Zhe Wang (NYU)A Driven Tagged Particle in One-dimensional Simple Exclusion Process

      Abstract: We study the long-time behavior of a driven tagged particle in a one-dimensional non-nearest- neighbor simple exclusion process.  We will discuss two scenarios when the tagged particle has a speed. Particularly, for the ASEP, the tagged particle can have a positive speed even when it has a drift with negative mean; for the SSEP with removals, we can compute the speed explicitly. We will characterize some nontrivial invariant measures of the environment process by using coupling arguments and color schemes.

      11-15-17

      *4:00-5:00pm*

      *G02*

      Daniel Sussman (BU)Multiple Network Inference: From Joint Embeddings to Graph Matching

      Abstract: Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiple-network framework remains a relatively under-explored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, face-to-face interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, we’ll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching.

      11-20-17

      *Monday

      12:00-1:00pm*

       Yue M. Lu

      (Harvard)

      Asymptotic Methods for High-Dimensional Inference: Precise Analysis, Fundamental Limits, and Optimal Designs
      Abstract: Extracting meaningful information from the large datasets being compiled by our society presents challenges and opportunities to signal and information processing research. On the one hand, many classical methods, and the assumptions they are based on, are simply not designed to handle the explosive growth of the dimensionality of the modern datasets. On the other hand, the increasing dimensionality offers many benefits: in particular, the very high-dimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will mention recent work on exploiting such blessings of dimensionality via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widely-used spectral method for nonconvex signal recoveries; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and mean-field limits to analyze nonconvex optimization algorithms for high-dimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with high-dimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices.
      11-29-17David Gamarink (MIT)(Arguably) Hard on Average Constraint Satisfaction Problems

      Abstract: Many combinatorial optimization problems defined on random instances such as random graphs, exhibit an apparent gap between the optimal value, which can be estimated by non-constructive means, and the best values achievable by fast (polynomial time) algorithms. Through a combined effort of mathematicians, computer scientists and statistical physicists, it became apparent that a potential and in some cases a provable obstruction for designing algorithms bridging this gap is an intricate geometry of nearly optimal solutions, in particular the presence of chaos and a certain Overlap Gap Property (OGP), which we will introduce in this talk. We will demonstrate how for many such problems, the onset of the OGP phase transition indeed nearly coincides with algorithmically hard regimes. Our examples will include the problem of finding a largest independent set of a graph, finding a largest cut in a random hypergrah, random NAE-K-SAT problem, the problem of finding a largest submatrix of a random matrix, and a high-dimensional sparse linear regression problem in statistics.

      Joint work with Wei-Kuo Chen, Quan Li, Dmitry Panchenko,  Mustazee Rahman, Madhu Sudan and Ilias Zadik.

      12-6-17

      *2:00-4:00pm*

      Philippe Rigollet (MIT)

      2-3 pm

      &

      Ankur Moitra (MIT)

      3-4 pm

      Philippe Rigollet (MIT), Exact Recovery in the Ising Block Model 

      Abstract: Over the past fifteen years, the problem of learning Ising models from independent samples has been of significant interest in the statistics, machine learning, and statistical physics communities. Much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models, primarily in the case where the interaction graph is sparse. In parallel, stochastic blockmodels have played a more and more preponderant role in community detection and clustering as an average case model for the minimum bisection model. In this talk, we introduce a new model, called Ising blockmodel for the community structure in an Ising model. It imposes a block structure on the interactions of a dense Ising model and can be viewed as a structured perturbation of the celebrated Curie-Weiss model. We show that interesting phase transitions arise in this model and leverage this probabilistic analysis to develop an algorithm based on semidefinite programming that recovers exactly the community structure when the sample size is large enough. We also prove that exact recovery of the block structure is actually impossible with fewer samples.

      This is joint work with Quentin Berthet (University of Cambridge) and Piyush Srivastava (Tata Institute).

      Ankur Moitra (MIT), A New Approach to Approximate Counting and Sampling 

      Abstract: Over the past sixty years, many remarkable connections have been made between statistical physics, probability, analysis and theoretical computer science through the study of approximate counting. While tight phase transitions are known for many problems with pairwise constraints, much less is known about problems with higher-order constraints.
      Here we introduce a new approach for approximately counting and sampling in bounded degree systems. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random. In our setting, the solution space is not even connected and we introduce alternatives to the usual Markov chain paradigm.

      12-14-17TBD
      DateNameTitle
      09-16-2015Scott Aaronson, MITBosonSampling and the Permanents of Gaussian Matrices
      09-23-2015Xin Sun, MITAlmost sure multi fractal spectrum of SLE
      09-28-2015Li-Cheng Tsai, StanfordKPZ equation limit of interacting particle systems
      09-30-2015Kyle Luh, YaleRandom Matrices: l1 Concentration and Dictionary Learning with Few Samples
      10-07-2015Martin Zirnbauer, Cologne/Simons CenterBott periodicity and the “Periodic Table” of topological insulators and superconductors
      10-14-2015Benjamin Schweinhart, Harvard CMSAUniversality Conjectures for Curvature Flow on Graphs
      10-21-2015Nicholas Cook, UCLA
      10-28-2015Vu-Lan Nguyen, Université Paris DiderotVariants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer
      11-04-2015Vadim Gorin, MITLargest eigenvalues in random matrix beta-ensembles: structures of the limit.
      11-18-2015Louis-Pierre Arguin, CUNYThe maximum of the characteristic polynomial of random unitary matrices 
      11-19-2015Nicholas Zygouras, Univ. of WarwickFrom disorder relevance to the 2d Stochastic Heat Equation
      11-25-2015ThanksgivingNo seminar
      12-02-2015Eero Saksman (Helsinki)The uniqueness of Gaussian multiplicative chaos revisited
      12-04-2015Guillaume Barraquand, ColumbiaRandom walks in Beta random environment
      01-27-2016Louigi Addario-Berry, McGillSlowdown of the front for branching Brownian motion with decay of mass
      02-03-2016Antti Knowles, ETH ZurichAn optimal rotational invariant estimator for general covariance matrices
      02-10-2016No Seminar this week
      02-17-2016Florent Bekerman, MITTransport Methods and Universality for beta-matrix models
      02-24-2016Aukosh Jagannath, Courant InstituteThe Parisi variational problem
      03-02-2016No Seminar this weekTwo next week
      03-09-2016Adam Marcus, PrincetonPolynomials and (finite) free probability
      03-11-2016Hao Shen, ColumbiaThe Sine-Gordon stochastic PDE and regularity structures
      03-16-2016Spring Recess
      03-23-2016Zeev Rudnick, Tel-Aviv and IASQuantum chaos, eigenvalue statistics and the Fibonacci sequence
      03-30-2016Nikolai Makarov, CaltechRandom normal matrices with hard edge spectrum
      04-06-2016Timo Seppalainen, WisconsinVariational formulas and Busemann functions for random paths in a random medium
      04-11-2016 (Science Center 530)Milton D. Jara, IMPAAround the strong KPZ universality conjecture
      04-20-2016Mark Rudelson, MichiganDelocalization of eigenvectors of random matrices
      04-27-2016Marek Biskup, UCLALocal limit theory for extreme values of 2D Discrete Gaussian Free Field
      05-04-2016No Talk
      05-11-2016 (2:30-3:30pm, Room G10)Laure Saint-Raymond, École Normale SupérieureFluctuating dynamics for a 2D rarified gas of hard disks
      06-01-2016Jun Yin, University of WisconsinGeneralized Circular Law
      06-08-2016Paul Bourgade, NYUExtremes of random matrices and log-correlated fields
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      During the 2021–22 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Aghil Alaee, Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form.

      The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      2/10/2022Tin Yau Tsang (UC Irvine)Title: Dihedral ridigity and mass

      Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).

      2/17/2022Shiraz Minwalla
      (Tata Institute of Fundamental Research, Mumbai)
      Title: Black Hole dynamics at Large D

      Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

      2/24/2022Achilleas Porfyriadis
      (Harvard Black Hole Initiative)
      Title: Extreme Black Holes: Anabasis and Accidental Symmetry

      Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2) transformation properties of the spherically symmetric linear perturbations of
      AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of  AdS_2.

      3/10/2022David Fajman (University of Vienna)Title: The Einstein-flow on manifolds of negative curvature

      Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.
      3/21/2022Prof. Arick Shao (Queen Mary University of London)Title: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

      Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

      In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

      This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

      3/24/2022Qian Wang, University of OxfordTitle: Rough solutions of the $3$-D compressible Euler equations

      Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $mega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density,  the result is known to hold for $mega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v,\varrho, mega) \in H^s\times H^s\times H^{s’}$, $s>2, \, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

      3/28/2022Emanuele Berti, Johns Hopkins UniversityTitle: Black Hole Spectroscopy

      Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

      4/7/2022CMSA General Relativity Conference
      4/14/2022Chao Liu, Huazhong University of Science and TechnologyTitle: Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4

      Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

      4/21/2022Jinhua Wang,
      Xiamen University
      Title: Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system

      Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.

      4/28/2022Allen Fang, Sorbonne UniversityTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

      Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/10/2021

      (10:30am – 11:30am (Boston time)

      Philippe G. LeFloch, Sorbonne University and CNRSTitle: Asymptotic localization, massive fields, and gravitational singularities

      Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild decay, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second, the Euclidian-Hyperboloidal Foliation Method, introduced in collaboration with Yue Ma, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third, in collaboration with Bruno Le Floch and Gabriele Veneziano, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and, by analyzing Einstein’s constraint equations, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org

      9/17/2021

      (10:30am – 11:30am (Boston time)

      Igor Rodnianski, Princeton UniversityTitle: Stable Big Bang formation for the Einstein equations

      Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.

      9/24/2021

      (10:30am – 11:30am (Boston time)

      Alex LupsascaTitle: On the Observable Shape of Black Hole Photon Rings

      Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.

      10/1/2021

      (10:30am – 11:30am (Boston time)

      Zhongshan An, University of ConnecticutTitle: Static vacuum extensions of Bartnik boundary data near flat domains

      Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.

      10/8/2021

      (10:30am – 11:30am (Boston time)

      Xiaoning Wu, Chinese Academy of SciencesTitleCausality Comparison and Postive Mass

      Abstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity

      10/15/2021

      (10:30am – 11:30am (Boston time)

      Jiong-Yue Li, Sun Yat-Sen UniversityTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations

      Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.

      10/22/2021

      (11:00am – 12:30pm (Boston time)

      Roberto Emparan, University of BarcelonaTitleThe Large D Limit of Einstein’s Equations

      Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

      10/28/2021Jorge Santos, University of CambridgeTitle: The classical interior of charged black holes with AdS asymptotics

      Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

      11/4/2021
      at 10 am ET
      Elena Giorgi, Columbia UniversityTitle: The stability of charged black holes

      Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

      11/11/2021
      *9:30 am ET*
      Siyuan Ma, Sorbonne UniversityTitle: Sharp decay for Teukolsky equation in Kerr spacetimes

      Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

      11/19/2021

      (10:30–11:30 am ET)

      Nishanth Gudapati, Clark UniversityTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes

      Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

      12/2/2021Professor Geoffrey Comp
      ére, Université Libre de Bruxelles
      Title: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger

      Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

      12/16/2021Xinliang An, University of SingaporeTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation

      Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker: Yifan Wang (NYU)

      Title: Fusion Category Symmetries in Quantum Field Theory

      Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti

      ble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.

    • Swampland Seminar
      10:30 am-12:00 pm
      12/01/2024

      During the 2021-22 academic year, the CMSA will be co-hosting a seminar on Swampland, with the Harvard Physics Department, organized by Miguel Montero, Cumrun Vafa, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend, please subscribe here.

      Talks will be posted on the Swampland Seminars YouTube channel. The schedule below will be updated as talks are confirmed.

      Spring 2022

      DateSpeakerTitle/Abstract
      1/31/2022Rafael Álvarez-García (DESY Hamburg)Title: Membrane Limits in Quantum Gravity
      2/7/2022Du Pei (Harvard CMSA)Title: Holomorphic CFTs and topological modular forms

      Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

      2/28/2022 Tom Rudelius (UC, Berkeley)Title: Generalized Global Symmetries and the Weak Gravity Conjecture
      3/7/2022Fernando Marchesano (UAM-CSIC, Madrid)  and Max Wiesner (Harvard CMSA)Title: 4d strings at strong coupling
      3/21/2022Patrick Draper (Univ. of Illinois) and Alvaro Herraez (IPhT Saclay).Open Mic Discussion
      Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)
      3/28/2022Fernando Quevedo (Cambridge)Title: On renormalisation group induced moduli stabilisation and brane-antibrane inflation

      Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

      4/5/2022Simon Caron-Huot (McGill University) and Julio Parra (Caltech)Title: Causality constraints on corrections to Einstein gravity

      Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

      4/11/2022Timm Wrase and Eduardo Gonzalo (Lehigh)Title: Type IIB flux compactifications with $h^{1,1}=0$

      Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.

      4/18/2022José Calderón (IFT Madrid)Open mic Swampland Discussion

      Topic: Cobordism

      5/9/2022Georges Obie (Harvard)Title: Inflation and light Dark Matter constraints from the Swampland

      Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

      Fall 2021

      DateSpeakerTitle/Abstract
      9/13/2021John Stout (Harvard)Title: Decoding Divergent Distances

      Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.

      9/20/2021Manki Kim (MIT)Title: Small Cosmological Constants in String Theory

      Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

      9/27/2021Eran Palti (Ben Gurion)Title: Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

      Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

      10/18/2021Thomas Van Riet (KU Leuven)Title: The Festina Lente Bound

      Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for  phenomenology, both top-down and bottom-up.

      10/25/2021Joe Conlon (Oxford)Title: Exploring the Holographic Swampland

      Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

      11/01/2021Pieter Bomans (Princeton)Title: Bubble instability of mIIA on AdS_4 x S^6

      Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

      11/15/2021Nima Arkani-Hamed (IAS), and Gary Shiu (UW-Madison) This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be Swampland constraints, Unitarity and Causality. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.
      11/22/2021Thomas Grimm (Utrecht University)Title: Taming the Landscape

      Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

      11/29/2021Timm Wrase (Lehigh University)Title: Scale separated AdS vacua?

      Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

      12/6/2021Lars Aalsma (University of Wisconsin-Madison)Title: Extremal Black Hole Corrections from Iyer-Wald

      Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024

      Speaker: Michail Savvas, UT Austin

      Title: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds

      Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
      In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

      Organizer: Seminars
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      peaker: Ady Stern & David Mross (Weizmann)

      Speaker: Ady Stern & David Mross (Weizmann

      Title: The nu=5/2 enigma: Recent insights from theory and experiment

      Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:30 pm
      12/01/2024

       

      Nathanan Tantivasadakarn (Harvard)

      Video

      TitleHybrid Fracton Orders

      Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”.  First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.

      Based on 2102.09555 and 2106.03842

       

       

       

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024
      CMSA-QMMP-12.01.21-1544x2048

      Speaker: Daniel Harlow (MIT)

      Title: Symmetry in quantum field theory and quantum gravity 1

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

    • Quantum Matter
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-11.24.21-1583x2048

      Speaker: Shinsei Ryu (Princeton University)

      Title: Multipartitioning topological phases and quantum entanglement

      Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024

      Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.
      In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by Maulik-Cao-Toda, vanish, as expected.

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      2/3/2021 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
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      12/01/2024
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      10:30 am-11:30 am
      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      12/01/2024
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      3/25/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      12/01/2024
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      3/27/2020 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      4/3/2020 General Relativity Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      4/16/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      4/29/2020 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
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      4/29/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:30 pm
      12/01/2024
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      5/4/2020 Mathematical Physics Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      5/14/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      5/28/2020 Condensed Matter Seminar
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      2/20/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • General Relativity Seminar
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      12/01/2024
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      12/01/2024
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      10/9/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      9/10/18 Topology Seminar
      10:30 am-12:00 am
      12/01/2024-09/11/2018
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      4/1/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      12/01/2024
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      12/01/2024
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      4/24/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      4/25/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      4/26/2019 Topology
      10:30 am-12:40 pm
      12/01/2024
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      10:30 am-11:42 am
      12/01/2024
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      9/13/2019 General Relativity
      10:30 am-11:30 am
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10:30 am-11:30 am
      12/01/2024
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      10:30 am-12:00 pm
      12/01/2024
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      10/2/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10/11/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      2/13/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10/16/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      10/18/2019 General Relativity
      10:30 am-11:30 am
      12/01/2024
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      General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      10/30/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      11/1/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      11/6/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      11/8/2019 General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
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      11/13/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      11/27/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
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      12/11/2019 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      2/06/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • General Relativity Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      6/18/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      7/9/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/16/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/17/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-12/23/2020
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-01/29/2021
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker:  Jaume Gomis (Perimeter PI)

      Title: Global Anomalies on the Hilbert Space

      Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers” that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker:  Xiao-Gang Wen (MIT)

      Title: A solution to the chiral fermion problem

      Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.

    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-02/25/2021
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-02/26/2021
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/7/2020 Math Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 am
      12/01/2024-03/18/2021

      Speaker: Silviu Pufu (Princeton University)

      Title: Exact symmetries and threshold states in two-dimensional models for QCD

      Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of confinement in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      5/12/2021 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/9/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/15/2020 Quantum Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      4/15/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
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      7/16/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      unnamed-3-600x338

      In the 2020-2021 academic year, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom.

      Cuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator, several fascinating phases emerge, including a d-wave superconductor, a pseudo-gap metal, and strange metal. After intensive studies from experimental, theoretical, and numerical communities for more than three decades, remarkable progress has been made, but basic questions remain:

      1. What is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling, spin fluctuations, or resonating-valence-bonds?
      2. How do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters, or do we need an unconventional picture involving fractionalization?
      3. Is the strange metal at optimal doping associated with a quantum critical point? And if so, what is the driving force of this phase transition?

      The cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics, such as quantum spin liquids, topological order, and non-Fermi liquids. In the coming years, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series, we hope to accelerate this process by bringing together deeper conversations between experimental, theoretical, and numerical experts with different backgrounds and perspectives.

      The Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar.

      Seminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard).

      Scientific program advisors: Professor Subir Sachdev (Harvard), Professor Patrick Lee (MIT).

      In order to learn how to attend this series, please fill out this form.

      For more information, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu)

      Spring 2022

      April 20, 2022 | 11:30 – 1:00 pm ET

      Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)

      Title: Superconductivity in infinite-layer nickelates

      Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.


      February 3, 2022 | 11:30 – 1:00 pm ET

      Lu Li (U Michigan)

      Title: Quantum Oscillations of Electrical Resistivity in an Insulator

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

      2020 – 2021

      September 2, 2020 | 10:30am ET

      Sachdev
      Subir Sachdev (Harvard)

      TitleMetal-to-metal quantum phase transitions not described by symmetry-breaking orders

      Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also
      describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

      Video

      September 23, 2020 | 10:30am ET

      Sachdev
      Subir Sachdev (Harvard)

      Title: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II

      Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.

      Video

      September 24, 2020 | 12:00pm ET

      hqdefault
      Inna Vishik (University of California, Davis)

      Title: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video

      October 15, 2020 | 10:30am ET

      unnamed
      Louis Taillefer (Université de Sherbrooke)

      TitleNew signatures of the pseudogap phase of cuprate superconductors

      Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.

      Video

      October 28, 2020 | 10:30am ET

      lee_patrick
      Patrick Lee (MIT)

      Title: The not-so-normal normal state of underdoped Cuprate

      Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.

      Video

      November 6, 2020 |12:30pm ET

      Shen
      Zhi-Xun Shen (Stanford University)

      Title: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors

      Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond.
      Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped
      magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional
      (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of
      experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

      [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
      [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
      [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
      [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
      [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
      [6] A. Lanzara et al., Nature 412, 510 (2001)
      [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
      [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
      [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
      [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
      [11] A.G. Loeser et al., Science 273, 325 (1996)
      [12] S. Chen et al., Science, 366, 6469 (2019)
      [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
      [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
      [15] Yu He et al., Science, 362, 62 (Oct. 2018)
      [16] Z. Chen, Y. Wang et al., preprint, 2020

      Video

      November 12, 2020 |10:30am ET

      Chandra-Varma
      Chandra Varma (Visting Professor, University of California, Berkeley.
      Emeritus Distinguished Professor, University of California, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:
      1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.
      2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.
      3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.
      4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting,
      (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.
      (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.
      (iii) Problems.Video

      November 18, 2020 |10:30am ET

      download
      Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)

      Title: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?

      Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.

      Video

      November 19, 2020 |10:30am ET

      Fradkin
      Eduardo Fradkin (University of Illinois at Urbana-Champaign)

      Title: Pair Density Waves and Intertwined Orders in High Tc Superconductors

      Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.

      Video

      November 25, 2020 |10:30am ET

      Si-1coborc
      Qimiao Si (Rice University)

      Title: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems

      Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.

      December 2, 2020 |10:30am ET

      Chubukov
      Andrey Chubukov (University of Minnesota)

      Title: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal 

      Abstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.

      December 9, 2020 |10:30am ET

      Hsieh
      David Hsieh (Caltech)

      Title:  Signatures of anomalous symmetry breaking in the cuprates  

      Abstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa2Cu3O[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.
      [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy,” Nature Phys. 13, 250 (2017).

      [2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2,” Preprint at https://arxiv.org/abs/2008.06516

      December 16, 2020 |10:30am ET

      weng
      Zheng-Yu Weng (Tsinghua University)

      TitleOrganizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors

      Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.

      December 17, 2020 |10:30am ET

      60cf9077a3c10b1135231e866012bda8
      Steven Kivelson (Stanford University)

      Title: What do we know about the essential physics of high temperature superconductivity after one third of a century?

      Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.

      January 20, 2021 |10:30am ET

      Devereaux
      Thomas Peter Devereaux (Stanford University)

      Title:  Numerical investigations of models of the cuprates

      Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”

      I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.

      February 3, 2021 |10:30am ET

      viewphoto
      Philip Phillips (University of Illinois Urbana-Champaign)

      Title: Beyond BCS: An Exact Model for Superconductivity and Mottness

      Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
      [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).

      February 10, 2021 |10:30am ET

      todadri_senthil
      Senthil Todadri (MIT)

      Title: Strange metals as ersatz Fermi liquids: emergent symmetries, general constraints, and experimental tests

      Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
      [1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.07896
      [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523

      April 1, 2021 |9:00am ET

      weng
      Naoto Nagaosa (University of Tokyo)

      TitleApplied physics of high-Tc theories

      Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

      April 22, 2021 |10:30am ET

      lee
      Dung-Hai Lee (UC Berkeley)

      Title: “Non-abelian bosonization in two and three spatial dimensions and some applications”

      Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.

      May 12, 2021 |10:30am ET

      weng
      André-Marie Tremblay (Université de Sherbrooke)

      Title: A unified theoretical perspective on the cuprate phase diagram

      Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

      August 11, 2021 |10:30am ET

      image
      Piers Coleman (Rutgers)

      Title: Order Fractionalization*

      Abstract: I will discuss the interplay of spin fractionalization with broken
      symmetry. When a spin fractionalizes into a fermion, the resulting particle
      can hybridize or pair with the mobile electrons to develop a new kind of
      fractional order parameter. The concept of “order fractionalization” enables
      us to extend the concept of off-diagonal order to encompass the formation of
      such order parameters with fractional quantum numbers, such as spinorial
      order[1].
      A beautiful illustration of this phenomenon is provided by a model
      which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This
      model explicitly exhibits order fractionalization and is expected to undergo a
      discrete Ising phase transition at finite temperature into an
      order-fractionalized phase with gapless Majorana excitations.
      The broader implications of these considerations for Quantum
      Materials and Quantum Field Theory will be discussed.
      Work done in collaboration with Yashar Komijani, Anna Toth and Alexei
      Tsvelik.
      [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018).
      [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).

      September 15, 2021 |10:30am ET

      0049_7858_headshot-scaled-aspect-ratio-420-334-2-scaled-840x668-c-default
      Liang Fu (MIT)

      Title: Three-particle mechanism for pairing and superconductivity

      Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

      [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
      [2] V. Crepel and L. Fu, arXiv:2103.12060
      [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

      September 29, 2021 |11:30am ET (special time)

      Ong
      Nai Phuan Ong (Princeton University)

      Title:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al., Nature Physics 17, 915 (2021).Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

      Date TBA |10:30am ET

      image_normal
      Suchitra Sebastian (University of Cambridge)

      Title: TBA

      Date TBA |10:30am ET

      hoffman
      Jenny Hoffman (Harvard University)

      Title: TBA

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/14/2020 Mathematical Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/21/2020 Math-Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      9/23/2020 Strongly Correlated Quantum Materials Series
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/1/2020 Quantum Matter seminar
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/05/2020 Math Physics Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/25/2020 Strongly Correlated Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/19/2020 Math Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      10/28/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/9/2020 Math-Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/12/2020 Condensed Matter Seminar
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/18/2020 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/19/20 Strongly Correlated Quantum Materials
      10:30 am-12:00 pm
      12/01/2024
    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-12.02.21-1544x2048-1

      Speaker: Daniel Harlow (MIT)

      Title: Symmetry in quantum field theory and quantum gravity 2

      Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/2/2020 Math-Physics Seminar
      10:30 am-11:30 am
      12/01/2024
    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Xueyang Song (MIT)

      Title: Phase transitions out of quantum Hall states in moire TMD bilayers

      Abstract: Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\’e Transition Metal Dichalcogenide (TMD) bilayers, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth.  At filling -2/3, we describe a direct transition between the FQAH state and a Charge Density Wave (CDW) insulator. The critical theory resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional Chern-Simons term. At filling -1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by  Barkeshli and McGreevy.   Crucially we show that translation symmetry alone is enough to enable a second order CFL-FL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order.  A striking signature is a universal jump of resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFL-FL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist.  We also present a critical theory for the CFL to FL transition at filling -3/4.  Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-04.06.2022-1583x2048-1

      Youtube Video

       

      Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024
      CMSA QMMP 02.17.23

      Quantum Matter Seminar

      Speaker: Rahul Sahay (Harvard)

      Title: Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics

      Abstract: While many-body quantum systems can in principle host exotic quantum spin liquid (QSL) states, realizing them as ground states in experiments can be prohibitively difficult. In this talk, we show how non-equilibrium dynamics can provide a streamlined route toward creating QSLs. In particular, we show how a simple Hamiltonian parameter sweep can dynamically project out condensed anyons from a family of initial product states (e.g. dynamically “un-Higgs”), yielding a QSL-like state. We christen such states “quantum spin lakes” which, while not thermodynamically large QSLs, enable their study in NISQ-era quantum simulators. Indeed, we show that this mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. Time permitting, we will discuss how our theory motivates a tree tensor network-based numerical tool—reliant on our theory—that quantitatively reproduces the experimental data two orders of magnitude faster than conventional brute-force simulation methods. Finally, we will highlight that even spin liquid states that are unstable in equilibrium—namely, 2 + 1D U(1) spin liquid states—can be robustly prepared by non-equilibrium dynamics.

       

      https://www.youtube.com/watch?v=ECT9nozk2SY&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=15

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Professor Harvey Reall (University of Cambridge) 

      Title: The second law of black hole mechanics in effective field theory

      Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs.

      Video
    • Quantum Matter
      10:30 am-12:30 pm
      12/01/2024

      Speaker: Kenichi Konishi (UNIPI.IT)

      Title: Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: Recent developments

      Abstract: After many years of efforts, still very little is known today about the physics of strongly-coupled chiral gauge theories in four dimensions, in spite of an important role they might play in the physics of fundamental interactions beyond the standard SU(3)xSU(2)xU(1) model. This is in stark contrast with the vectorlike gauge theories for which we have many solid results, thanks to some exact theorems, to the lattice simulation studies, to the Seiberg-Witten exact solution of N=2 supersymmetric gauge theories, and last, but not the least, to the real-world strong-interaction phenomenology and experimental tests of Quantum Chromodynamics.

      The purpose of this seminar is to discuss the results of our recent efforts to improve the understanding of the strongly-coupled chiral gauge theories. Among the main tools of analysis are the consideration of anomalies. We use both the conventional ’t Hooft anomaly-matching ideas, and new, more stringent constraints coming from the generalized anomalies involving some higher-form symmetries. Also, the so-called strong anomalies, little considered in the context of chiral gage theories, are found to carry significant implications.

      As the playground we study several classes of SU(N) gauge theories, the so-called Bars-Yankielowicz models, the generalized Georgi-Glashow models, as well as a few other simple theories with the fermions in complex, anomaly-free representations of the color SU(N).

      Color-flavor-locked dynamical Higgs phase and dynamical Abelianization, emerge, among others, as two particularly interesting possible phases the system can flow into in the infrared, depending on the matter fermion content of the model.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Sheldon Katz, UIUC

      Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants

      Abstract:  A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3.  These X are nodal CY threefolds which do not admit a projective small resolution.  B-model techniques can be applied to compute GV invariants up to g \le 32.  This raises the question: what is the geometric meaning of these invariants?

      Evidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by Kuznetsov.  One of these moduli stacks is a stacky small resolution X’ of X itself.  This leads to another geometric interpretation of the invariants as being associated with moduli of sheaves on X’ twisted by a Brauer class.  Geometric computations based on these working definitions always agree with the B-model computations.

      This talk is based on joint work with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe.

       

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      Virtual and in 20 Garden Street, Room G10

      Speaker: Seth Koren (University of Chicago)

      Title: Baryon Minus Lepton Number BF Theory for the Cosmological Lithium Problem

      Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+  3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      unnamed-file

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024

      Topological Quantum Matter Seminar

      Speaker: Amanda Young, UIUC

      Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential

      Abstract: Haldane pseudopotentials were first introduced as Hamiltonian models for the fractional quantum Hall effect, and it has been long expected that they should exhibit the characteristic properties of this exotic phase of matter, including a spectral gap above the ground state energy. We will discuss recent work that verified this gap conjecture for a truncated version of the 1/3-filled Haldane pseudopotential in the cylinder geometry. Numerical evidence suggested that for open boundary conditions the gap of the truncated model closes as the cylinder radius converges to zero and that this closure is due to the presence of edge modes; in contrast, for periodic boundary conditions, the gap remains robustly order one in the same radius limit. The standard scheme for applying spectral gap estimating techniques to the model with periodic boundary conditions, though, produces a lower bound on the bulk gap that still reflects the energy of the edge modes. To obtain an estimate on the bulk gap that reflects its true behavior, a new gap estimating strategy was developed. By customizing the spectral gap method to key invariant subspaces of the Hamiltonian, we are able to successfully avoid the edge states and produce a more accurate lower bound on the bulk gap. In this talk, we discuss this invariant subspace strategy for proving bulk gaps in the presence of edge states. This is based off joint work with S. Warzel.

       

       

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-04.28.22-1583x2048

      Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Superconductivity in infinite-layer nickelates
      10:30 am-1:00 pm
      12/01/2024
      CMSA-Strongly-Correlated-Quantum-Materials-and-High-Temperature-Superconductors-04.20.21-1583x2048

      Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Thorsten Schimannek (Utrecht University)

      Title: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants

      Abstract: The physics of M-theory and Type IIA strings on a projective nodal CY 3-folds is determined by the geometry of a small resolution, even if the latter is not Kähler. We will demonstrate this explicitly in the context of a family of Calabi-Yau double covers of P^3. Using conifold transitions, we prove that the exceptional curves in any small resolution are torsion while M-theory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary Gopakumar-Vafa invariants, that is associated to the singular Calabi-Yau and captures the enumerative geometry of the non-Kähler resolutions. We further argue that twisted circle compactifications of the 5d theory are dual to IIA compactifications on the nodal CY 3-fold with a flat but topologically non-trivial B-field. As a result, the torsion refined invariants are encoded in the topological string partition functions with different choices for the global topology of a flat B-field.

      The talk is based on 2108.09311, 2212.08655 (with S. Katz, A. Klemm, and E. Sharpe) and 2307.00047 (with S. Katz).

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: An Huang (Brandeis)

      Pre-talk Speaker: TBA: 10:00-10:30 am

      Title: A p-adic Laplacian on the Tate curve

      Abstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.30.2022-1583x2048-1

      Youtube Video

       

      Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy.  This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport.  We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation.  Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem.  The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories.  Our techniques generalize to other RG flow equations beyond Polchinski’s.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 09.15.22
      General Relativity Seminar
      Title: The Gregory-Laflamme instability of black strings revisited
       
      Abstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string.
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA GR Seminar 04.27.23

      General Relativity Seminar

      Speaker: Philippe G. LeFloch, Sorbonne University and CNRS

      Title: The localized seed-to-solution method for the Einstein constraints

      Abstract: I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set, we define a “localized seed-to-solution” map, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly, as we prove it, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis, we discover the notion of ‘asymptotic modulators’, as we call them, or “correctors” to the standard ADM invariants.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.23.2022-1583x2048

      Youtube Video

       

      Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.16.2022-1544x2048-1

      Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv  2201.00903.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024

      Speaker: Petr Hořava (UC Berkeley)

      Title: Topological Quantum Gravity and the Ricci Flow – Part I

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-02.16.2022-1544x2048

      Speaker: Petr Hořava (UC Berkeley)

      Title: Topological Quantum Gravity and the Ricci Flow – Part I

      Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Jonah Herzog-Arbeitman, Princeton University

      Title: Exact Results in Flat Band Hubbard Models

      Abstract: Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multi-orbital case: the mean-field theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and low-energy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution reveals the importance of quantum geometry in escaping (some of) BCS phenomenology within a tractable and nontrivial strong coupling theory.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.09.2022-1544x2048-1

      Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Pre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am

      Speaker: Kai Xu (CMSA)

      Title: Motivic decomposition of moduli space from brane dynamics

      Abstract: Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-03.02.2022-1544x2048

      Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Ho Tat Lam, MIT

      Title: Dipolar and modulated symmetry protected topological phases

      Abstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-02.24.2022-1544x2048-1

      Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Maksym Fedorchuk (Boston College)

      Title: CM-minimizers and standard models of Fano fibrations over curves

      Abstract: A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of K-stable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CM-minimizers without base change. In answering this question, we arrive at a theory of Koll\’ar stability for fibrations over one-dimensional bases, and standard models of Fano fibrations. I will explain the joint work with Hamid Abban and Igor Krylov in which we show that the CM-minimizers for del Pezzo fibrations are Corti’s standard models and related work in progress on quartic threefold hypersurfaces.

       

    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024

      Quantum Matter Seminar

      Speaker: Ho Tat Lam (MIT)

      Title: Non-invertible Symmetry Enforced Gaplessness

      Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

       

      https://www.youtube.com/watch?v=A-47aZ4HS1k&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=16

    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: David Favero, University of Minnesota

      Title: Gauged Linear Sigma Models and Cohomological Field Theories

      Abstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker.  Gauged Linear Sigma Models (GLSMs)  serve as a means of interpolating between Kahler geometry and singularity theory.  In enumerative geometry, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.   In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs.  Furthermore, we proved that these invariants form a Cohomological Field Theory.   In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss the construction of these general invariants.  Briefly, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”.  This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Professor Oscar Dias (University of Southampton)

      Title: Strong Cosmic Censorship

      Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally, I will discuss some possibilities (quantum effects, non-smooth initial data,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

    • Topological Quantum Matter Seminar
      10:30 am-11:30 am
      12/01/2024

      Topological Quantum Matter Seminar

      Speaker: Shenghan Jiang, Kavli Institute for Theoretical Sciences UCAS

      Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States

      Abstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has been established that topological insulator phases persist as stable phases. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wavefunctions for numerical simulations is highly desirable.
      In this talk, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions, we write down tensor equations, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems.

       

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Naqing Xie (Fudan University)

      Title: Gravitational Wave, Angular Momentum, and Supertranslation Ambiguity
      Abstract: The supertranslation ambiguity of angular momentum is a long-standing and conceptually important issue in general relativity. Recently, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However, in the compact binary coalescence community, supertranslation ambiguity is often ignored. We have shown that, in the linearised theory of gravitational wave, the new angular momentum coincides with the classical definition at the quadrupole level. This talk is based on a recent joint work with Xiaokai He and Xiaoning Wu.
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar

      General Relativity Seminar

      Speaker: Nikolaos Athanasiou
      Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
      Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.
    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Sergei Dubovsky (New York University)
      Title: Love Symmetry of Black Holes
      Abstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2,ℝ) symmetry in the suitably defined near zone approximation. We show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2,ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2,ℝ) representations. It is this highest-weight property that forces the static Love numbers to vanish. We show that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. The Love symmetry also exhibits a peculiar UV/IR mixing.
    • Quantum Matter
      10:30 am-11:30 am
      12/01/2024
      CMSA QMMP 02.03.23

      Quantum Matter Seminar

      Speaker: Han Yan (Rice U)

      Title: Fracton orders in hyperbolic space and its excitations with fractal mobility

      Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.

      Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

       

      https://www.youtube.com/watch?v=ekfKNCKzZyE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=17

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA GR Seminar 09.29.22

      General Relativity Seminar

      Speaker: Marcelo Disconzi, Vanderbilt University

      Title: Generalrelativistic viscous fluids
      Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.
    • Algebraic Geometry in String Theory Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Andrew Harder, Lehigh University

      Pre-talk Speaker: TBA: 10:00-10:30 am

      Title: Deformations of Landau-Ginzburg models and their fibers

      Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

    • Quantum Matter
      10:30 am-12:00 pm
      12/01/2024
      CMSA-QMMP-12.08.21-1544x2048

      Speaker: Fei Yan (Rutgers)

      Title: Defects, link invariants and exact WKB

      Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024

      General Relativity Seminar

      Speaker: Pengyu Le (BIMSA)

      Title: Asymptotic geometry of null hypersurface in Schwarzschild spacetime and null Penrose inequality

      Abstract: Null Penrose inequality is an important case of the well-known Penrose inequality on a null hypersurface. It conjectures the relation between the area of the outmost marginally trapped surface and the Bondi mass at null infinity. Following the proposal of Christodoulou and Sauter, we employ the perturbation method to study the asymptotic geometry of null hypersurfaces at null infinity in a perturbed vacuum Schwarzshild spacetime. We explain how to apply this perturbation theory to prove null Penrose inequality on a nearly spherically symmetric null hypersurface in a perturbed vacuum Schwarzschild spacetime.

    • General Relativity Seminar
      10:30 am-11:30 am
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Uri Kol, CMSA

      Title: Duality in Einstein’s Gravity

      Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-02-2016 Random Matrix & Probability Theory Seminar
      10:32 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      10:36 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-07-16 Mathematical Physics Seminar
      10:38 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      11-04-16 Special Seminar
      10:42 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      10:43 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-09-2016 Random Matrix & Probability Theory Seminar
      10:44 am
      12/01/2024

      No additional detail for this event.

    • Program
      10:44 am-11:04 am
      12/01/2024-06/12/2021
      CMSA-2-600x338

      The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description:

      Summer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department)

      In this course, we will start with an introduction to computer programming, algorithm, and scientific computing. Then we will discuss topics in topology, classical geometry, projective geometry, differential geometry, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning, different deep neural network models, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography, introducing some of the iconic topics: Yao’s Millionaires’ problem, zero-knowledge proof, the multi-party computation algorithm, and its proof.

      The course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events.

      This program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard related perks (such as a place to live if you are in Boston over the summer.)

      However: As with the summer tutorials, those enrolled are eligible* to receive a stipend of $700, and if you are a Mathematics concentrator, any written paper for the course can be submitted to fulfill the Math Concentration third year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program, nor is it available for PRISE participants or participants in the Herchel Smith program.)

      If you wish to join this program, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited to 10 people, so don’t wait too long to apply.

    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Quantum Matter Seminar
      10:45 am-12:45 pm
      12/01/2024
    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Birational geometry
      10:45 am-12:15 pm
      12/01/2024
      Lecture_Shokurov-pdf

      Vyacheslav V. Shokurov (Johns Hopkins University)

      Title: Birational geometry

      Abstract: About main achievements in birational geometry during the last fifty years.

      Talk chair: Caucher Birkar

      Video

    • Seminars
      Seminars Colloquia & Seminar
      9-29-2016 Homological Mirror Symmetry Seminar
      10:46 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-08-2016 Social Sciences Applications Forum
      10:56 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-15-2016 Social Sciences Applications Forum
      10:57 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-14-16 Mathematical Physics Seminar
      10:58 am
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Rodrigo Silva, University of Maryland

      Title: Quantization of causal diamonds in 2+1 dimensional gravity

      Abstract: We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with a fixed boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that has the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required — in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham’s group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

       

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Black Hole Formation
      11:00 am-12:00 pm
      12/01/2024
      Lecture_Bieri-pdf

      Lydia Bieri (University of Michigan)

      Title: Black Hole Formation

      Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the dynamical mathematical structures of the Einstein equations. Black holes are related to the presence of trapped surfaces in the spacetime manifold. Christodoulou proved that in the regime of pure general relativity and for arbitrarily dispersed initial data, trapped surfaces form through the focusing of gravitational waves provided the incoming energy is large enough in a precisely defined way. The proof combines new ideas from geometric analysis and nonlinear partial differential equations as well as it introduces new methods to solve large data problems. These methods have many applications beyond general relativity. D. Christodoulou’s result was generalized in various directions by many authors. It launched mathematical activities going into multiple fields in mathematics and physics. In this talk, we will discuss the mathematical framework of the above question. Then we will outline the main ideas of Christodoulou’s result and its generalizations, show relations to other questions and give an overview of implications in other fields.

      Video

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Michael Freedman
      11:00 am-12:30 pm
      12/01/2024
      20bottfeatureplain-1

      20bottfeatureplain
      On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.

      This will be the third annual lecture series held in honor of Raoul Bott.

      Lecture 1
      October 4th, 11:00am (Boston time)
      Title: The Universe from a single Particle

      Abstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.

      Video

      Lecture 2
      October 5th, 11:00am (Boston time)
      Title: Controlled Mather Thurston Theorems.

      Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374  

      Video

       

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Shuaijie Qian (Harvard CMSA)

      Title: Some non-concave dynamic optimization problems in finance

      Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present our recent work on some non-concave dynamic optimization problems, where the concavification principle may not hold and the resulting value function is indeed non-concave.

      The first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation, where the average tax basis and the average mining cost serves as an approximation, respectively. This approximation results in a non-concave value function, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover, the penalty method still works and converges to the value function.

      The second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints, which makes the concavification principle invalid, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous, we introduce a new definition of viscosity solution, prove the corresponding comparison principle, and show that a monotone, stable, and consistent finite difference scheme converges to the solution of the utility maximization problem.

       

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Mauricio Romo

      Title: Quantum trace and length conjecture for hyperbolic knot

      Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Diandian Wang(Harvard University)

      Title: Pole skipping, quasinormal modes, shockwaves and their connection to chaos

      Abstract: A chaotic quantum system can be studied using the out-of-time-order correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function — that seems to also know things: things like the Lyapunov exponent and the butterfly velocity, which are important quantifiers of the OTOC. Then I will talk about a systematic way of deriving pole-skipping conditions for general holographic CFTs dual to classical bulk theories and how to use this framework to derive a few interesting statements including: (1) theories with higher spins generally violate the chaos bound; (2) the butterfly velocity calculated using pole skipping agrees with that calculated using shockwaves for arbitrary higher-derivative gravity coupled to ordinary matter; (3) shockwaves are related to a special type of quasinormal modes. As we will see, the techniques are entirely classically gravitational, which I will go through with a certain level of details.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Maria Rodriguez (Utah)

      Title: Tidal Squeezing of Black Holes

      Abstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Chethan Krishnan (IISc Bangalore)

      Title: A Smooth Horizon without a Smooth Horizon

      Abstract: I will talk about some work that is about to appear, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls, fuzzballs, Type I algebras,…)

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Alejandro Poveda

      Title: Compactness and Anticompactness Principles in Set Theory

      Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.

    • Seminars
      Seminars Colloquia & Seminar
      3/30/2020 Math Physics Seminar
      11:00 am-12:00 pm
      12/01/2024
    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      17 Oxford St, Cambridge, MA 02138

      Swampland Seminar

      Location: Jefferson Physical Laboratory, Seminar room J356

      Speaker: Markus Dierigl (LMU Munich)

      Title: IIB Explored – Dualities, Bordisms, and the Swampland

      Abstract: In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries, we discuss which defects need to be included to break them completely. Interestingly, we find many backgrounds that are well-known in the F-theory literature, such as [p,q]-7-branes, non-Higgsable clusters, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications, which I will discuss in more detail.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Damian van de Heisteeg

      Title: Light states in the interior of CY moduli spaces

      Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Lionel Mason (Oxford)

      Title: Geometry at Strong coupling for amplitudes/Wilson loops

      Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024

      General Relativity Seminar

      Speaker: Andras Vasy (Stanford)

      Title: The Feynman propagator and self-adjointness

      Abstract: In this talk I will discuss the Feynman and anti-Feynman inverses for wave operators on certain Lorentzian manifolds; these are two inverses which from a microlocal analysis perspective are more natural than the standard causal (advanced/retarded) ones. For instance, for the spectral family of the wave operator, these are the natural inverses when the spectral parameter is non-real. Indeed, I will explain that these connect to the self-adjointness of the wave operator, and the positivity properties that follow.

       

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Fernando Marchesano (IFT Madrid)

      Title: EFT strings and emergence

      Abstract: We revisit the Emergence Proposal in 4d N=2 vector multiplet sectors that arise from  type II string Calabi-Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA compactifications, where EFT strings arise from NS5-branes wrapping internal four-cycles, and consider a set of infinite-distance moduli-space limits that can be classified in terms of a scaling weight w=1,2,3. It has been shown before how one-loop threshold effects of an infinite tower of BPS particles made up of D2/D0-branes generate the asymptotic behaviour of  the gauge kinetic functions along limits with $w=3$. We extend this result to w=2 limits, by taking into account D2-brane multi-wrapping numbers. In w=1 limits the leading tower involves EFT string oscillations, and one can reproduce the behaviour of both weakly and strongly-coupled U(1)’s independently on whether the EFT string is critical or not, by assuming that charged modes dominate the light spectrum.

    • Seminars
      Seminars Colloquia & Seminar
      5/8/2020 General Relativity Seminar
      11:00 am
      12/01/2024
    • Active Matter Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter
      Active Matter Seminar
      Speaker: Shenshen Wang, UCLA
      Title:  Limit and potential of adaptive immunity
      Abstract: The adaptive immune system is able to learn from past experiences to better fit an
      unforeseen future. This is made possible by a diverse and dynamic repertoire of cells
      expressing unique antigen receptors and capable of rapid Darwinian evolution within an
      individual. However, naturally occurring immune responses exhibit limits in efficacy,
      speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical
      frameworks we developed to (1) explore functional impacts of non-equilibrium antigen
      recognition, and (2) identify conditions under which natural selection acting local in time
      can find adaptable solutions favorable in the long run, through exploiting environmental
      variations and functional constraints.
    • Seminars
      Seminars Colloquia & Seminar
      5/15/2020 General Relativity Seminar
      11:00 am
      12/01/2024
    • Probability Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA Probability Seminar 03.09.23

      Probability Seminar

      Speaker: Jean-Christophe Mourrat (ENS Lyon)

      Title: On the free energy of spin glasses with multiple types

      Abstract: In the simplest spin-glass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups, which we can visualize as forming two layers, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there, and some partial progress.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Member Seminar
      Speaker: Shai Chester
      Title: Derivation of AdS/CFT for Vector Models

      Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories, and at finite temperature.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Ben McKenna

      Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance

      Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Jake McNamara (Caltech)
      Title: Parity and Cobordism
      Abstract: The swampland cobordism conjecture provides a convenient way to discuss conserved charges associated with the topology of spacetime. However, much of the power of the cobordism conjecture comes from a mathematical black box: the Adams spectral sequence. In this talk, I will give physical meaning to this black box through a concrete example: domain walls arising from the spontaneously breaking of parity symmetry, which arise in particle physics in Nelson-Barr models. I will argue that parity domain walls are exactly stable, and interpret this stability as the result of an unusual type of gauge symmetry that can only occur in gravitational theories.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-16-2016 Random Matrix & Probability Theory Seminar
      11:00 am
      12/01/2024

      No additional detail for this event.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Jie Wang

      Title: Kahler geometry in twisted materials

      Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making many-body states less stable in flatbands.

      In this talk, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform, but still exhibit exact properties such as model wavefunctions, density algebra, exact parent Hamiltonians. I will discuss both the theory of ideal flatband, its experimental realization in Dirac materials as well as implications.

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar 

      Speaker: Zhigang Yao

      Title: Principal flow, sub-manifold and boundary

      Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold, a manifold passing through the center of the data, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find, use and interpret the principal sub-manifold, by which a principal boundary can be further defined for data sets on manifolds.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Swampland Seminar
      Speaker: Aasmund Folkestad (MIT)
      Title: The Penrose Inequality as a Constraint on Low Energy Quantum Gravity
      Abstract: In this talk, I argue that the Penrose inequality (PI) can be used to constrain low energy theories compatible AdS/CFT, and possibly also quantum gravity in flat space. Focusing on AdS/CFT, it is shown that the PI can be violated for minimally coupled scalar fields, and I produce exclusion plots on couplings that respect the PI. I also present numerical evidence that top-down scalar theories and supersymmetric theories respect the PI. Finally, similar to the Breitenlohner-Freedman bound, I give a necessary condition for the stability AdS that constrains coupling constants (beyond the scalar mass).
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/28/2020 Mathematical Physics Seminar
      11:00 am-12:00 pm
      12/01/2024
    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: David Andriot (Annecy, LAPTH)

      Title: String theory scalar potentials and their critical points

      Abstract: Positive scalar potentials in string effective theories could provide an origin to Dark Energy, responsible for the accelerated expansion of our universe today or during inflation. It is thus crucial to characterize these scalar potentials, namely their slope, their critical points (de Sitter solutions) and the associated stability, as also advocated by the Swampland Program. We will present such characterizations. Going further, we will also discuss negative scalar potentials, and make related observations on anti-de Sitter solutions, in particular on a new mass bound, as well as comments on scale separation.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Paul-Konstantin Oehlmann(Northeastern)

      Title: Anomalies of Discrete Gauge Symmetries and their Cancellation in 6D F-theory

      Abstract: We consider 6D SUGRAs with a discrete gauge group G, engineered via F-theory compactifications on genus-one fibered threefolds. We argue that group G suffers from Dai-Freed anomalies that can be canceled via a discrete Green-Schwarz mechanism. We comment on the ambiguity to assign this GS term in the 7D Anomaly theory which leads to choices that are not all compatible with F-theory.

      In F-theory we then deduce this Anomaly coefficient explicitly by computing the elliptic genera of the non-critical strings that couple to the 6D two-form fields: Their 2D worldsheet theories inherits a G Flavor symmetries whose t’Hooft anomaly cancels the 6D Dai-Freed anomaly in the bulk via inflow. This talk is based on work in preparation together with Markus Dierigl and Thorsten Schimmanek.

    • CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
      11:00 am-8:45 pm
      12/01/2024-05/09/2021
      Summer,Warm,Sun,Light,Forest,Aerial,View

      This workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom

      The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data.

      This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes.

      The first half of the workshop will feature talks aimed at graduate students, newcomers, and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications.

      For the discussions, we are soliciting open problems in mathematical theory and applications of shape analysis. You are encouraged to post problems by sending an email to geometricproblemsfrg@gmail.com.

      We invite junior researchers to present a short talk in the workshop. The session will be held on Friday, May 7th or Saturday, May 8th at 4pm and are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks, the organizers will review the submissions and let you know if you have been selected. If you are interested please send your title and abstract to tianqi@cmsa.fas.harvard.edu by the end of May 2nd.

       

      Organizers:

      • David Glickenstein, University of Arizona
      • Joel Hass, University of California, Davis
      • Patrice Koehl, University of California, Davis
      • Feng Luo, Rutgers University, New Brunswick
      • Tianqi Wu, Harvard University
      • Shing-Tung Yau, Harvard University

      Featured lectures:

      • Christopher Bishop, Stony Brook
      • Keenan Crane, Carnegie Mellon

      Speakers include:

      • Miri Ben-Chen, Technion – Israel Institute of Technology
      • Alexander Bobenko, Technische Universität Berlin, Germany
      • Ulrike Buecking, Free University, Germany
      • Nadav Dym, Duke University
      • Ivan Izmestiev, Vienna University of Technology
      • Yanwen Luo, Rutgers
      • Stephan Tillmann, The University of Sydney
      • Max Wardetzky, University of Goettingen
      • Xu Xu, Wuhan University
    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics

      Title: Quantum magnet chains and Kashiwara crystals

      Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva, Joel Kamnitzer, and Alex Weekes.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Swampland Seminar
      Speaker: Samir Mathur (Ohio State)
      Title: The story of the information paradox
      Abstract:  In 1975 Hawking argued that black hole evaporation would lead to a loss of unitarity in quantum theory.  The small corrections theorem made Hawking’s argument into a precise statement: if semiclassical physics hold to leading order in any gently curved region of spacetime, then there can be no resolution to the paradox. In string theory, whenever people have been able to construct microstates explicutly, the states turned out to be horizon sized objects (fuzzballs) with no horizon; such a structure of microstates resolves the information paradox since their is no pair creation at a vacuum horizon. There have been a set of parallel attempts to resolve the paradox (with ideas involving wormholes, islands etc) where the horizon is smooth in some leading approximation. An analysis of such models however indicated that in each case the exact quantum gravity theory would either have to be nonunitary or to have dynamics at infinity that is conflict with usual low energy physics in the lab.
    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Swampland Seminar 01.30.23

      Swampland Seminar

      Speaker: Ignatios Antoniadis (LPTHE Paris)
      Title: Swampland program, extra dimensions and supersymmetry breaking
      Abstract: I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalisation of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.
    • Colloquium
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 04.03.2023

      Colloquium

      Speaker: Luca Iliesiu, Stanford

      Title: Black hole microstate counting from the gravitational path integral

      Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Swampland Seminar 04.10.23

      Swampland Seminar

      Speaker: Seung-Joo Lee (IBS Daejeon)

      Title: Swampland bounds on the abelian gauge sectors

      Abstract: In this talk we will derive various bounds on the 0-form and the 1-form abelian gauge sectors of gravitational effective theories in 6 dimensions with minimal supersymmetry. We will start by considering 6-dimensional F-theory vacua with at least one tensor multiplets, to bound for them the number of the (0-form) U(1) gauge factors as well as the cyclic orders of the 1-form discrete gauge factors. While the two abelian gauge sectors may look rather independent, we will observe that both are heavily constrained by the solitonic heterotic strings present in the spectrum, which provide a common intuition for the derived bounds. Building upon the heterotic intuition, we will also try extending the arena to address analogous bounds for all F-theory vacua in 6 dimensions and even beyond. If time permits, several applications and future directions of research will be discussed at the end of the talk.

    • Math Science Literature Lecture Series
      11:00 am-12:30 pm
      12/01/2024

      Sergiu Klainerman (Princeton University)

      Title: Nonlinear stability of Kerr black holes for small angular momentum

      Abstract: According to a well-known conjecture,  initial data sets,  for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon)   which approaches  (globally)  a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $|a|/m $ sufficiently small. The work, ArXiv:2104.11857v1,  also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr,  with Szeftel and Elena Giorgi,  which I will also describe.

      Talk chair: Lydia Bieri 

      Video

    • Member Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin

      Title: Explicit Ramsey Graphs and Two Source Extractors

      Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      Jefferson Hall Room 368, 17 Oxford St, Cambridge, MA 02138

      Swampland Seminar

      Speaker: Thomas Grimm (Utrecht U.)

      Title: The Tameness of Quantum Field Theories

      Abstract: Tameness is a generalized notion of finiteness that is restricting the geometric complexity of sets and functions. The underlying mathematical foundation lies in tame geometry, which is built from o-minimal structures introduced in mathematical logic. In this talk I formalize the connection between quantum field theories and logical structures and argue that the tameness of a quantum field theory relies on its UV definition. I quantify our expectations on the tameness of effective theories that can be coupled to quantum gravity and on CFTs. In particular, I present tameness conjectures about CFT observables and propose universal constraints that render spaces of CFTs to be tame sets. I then highlight the relation of these conjectures to other swampland conjectures, e.g., by arguing that the tameness of CFT observables restricts having parametrical gaps in the operator spectrum.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Swampland Seminar 03.27.23

      Swampland Seminar

      Speaker: Valerio De Luca (UPenn)

      Title: Recent developments on the tidal Love numbers of black holes

      Abstract: Tidal Love numbers describe the deformability of compact objects under the presence of external tidal perturbations, and are found to be exactly zero for black holes in pure General Relativity. This property is however fragile, since they receive corrections from higher-order derivative terms in the theory. We show that the tidal deformability of neutral black holes is constrained by the Weak Gravity Conjecture.

    • Swampland Seminar
      11:00 am-12:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Swampland Seminar

      Speaker: Alvaro Herraez (Saclay)

      Title: The Emergence Proposal in Quantum Gravity and the Species Scale

      Abstract: The Emergence Proposal claims that in Quantum Gravity the kinetic terms of the fields in the IR emerge from integrating out (infinite) towers of particles up to the QG cutoff. After introducing this proposal in the context of the Swampland Program, I will explain why it is natural to identify this QG cutoff with the Species Scale, motivating it by direct computation in the presence of the relevant towers. Then, I will present evidence for this proposal by directly studying how it is realized in different string theory setups, where the kinetic terms of scalars, p-forms and even scalar potentials can be shown to emerge after integrating out such towers.

       

       

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024

      General Relativity Seminar

      Speaker: Daniel Kolb (Max Planck Institute)

      Title: Quasi-Local Mass in a Binary Black Hole Merger

      Abstract: One of the major open problems in classical general relativity is how one should define the mass of a finite region of space. In this talk, we will investigate a promising definition proposed by Wang and Yau in 2009. A closed 2-surface bounding the region of interest is embedded isometrically into Minkowski space. The mass is then calculated by comparing the extrinsic geometries. The Wang-Yau mass has many desirable properties, but it has previously not been calculated for surfaces in dynamical spacetimes. To remedy this, we will discuss how the Wang-Yau mass can be computed in practice and extend the definition to surfaces important in black hole dynamics: their quasi-local horizons. Finally, we look at how this mass behaves in a merger of black holes.

    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: David Kubiznak (Charles University)

      Title: Remarkable symmetries of rotating black holes

      Abstract: It is well known that the Kerr geometry admits a non-trivial Killing tensor and its ‘square root’ known as the Killing-Yano tensor. These two objects stand behind Carter’s constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object — the principal Killing-Yano tensor — generates a tower of explicit and hidden symmetries responsible for integrability of geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes described by the `magic square’ version of the Lense-Thirring solution, giving rise to a geometrically preferred spacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.

    • General Relativity Seminar
    • General Relativity Seminar
    • General Relativity Seminar
    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      General Relativity Seminar

      Speaker: Leo Stein (Mississippi)

      Title: Resolving memory in numerical relativity, and fixing BMS frames for modeling

      Abstract: Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE), and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames, we can extract well-defined remnant quantities, perform precision ringdown modeling, and build complete surrogate waveform models that capture memory effects.

    • Seminars
      Seminars Colloquia & Seminar
      3-2-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      12/01/2024-03/03/2018
    • Seminars
      Seminars Colloquia & Seminar
      2-16-2018 Mirror Symmetry Seminar
      11:00 am
      12/01/2024
    • General Relativity Seminar
      11:00 am-12:00 pm
      12/01/2024
      20 Garden Street, Cambridge MA 02138

      General Relativity Seminar

      Speaker: David Fajman (Vienna)

      Title: Fluid stabilization in slowly expanding cosmological spacetime

      Abstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.

       

      Talk via Zoom, broadcast in G10

       

    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      4-13-2018 Mirror Symmetry Seminar
      11:00 am-12:00 am
      12/01/2024-04/14/2018
    • Seminars
      Seminars Colloquia & Seminar
      10/19/2018 Mirror Symmetry Seminar
      11:00 am-11:00 pm
      12/01/2024
    • General Relativity Seminar
    • Seminars
      Seminars Colloquia & Seminar
      02-09-2018 Mirror Symmetry Seminar
      11:00 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2-23-2018 Mirror Symmetry Seminar
      11:00 am
      12/01/2024
    • Member Seminar
      11:01 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-21-16 Mathematical Physics Seminar
      11:02 am
      12/01/2024

      No additional detail for this event.

    • Algebraic Geometry in String Theory Seminar
      11:02 am-12:02 pm
      12/01/2024

      Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      11:03 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:03 am-11:04 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:04 am
      12/01/2024

      The  CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

      Spring 2020

      DateSpeakerTitle/Abstract
      1/29/2020David Yang (Harvard)

      Abstract: Data-intensive technologies such as AI may reshape the modern world. We propose that two features of data interact to shape innovation in data-intensive economies: first, states are key collectors and repositories of data; second, data is a non-rival input in innovation. We document the importance of state-collected data for innovation using comprehensive data on Chinese facial recognition AI firms and government contracts. Firms produce more commercial software and patents, particularly data-intensive ones, after receiving government public security contracts. Moreover, effects are largest when contracts provide more data. We then build a directed technical change model to study the state’s role in three applications: autocracies demanding AI for surveillance purposes, data-driven industrial policy, and data regulation due to privacy concerns. When the degree of non-rivalry is as strong as our empirical evidence suggests, the state’s collection and processing of data can shape the direction of innovation and growth of data-intensive economies.

      2/5/2020Scott Aaronson (UT Austin)

      Video

      Title: Gentle Measurement of Quantum States and Differential Privacy

      Abstract: I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography”
      of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).

      Based on joint work with Guy Rothblum (arXiv:1904.08747)

      2/12/2020Scott Kominers (Harvard)Title: A Compact, Logical Approach to Large-Market Analysis

      Abstract: In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

      2/19/2020Peter Shor (MIT)Title: Quantum Money from Lattices

      Abstract: Quantum money is  a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

      2/26/2020Daneil Wise (McGill)Title: The Cubical Route to Understanding Groups

      Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds and simultaneously dramatically extended our understanding of many infinite groups.
      3/4/2020

      4:45 – 5:45pm

      Salil Vadhan (Harvard)Title: Derandomizing Algorithms via Spectral Graph Theory

      Abstract: Randomization is a powerful tool for algorithms; it is often easier to design efficient algorithms if we allow the algorithms to “toss coins” and output a correct answer with high probability. However, a longstanding conjecture in theoretical computer science is that every randomized algorithm can be efficiently “derandomized” — converted into a deterministic algorithm (which always outputs the correct answer) with only a polynomial increase in running time and only a constant-factor increase in space (i.e. memory usage).

      In this talk, I will describe an approach to proving the space (as opposed to time) version of this conjecture via spectral graph theory. Specifically, I will explain how randomized space-bounded algorithms are described by random walks on directed graphs, and techniques in algorithmic spectral graph theory (e.g. solving Laplacian systems) have yielded deterministic space-efficient algorithms for approximating the behavior of such random walks on undirected graphs and Eulerian directed graphs (where every vertex has the same in-degree as out-degree). If these algorithms can be extended to general directed graphs, then the aforementioned conjecture about derandomizing space-efficient algorithms will be resolved.

      3/11/2020

      Postponed

      Jose Scheinkman

      (Columbia)

      This colloquium will be rescheduled at a later date. 

      Title: Menu Costs and the Volatility of Inflation

      Abstract: We present a state-dependent equilibrium pricing model that generates inflation rate fluctuations from idiosyncratic shocks to the cost of price changes of individual firms.  A firm’s nominal price increase lowers other firms’ relative prices, thereby inducing further nominal price increases. We first study a mean-field limit where the equilibrium is characterized by a variational inequality and exhibits a constant rate of inflation. We use the limit model to show that in the presence of a large but finite number n of firms the snowball effect of repricing causes fluctuations to the aggregate price level  and these fluctuations converge to zero slowly as n grows. The fluctuations caused by this mechanism are larger when the density of firms at the repricing threshold is high, and the density at the threshold is high when the trend inflation level is high. However a calibration to US data shows that this mechanism is quantitatively important even at modest levels of trend inflation and  can account for the positive relationship between inflation level and volatility that has been observed empirically.

      3/12/2020

      4:00 – 5:00pm

      Daniel Forger (University of Michigan)This meeting will be taking place virtually on Zoom.

      Title: Math, Music and the Mind; Mathematical analysis of the performed Trio Sonatas of J. S. Bach

      Abstract: I will describe a collaborative project with the University of Michigan Organ Department to perfectly digitize many performances of difficult organ works (the Trio Sonatas by J.S. Bach) by students and faculty at many skill levels. We use these digitizations, and direct representations of the score to ask how music should encoded in the mind. Our results challenge the modern mathematical theory of music encoding, e.g., based on orbifolds, and reveal surprising new mathematical patterns in Bach’s music. We also discover ways in which biophysical limits of neuronal computation may limit performance.

      Daniel Forger is the Robert W. and Lynn H. Browne Professor of Science, Professor of Mathematics and Research Professor of Computational Medicine and Bioinformatics at the University of Michigan. He is also a visiting scholar at Harvard’s NSF-Simons Center and an Associate of the American Guild of Organists.

      3/25/2020Cancelled
      4/1/2020Mauricio Santillana (Harvard)This meeting will be taking place virtually on Zoom.

      Title: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring

      Abstract: I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.

      4/8/2020Juven Wang (CMSA)This meeting will be taking place virtually on Zoom.

      Title: Quantum Matter Adventure to Fundamental Physics and Mathematics (Continued)

      Abstract: In 1956, Parity violation in Weak Interactions is confirmed in particle physics. The maximal parity violation now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary
      explanation.  We will see how the topology and cobordism in mathematics may come into play of anomalies and non-perturbative interactions in
      fundamental physics. Perhaps some of you (geometers,  string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond

      4/15/2020
      Lars Andersson (Max-Planck Institute for Gravitational Physics)
      This meeting will be taking place virtually on Zoom.

      Title: Stability of spacetimes with supersymmetric compactifications

      Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.

      4/22/2020William Minicozzi (MIT)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow in high codimension

      Abstract: I will talk about joint work with Toby Colding on higher codimension mean curvature flow.  Some of the ideas come from function theory on manifolds with Ricci curvature bounds.

      4/29/2020Gerhard Huisken (Tübingen University / MFO)This meeting will be taking place virtually on Zoom.

      Title: Mean curvature flow of mean-convex embedded 2-surfaces in 3-manifolds

      Abstract: The lecture describes joint work with Simon Brendle on the deformation of embedded surfaces with positive mean curvature in Riemannian 3-manifolds in direction of their mean curvature vector. It is described how to find long-time solutions of this flow, possibly including singularities that are overcome by surgery, leading to a comprehensive description of embedded mean-convex surfaces and the regions they bound in a 3-manifold. The flow can be used to sweep out the region between space-like infinity and the outermost horizon in asymptotically flat 3-manifolds arising in General Relativity. (Joint with Simon Brendle.)

      5/6/2020Lydia Bieri (UMich)This meeting will be taking place virtually on Zoom.

      Title: Energy, Mass and Radiation in General Spacetimes

      Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. Isolated gravitating systems such as binary stars, black holes or galaxies can be described in GR by asymptotically flat (AF) solutions of these equations. These are solutions that look like flat Minkowski space outside of spatially compact regions. There are well-defined notions for energy and mass for such systems. The energy-matter content as well as the dynamics of such a system dictate the decay rates at which the solution tends to the flat one at infinity. Interesting questions occur for very general AF systems of slow decay. We are also interested in spacetimes with pure radiation. In this talk, I will review what is known for these systems. Then we will concentrate on spacetimes with pure radiation. In particular, we will compare the situations of incoming radiation and outgoing radiation under various circumstances and what we can read off from future null infinity.

      5/13/2020Mikhail Lukin (Harvard)

      Video

      This meeting will be taking place virtually on Zoom.

      Title: Exploring New Frontiers of Quantum Science with Programmable Atom Arrays

      Abstract: We will discuss recent work at a new scientific interface between  many-body physics and quantum information science. Specifically, we will  describe the advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of one dimensional spin models, discovered a new type of non-equilibrium quantum dynamics associated with the so-called many body scars and created large-scale entangled states. We will also describe the most recent developments that now allow the control over 200 atoms in two-dimensional arrays.   Ongoing efforts  to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.

      5/20/2020This meeting will be taking place virtually on Zoom.

      Fall 2019

      DateSpeakerTitle/Abstract
      9/18/2019Bill Helton (UC San Diego)Title:  A taste of noncommutative convex algebraic geometry

      Abstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example,

      ◦ A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials.

      ◦ A convex NC semialgebraic set has a linear matrix inequality representation.

      ◦ The natural Nullstellensatz are falling into place.

      The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.

      9/25/2019Pavel Etingof (MIT)

       

      Title: Double affine Hecke algebras

      Abstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.

      10/2/2019Spiro Karigiannis (University of Waterloo)Title: Cohomologies on almost complex manifolds and their applications

      Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.

      10/9/2019Hans Lindblad (Johns Hopkins University)Title:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition

       

      Abstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition  satisfy the preserved wave coordinate condition.

       

      Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times.

      John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas  lainerman came up with the ‘null condition’, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition.

      Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition.

      Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to afraction and has now been used to prove global existence also with matter fields.

      Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equationsbackwards to obtain global solutions with given data at infinity.

      10/16/2019Aram Harrow (MIT)

      Video

      Title: Monogamy of entanglement and convex geometry

      Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems.

      10/23/2019No talk
      10/30/2019Nima Arkani-Hamed (IAS)

      Video

      Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity
      11/6/2019Kevin Costello (Perimeter Institute)

      Video

      Title: A unified perspective on integrability

       

      Abstract: Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics.   I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu.

      11/13/2019Heather  Harrington (University of Oxford)Title:  Algebra, Geometry and Topology of ERK Enzyme Kinetics

      Abstract: In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

      11/20/2019Xi Yin (Harvard)

      Video

      Title: An Introduction to the Non-Perturbative Bootstrap

      Abstract: I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap

      11/25/2019

      Monday

      Madhu Sudan (Harvard)
      Abstract: The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits.

      In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction.

      Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard).

      12/4/2019Xiao-Gang Wen (MIT)
      Video
      Title: Emergence of graviton-like excitations from a lattice model

      Abstract: I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases.

      2018-2019

      DateSpeakerTitle/Abstract
      9/26/2018Xiao-Gang Wen (MIT)Title: A classification of low dimensional topological orders and fully extended TQFTs

      Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs.

      10/03/2018Richard Schoen (Stanford)Title: Perspectives on the scalar curvature

      Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied.

      10/10/2018Justin Solomon (MIT)Title: Correspondence and Optimal Transport for Geometric Data Processing

      Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured data.

      10/17/2018Jeremy England (MIT)Title: Wisdom of the Jumble

      Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components.

      In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means.

      10/31/2018Moon Duchin (Tufts)Title: Exploring the (massive) space of graph partitions

      Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts).  I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics.

      11/14/2018Dusa McDuff (Columbia)Title: The virtual fundamental class in symplectic geometry

      Abstract: Essential to many constructions and applications of symplectic  geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well  understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so  that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there  are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a  construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim.

      11/19/2018Xiaoqin Wang (Johns Hopkins)Title: Computational Principles of Auditory Cortex

      Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.

      11/28/2018Robert Haslhofer (University of Toronto)Title: Recent progress on mean curvature flow

      Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.

      12/5/2018Robert McCann (University of Toronto)Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity

      Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of  probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics.

      Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf

      12/12/2018Zhiwei Yun (MIT)Title: Shtukas: what and why

      Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them.

      1/30/2019Richard Freeman (Harvard)Title:  Innovation in Cell Phones in the US and China: Who Improves Technology Faster?

      Abstract:  Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps.  Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones.  Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality.  The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being.

      2/7/2019

      *Thursday*

      Ulrich Mueller (Princeton)Title: Inference for the Mean

      Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.

      2/13/2019Christian Santangelo (UMass Amherst)Title: 4D printing with folding forms

      Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome.

      2/20/2019Michael Woodford (Columbia)Title: Optimally Imprecise Memory and Biased Forecasts

      Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings.

      [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)]

      2/27/2019

      2:30pm

      Ian Martin (LSE)Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs

      Abstract: We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou]

      3/6/2019

      2:30pm

      Philippe Sosoe (Cornell)Title:  A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation

      Abstract:  In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors.  (Joint work with Tadahiro Oh and Leonardo Tolomeo)

      3/13/2019

      5:15pm

      Greg Galloway (University of Miami)Title:  On the geometry and topology of initial data sets in General Relativity

      Abstract:  A theme of long standing interest (to the speaker!)  concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness).  Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple.  The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces,  which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

      3/20/2019Sonia Jaffe (Microsoft)Title:  Quality Externalities on Platforms:  The Case of Airbnb

      Abstract:  We explore quality externalities on platforms:  when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business.  We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform.  We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus.  (Joint work with Peter Coles, Steven Levitt, and Igor Popov.)

      3/27/2019

      5:15pm

      Tatyana Sharpee (Salk Institute for Biological Studies)Title: Hyperbolic geometry of the olfactory space.

      Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

      4/3/2019

      2:30pm

      Sarah Moshary (Chicago Booth)Title:  Deregulation through Direct Democracy:  Lessons from Liquor

      Abstract:  This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

      4/10/2019

      2:30pm

      Pietro Veronesi (Chicago Booth)Title: Inequality Aversion, Populism, and the Backlash Against Globalization

      Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

      Paper

      Online Appendix

      4/17/2019Yi-Zhuang You (UCSD)Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

      Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

      .

      [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103

      [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804

      [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

      4/24/2019Shengwu Li (Harvard)
      Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
      Date…………SpeakerTitle
      02-09-2018 *Friday       Fan Chung

      (UCSD)

      Sequences: random, structured or something in between

      There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns;

      testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems.

      02-14-2018Zhengwei Liu

      (Harvard Physics)

      A new program on quantum subgroups

      Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing.

      02-21-2018Don Rubin

      (Harvard)

      Essential concepts of causal inference — a remarkable history

      Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis.

      02-26-2018 *MondayTom Hou

      (Caltech)

      Computer-assisted analysis of singularity formation of a regularized 3D Euler equation

      Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu.

      03-07-2018Richard Kenyon

      (Brown)

      Harmonic functions and the chromatic polynomial

      Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam.

      03-14-2018
      03-21-2018
      03-28-2018Andrea Montanari (Stanford)A Mean Field View of the Landscape of Two-Layers Neural Networks

      Abstract: Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD).  Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties?

      We consider a simple case, namely two-layers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well.
      [Based on joint work with Song Mei and Phan-Minh Nguyen]

      03-30-2018
      04-04-2018Ramesh Narayan 

      (Harvard)

      Black Holes and Naked Singularities

      Abstract: Black Hole solutions in General Relativity contain Event Horizons and
      Singularities. Astrophysicists have discovered two populations of
      black hole candidates in the Universe: stellar-mass objects with
      masses in the range 5 to 30 solar masses, and supermassive objects
      with masses in the range million to several billion solar
      masses. There is considerable evidence that these objects have Event
      Horizons. It thus appears that astronomical black hole candidates are
      true Black Holes. Direct evidence for Singularities is much harder to
      obtain since, at least in the case of Black Holes, the Singularities
      are hidden inside the Event Horizon. However, General Relativity also
      permits Naked Singularities which are visible to external
      observers. Toy Naked Singularity models have been constructed, and
      some observational features of accretion flows in these spacetimes
      have been worked out.

      04-11-2018Pablo Parrilo

      (MIT)

      Graph Structure in Polynomial Systems: Chordal Networks

      Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).

      04-18-2018Washington Taylor

      (MIT)

      On the fibration structure of known Calabi-Yau threefolds

      Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.

      04-25-2018 Xi Yin

      (Harvard)

      How we can learn what we need to know about M-theory

      Abstract: M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory.

      05-02-2018
      05-09-2018

      2016-2017

      DateNameTitle/Abstract
      01-25-17Sam Gershman, Harvard Center for Brain Science, Department of Psychology

      Title: Spectral graph theory of cognitive maps

      Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory.

      02-01-17Sean Eddy, Harvard Department of Molecular and Cellular Biology

      Sean_Eddy

      Title: Biological sequence homology searches: the future of deciphering the past 

      Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK.

      02-08-17Matthew Headrick, Brandeis University

      matthew_headrick

      Title: Quantum entanglement, classical gravity, and convex programming: New connections

      Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

      02-15-17Masahito Yamazaki, IMPU

      Masahito Yamazaki

       Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

      Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras.

      Video

      02-22-17Steven Rayan, University of Saskatchewan

      Title: Higgs bundles and the Hitchin system

      Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics.  As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence.  From this point of view, the Hitchin map and spectral curves emerge.  We’ll use these to form an impression of what the moduli space “looks like”.  I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry.

      Video

      03-01-17Jun Liu, Harvard University

      Jun liu

      Title: Expansion of biological pathways by integrative Genomics

      Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays.

      Based on the joint work with Yang Li and the Vamsi Mootha lab.

      Video

      03-08-17Gabor Lippner, Northeastern University

      ---

      Title: Evolution of cooperation in structured populations

      Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics.  Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies.  It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution.

      In this talk I will present new results about the model where the population is represented by an interaction network.  We study the likelihood of a random mutation spreading through the entire population.  The main question is to understand how the network influences this likelihood.  After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.
      03-15-17 Spring Break: No session
      03-22-17Gunther Uhlmann, University of Washington

      guntherUhlman

      Abstract We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
      waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
      The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.
      We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.
      03-29-17Leslie Greengard, Courant InstituteLeslie_GreengardTitle: Inverse problems in acoustic scattering and cryo-electron microscopy

      Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy.

      NOTE: This talk will begin at 4:00pm

      04-05-17Gongjie Li, Harvard University

      GongjieLi

      Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches

      Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems.

      Video

      04-12-17Shlomo Razamat, Israel Institute of Technology

      ShlomoRazamat

      Title: Complicated four-dimensional physics and simple mathematics

      Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index,  of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven.

      Video

      04-19-17Cumrun Vafa, Harvard University

      CumrunVafa

      Title: String Swampland

      Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography.

      04-27-17Mehran Kardar, MIT

      MehranKardar

      Title: Levitation by Casimir forces in and out of equilibrium

      Abstract: Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint.

      Note: This talk will begin at 3:00pm

      05-02-17Simona Cocco, Laboratoire de Physique Statistique de l’ENSTitle: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions

      Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing
      similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models
      have led to substantial progress in protein structural and functional
      predictions.

      Note:  This talk will begin at 4:00pm

      05-03-17Xue-Mei Li, University of WarwickTitle: Perturbation to conservation law and stochastic averaging

      Abstract: A deterministic or random system with a conservation law is often used to
      approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces.

      Note: This talk will be held in the Science Center, Room 507

      05-10-17
      05-17-17Kwok Wai Chan, Chinese University of Hong KongTitle: Scattering diagrams from asymptotic analysis on Maurer-Cartan equations

      Abstract:  In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015).

      05-24-17 NO COLLOQUIUM
      05-31-17Peter Michor, University of Vienna

       Title: Geometry of shape spaces and diffeomorphism groups and some of their uses

      Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces.

      DateNameTitle
      09-09-16

      Bong Lian, Brandeis

      portrait

      Title: Riemann-Hilbert Problem and Period Integrals

      Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

      09-14-16Sze-Man Ngai, Georgia Southern UniversityngaiTitle: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

      Abstract: Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum.  The asymptotic behavior of the eigenvalue counting function for the associated  Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results.

      09-21-16Prof. L. Mahadevan, Harvard SEAS

      Mahadevan_200x300

      Title: “Morphogenesis: Biology, Physics and Mathematics”

      Abstract:  A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology.  Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains.  I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology.

      09-28-16Hong Liu, MIT

      liu_hong

      Title: A new theory of fluctuating hydrodynamics

      Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate  for capturing  fluctuations.  In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure.

      We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular,  the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations.

      Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry.

      10-05-16

      Alexander LogunovTel-Aviv University

      alex

      Title: Zeroes of harmonic functions and Laplace eigenfunctions

       Abs: Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete.

      10-12-16 Conan Nai Chung Leung, CUHK

      conan_profile

      Title:  Coisotropic A-branes and their SYZ transform

      Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

      10-19-16Vaughan Jones, UC Berkeley

      vj6

      Title: Are the Thompson groups any good as a model for Diff(S^1)?

      Abstract. The Thompson groups are by definition groups of piecewise linear
      diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
      be conjugated to a group of smooth diffeomorphisms. That’s the good news.
      The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
      procedure analogous to the constructions of the central extension of Diff(S^1)?
      I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

       10-26-16

      Henry Cohn, Microsoft

      ????????????????????????????????????

      Sums of squares, correlation functions, and exceptional geometric structures

      Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding.  How can we understand and prove their optimality?  In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems.

      11-02-16

      Christian Borgs, Microsoft

      Borgs

      Title:  Graphon processes and limits of   sparse graph sequences

      Abstract:  The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for so-called exchangeable random graphs.   Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection.  While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model.  

      In this talk I describe a new model, where the underlying probability space is replaced by a sigma-finite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits.  The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life.

      11-09-16

      TIME CHANGE: 4PM

      Norden E. HuangNational Central University, (Taiwan)

      member1_clip_image003

      Title: On Holo-Hilbert Spectral Analysis

      Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

      11-16-16Tristan Collins, Harvard University

      image

      TIME CHANGE: 3:30PM

      Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

      Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

      11-22-16 TUESDAY

      TIME CHANGE: 4-5PM

      Xiangfeng Gu, Stonybrook

      Title: Differential Geometric Methods for Engineering Applications

      Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation.

      11-30-16

      TIME CHANGE: 4:20PM

      Sharad Ramanathan, Harvard MCB & SEAS

      Ramanathan.Sharad_200x300

      Title: Finding co-ordinate systems to monitor the development of mammalian embryos
       12-07-16

      Valentino Tosatti, Northwestern

      Title: Metric limits of hyperkahler manifolds

      Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

       12-14-16

      2015-2016

      DateNameTitle
      09-02-2015Madhu SudanRobust low-degree testing
      09-09-2015Mithat Unsal
      What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
      09-16-2015Subir SachdevBekenstein-Hawking entropy and strange metals
      09-23-2015Felix FinsterLinear hyperbolic equations in a rotating black hole geometry
      09-30-2015Leslie ValiantHolographic Algorithms
      10-07-2015Christopher RoganExploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond
      10-14-2015Boaz Barak, Harvard SEASConvexity, Bayesianism, and the quest towards Optimal Algorithms
      10-21-2015Zhouping XinEntropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems
      10-28-2015Cristopher MooreStatistical inference, statistical physics, and the community detection problem
      11-04-2015Tom HouBlowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations
      11-11-2015Stan Osher, UCLAOvercoming the curse of dimensionality for certain Hamilton-Jacobi (HJ) equations arising in control theory and elsewhere
      11-18-2015Xiaole Shirley LiuInference of transcriptional regulation in cancers
      11-25-2015ThanksgivingNo seminar
      12-02-2015Scott KominersGeneralized Matching Market Design: Theory and Practice
      12-09-2015Matthew HolmanDynamical Chaos in Kepler Planetary Systems
      01-27-2016Conan LeungSome modern aspects of Morse theory 
      02-03-2016Camillo De LellisFrom Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence
      02-10-2016Chun Peng Wang
      02-17-2016Samuel Kou, Harvard StatisticsBig data, Google and disease detection: the statistical story
      02-24-2016Dan Xie, Harvard CMSASingularity theory and supersymmetric field theory
      03-02-2016Lydia BieriMathematical General Relativity
      03-09-2016Piotr ChruscielThe mathematics of gravitation
      03-16-2016Spring BreakNo Talk
      03-23-2016Richard Freeman, Harvard EconomicsPulling Apart of Wages and Productivity: why “identical” workers have increasingly different pay and productivity.
      03-30-2016David Garfinkel, Oakland UniversityGravitational Wave Memory
      04-04-2016 (Hall A, Science Center)Xianfeng David Gu, Stony Brook UniversityA Discrete Variational Approach for Solving Monge-Ampere Equation
      04-06-2016Lars Hernquist, HarvardNext Generation Cosmological Simulations: Galaxy Assembly and Evolution
      04-13-2016Jun Zhang, Univ. of Michigan-Ann ArborKahler and Para-Kahler Structure in Information Geometry
      04-20-2016Sijue Wu, Univ. of MichiganOn two dimensional gravity water waves with angled crests
      04-27-2016Paul Seidel, MITTopological quantum field theory and the Gauss-Manin connection
      05-04-2016Hirosi Ooguri, CaltechString Theory And Its Applications in Mathematics and Physics
      05-11-2016      (4pm – 5pm)Juerg Froehlich, ETH and IASImplications of the Chiral Anomaly – From the Quantum Hall Effect to Topological Insulators and Out to Space
    • Colloquium
      11:05 am-11:06 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:07 am-11:08 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:08 am-11:09 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-22-2016 Random Matrix & Probability Theory Seminar
      11:12 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-07-2016 Random Matrix & Probability Theory Seminar
      11:16 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-05-16 Mathematical Physics Seminar
      11:17 am
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
      11:19 am
      12/01/2024-11/14/2019
      Dynamics-12-x-18-683x1024

      On November 12-14, 2019 the CMSA will be hosting a workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Biological cells are the fundamental units of life, and predictive modeling of cellular dynamics is essential for understanding a myriad of biological processes and functions. Rapid advances in technologies have made it possible for biologists to measure many variables and outputs from complex molecular and cellular networks with various inputs and environmental conditions. However, such advances are far ahead of the development of mathematical theory, models and methods needed to secure a deep understanding of how high-level robust behaviors emerge from the interactions in complex structures, especially in dynamic and stochastic environments. This workshop will bring together mathematicians and biological scientists involved in developing mathematical theories and methods for understanding, predicting and controlling dynamic behavior of molecular and cellular networks. Particular emphasis will be placed on efforts directed towards discovering underlying biological principles that govern function, adaptation and evolution, and on the development of associated mathematical theories.

      Organizers: Jeremy Gunawardena (Harvard) and Ruth Williams (University of California, San Diego)

      A limited amount of funding is available to help in defraying the travel costs of early career researchers, women, and underrepresented minorities, participating the workshop. Early career researchers are researchers who received their Ph.D. in 2014 or later, or who are Ph.D. students expecting to complete their Ph.D. by the end of 2020.

      To apply, please send a CV, a statement of why you wish to attend, and, if you are a grad student, a letter of support from your advisor to Sarah LaBauve at slabauve@math.harvard.edu

      All applications received by 5pm, EDT, October 28, 2019 will receive full consideration.

      Speakers: 

      Videos from the workshop can be found in the Youtube playlist.

    • Seminars
      11:21 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:21 am-11:22 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-14-2016 Random Matrix & Probability Theory Seminar
      11:22 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      11:24 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      11:25 am
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Learning from health data in the million genome era
      11:26 am
      12/01/2024

      On November 12019 the CMSA will be hosting a conference organized by Seven Bridges Genomics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Projects currently underway around the world are collecting detailed health and genomic data from millions of volunteers. In parallel, numerous healthcare systems have announced commitments to integrate genomic data into the standard of care for select patients. These data have the potential to reveal transformative insights into health and disease. However, to realize this promise, novel approaches are required across the full life cycle of data analysis. This symposium will include discussion of advanced statistical and algorithmic approaches to draw insights from petabyte scale genomic and health data; success stories to date; and a view towards the future of clinical integration of genomics in the learning health system.

      Speakers: 

      • Heidi Rehm, Ph.D.
        Chief Genomics Officer, MGH; Professor of Pathology, MGH, BWH & Harvard Medical School; Medical Director, Broad Institute Clinical Research Sequencing Platform.
      • Saiju Pyarajan, Ph.D.
        Director, Centre for Data and Computational Sciences,VABHS, and Department of Medicine, BWH and HMS
      • Tianxi Cai, Sci.D
        John Rock Professor of Population and Translational Data Sciences, Department of Biostatistics, Harvard School of Public Health
      • Susan Redline, M.D., M.P.H
        Farrell Professor of Sleep MedicineHarvard Medical School, Brigham and Women’s Hospital and Beth Israel Deaconess Medical Center
      • Avinash Sahu, Ph.D.
        Postdoctoral Research Fellow, Dana Farber Cancer Institute, Harvard School of Public Health
      • Peter J. Park, Ph.D.
        Professor of Biomedical Informatics, Department of Biomedical Informatics, Harvard Medical School
      • David Roberson
        Community Engagement Manager, Seven Bridges

      Registration & Schedule

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      9/29/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      4/20/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      12/15/2020 Computer Science for Math
      11:30 am-12:30 pm
      12/01/2024
    • Quantum Matter
      11:30 am-1:00 pm
      12/01/2024

      Quantum Matter Seminar

      Speaker: Daniel S. Freed (U Texas)

      Title: Topological symmetry in field theory

      Abstract: Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries,” “higher symmetries,” “noninvertible symmetries,” etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory. This is joint work with Constantin Teleman and Greg Moore.

       

      https://www.youtube.com/watch?v=y5uHfqVGunA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=26

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Quantum Field Theory Seminar
      11:30 am-12:00 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/24/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Quantum Oscillations of Electrical Resistivity in an Insulator
      11:30 am-1:00 pm
      12/01/2024
      CMSA-QMMP-02.03.2022

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      9/22/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      9/15/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      10/6/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      Rank-Based Independence Testing in Near Linear Time
      11:30 am-12:30 pm
      12/01/2024

      Speaker: Chaim Even-Zohar (Alan Turing Institute, London)

      Title: Rank-Based Independence Testing in Near Linear Time

      Abstract: In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.
      We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.

      Joint work with Calvin Leng.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      10/20/2020 Computer Science for Math
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      5/11/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/3/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      4/6/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      10/27/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      01-30-2017 Mathematical Physics Seminar
      11:30 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/23/2020 Mathematical Physics Seminar
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/17/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/2/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/23/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      3/2/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Quantum Matter
      11:30 am-1:00 pm
      12/01/2024

      Speaker: Lu Li (U Michigan)

      Title: Quantum Oscillations of Electrical Resistivity in an Insulator

      Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      11/10/2020 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      3/9/2021 Computer Science for Mathematicians
      11:30 am-12:30 am
      12/01/2024-03/10/2021
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      3/23/2021 Computer Science for Mathematicians
      11:30 am-12:30 pm
      12/01/2024
    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/9/2021 Computer Science for Math
      11:30 am-12:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-07-2017 Social Sciences Applications Forum
      11:32 am
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      11:33 am-1:33 pm
      12/01/2024

      Title: Symmetry types in QFT and the CRT theorem

      Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation.  I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups.  In particular, I expand on a subtlety first flagged by Greaves-Thomas.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-06-2017 Mathematical Physics Seminar
      11:33 am
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      02-13-2017, Mathematical Physics Seminar
      11:34 am
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      11:35 am
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Spacetime and Quantum Mechanics Master Class Workshop
      11:36 am
      12/01/2024-10/30/2019
      Space-Time-poster-5

      As part of the program on Spacetime and Quantum Mechanics, Total Positivity and Motives, the CMSA will host a “Master Class Workshop”  on October 28-30, 2019. Each day of the workshop will feature an intensive full day of pedagogical lectures, with the aim of bringing actively interested but non-expert physicists and mathematicians up to speed on the featured topics.

      Everyone is welcome to attend the lectures.

      The master class workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Photos of the event

      Organizers:

    • Member Seminar
      11:37 am
      12/01/2024

      Hansol Hong, Harvard

      Title: Homological Mirror Functors

      Abstract: I will first give a brief introduction to mirror symmetry, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.

    • Colloquium
      11:39 am-11:40 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:40 am-11:41 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-14-2017 Social Science Applications Forum
      11:42 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:43 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:45 am
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      11:47 am-1:47 pm
      12/01/2024

      Title: Applications of instantons, sphalerons and instanton-dyons in QCD

      Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

      Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes  and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

    • Quantum Matter
      11:48 am-1:48 pm
      12/01/2024

      Title: Oscillations in the thermal conductivity of a spin liquid*

      Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

      *Czajka et al., Nature Physics 17, 915 (2021).

      Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

    • Quantum Matter
      11:49 am-1:49 pm
      12/01/2024

      Title: Line defects in CFTs: Renormalization group flows and semiclassical limits

      Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

    • Seminars
      Seminars Colloquia & Seminar
      10/24/2019 Quantum Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/21/2019 Condensed Matter seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/5/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/12/2019 Quantum Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/7/2019 Quantum Matter Seminar
      11:50 am
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/31/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Condensed Matter Seminar
      11:50 am-1:00 pm
      12/01/2024
    • CMSA EVENT: Quantum Information Workshop
      11:52 am-11:53 am
      12/01/2024
      Asset-6-600x338

      Please note, this workshop has been postponed to a later date. Details will be posted to this page when they are available.

      The CMSA will host a workshop on Quantum Information. This workshop will be held virtually using Zoom.

      The workshop on Quantum information is organized by Mikhail LukinHorng-Tzer Yau, and Norman Yao.

      More information to follow.

    • Quantum Matter
      11:54 am-1:54 pm
      12/01/2024

      Title: A tour of categorical symmetry

      Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-12-2017 Random Matrix & Probability Theory Seminar
      11:56 am
      12/01/2024

      No additional detail for this event.

    • Colloquium
      11:56 am
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-22-2017 Random Matrix & Probability Theory Seminar
      11:58 am
      12/01/2024

      No additional detail for this event.

    • Algebraic Geometry in String Theory Seminar
      11:58 am-12:58 pm
      12/01/2024

      Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.

    • Colloquium
      11:58 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-21-2017 Social Science Applications Forum
      11:59 am
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4/1/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Chuck Doran

      Title: Modularity of Landau-Ginzburg Models

      Abstract:  Fano varieties are the basic building blocks of algebraic varieties.  Smooth Fano varieties have been classified in dimensions one (the projective line), two (del Pezzo surfaces), and three (Mori-Mukai classification).  What does Mirror Symmetry have to say about such classifications?  By studying the Landau-Ginzburg models mirror to smooth Fano threefolds we can transform the Mori-Mukai classification into an effective uniruledness result for moduli spaces of certain K3 and abelian surfaces.  This is joint work with Andrew Harder, Ludmil Katzarkov, Mikhail Ovcharenko, and Victor Przjalkowski (arXiv:2307.15607).

       

       

    • Seminars
      Seminars Colloquia & Seminar
      3/02/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3/19/2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/9/2020 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Samy Jelassi

      Title: An introduction to mixture of experts in deep learning

      Abstract: Scale has opened new frontiers in natural language processing – but at a high cost. Mixture-of-Experts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By doing so, the parameter count is decoupled from the compute per example leading to very large, but efficient models. In this talk, I will review the concept of mixture of experts, provide a basic description of the Switch Transformers model, characterize some of their behaviors and conclude by highlighting some open problems in the field. This talk is mainly based on the following papers: https://arxiv.org/pdf/2101.03961.pdfhttps://arxiv.org/pdf/2209.01667.pdf .

    • Seminars
      Seminars Colloquia & Seminar
      1/28/2018 Mathematical Physics Seminar
      12:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/24/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/22/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Mike Douglas

      Title: AI and Theorem Proving

      Abstract: We survey interactive theorem proving and the Lean theorem prover, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.

    • Seminars
      Seminars Colloquia & Seminar
      3/23/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/4/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Zi Yang Kang

      Title: Deformations of Landau-Ginzburg models and their fibers

      Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.

    • Seminars
      Seminars Colloquia & Seminar
      4/25/2019 Fluid Dynamics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/25/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Kai Xu (CMSA)

      Title: Moduli of vector bundles on curve and semiorthogonal decomposition

      Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived Θ-stratification.

       

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      9/24/2020 Strongly Correlated Quantum Materials
      12:00 pm-1:30 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Juven Wang

      Title: Categorical Symmetry of the Standard Model from Gravitational Anomaly

      Abstract: In the Standard Model, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.147652204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ16 respectively. For this construction, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, or the 3d boundary topological order of 4d ℤTF4-time-reversal symmetric topological superconductor [2302.14862].

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Benjamin McKenna

      Title: Random matrices and large deviations

      Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson.

       

    • Seminars
      Seminars Colloquia & Seminar
      3/4/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Daniel Kapec (CMSA)

      Title: Black Holes as Quantum Systems

      Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles.

       

    • Seminars
      Seminars Colloquia & Seminar
      12/18/2019 Quantum Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/25/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/8/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/11/2019 Mathematical Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Max Wiesner

      Title: Quantum Gravity constraints beyond asymptotic regimes

      Abstract: Not every effective field theory that is consistent in the absence of gravity can be completed to a consistent theory of quantum gravity. The goal of the Swampland program is to find general criteria that distinguish effective field theories, that can be obtained as a low-energy approximation of quantum gravity, from those that are inconsistent in the presence of gravity. These criteria are oftentimes motivated by patterns observed in explicit compactifications of perturbative string theory and have passed many non-trivial tests in asymptotic regions of the field space such as, e.g., weak coupling limits. Still, the Swampland criteria should equally apply to effective theories that do not arise in asymptotic regions of the field space of string theory compactifications. In this talk I will summarize some of my recent works that studies the interior of regions of the field space of string theory in the context of the Swampland program.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/3/2020 Math-Physics
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/2/2019 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/3/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/4/2019 Math Physics Seminar
      12:00 pm-2:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/13/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024-04/22/2020
    • Seminars
      Seminars Colloquia & Seminar
      4/15/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2/10/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/29/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Sunghyuk Park

      Title: Quantum UV-IR map and curve counts in skeins

      Abstract: Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong.

      In this talk, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules, using skein-valued curve counts of Ekholm and Shende.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/29/2018 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Farzan Vafa

      Title: Dynamics of active nematic defects on cones

      Abstract: In the first part of the talk, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge, which in analogy to electrostatics, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle, which is determined by charged defects screening the effective apex charge: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk, we investigate the dynamics of an active nematic on a cone, and via simulations find long-time circular orbits of either one or two flank defects, with transitions between these states mediated by the apex via defect absorption, emission, or defect pair creation.

    • Probability Seminar
      12:00 pm-1:00 pm
      12/01/2024

      Probability Seminar

      Speaker: Jun Yin (UCLA)

      Title: A random matrix model towards the quantum chaos transition conjecture

      Abstract: The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE.

      This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of the same phenomenon, shedding light on the intricacies of this long-standing conjecture.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/5/2018 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Dan Kapec

      Title: Hints of Flat Space Holography

      Abstract: Despite our detailed understanding of holography in Anti-de Sitter space, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space, bulk gravitons produce a boundary stress tensor, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Changji Xu

      Title: Spectral gap and two-point functions in spin glasses

      Abstract: Many have worked on spin glass models over the past 50 years, including physicists, mathematicians, and computers. A question that arises is whether computers yield dependable simulation results. In this talk, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.

    • Algebraic Geometry in String Theory Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Algebraic Geometry in String Theory Seminar

      Speaker: Oliver Schlotterer (Uppsala University)

      Title: Modular graph forms and iterated integrals in string amplitudes

      Abstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful cross-talk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress in clarifying their connection with modular graph forms.

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Faidra Monachou

      Title: Optimal Dynamic Allocation: Simplicity through Information Design

      Abstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that, when the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the information disclosed about each object is an interval containing the object quality, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases, these intervals become coarser, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality, in terms of the Lorenz order.

    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Freid Tong

      Title: On complete Calabi-Yau metrics and some related Monge-Ampere equations

      Abstract: We will give a basic introduction to constructions for complete Calabi-Yau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of Tian-Yau in the 90s and have attracted a lot of attention in recent years. I will discuss some joint work with B. Guo and T. Collins on a singular version of such a construction, as well as some ongoing work with Prof. Yau on some related boundary value problems.

       

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Jue Liu

      Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds

      Abstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass, we define a new quasilocal mass using the Hamilton method. With this definition, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture, that is under what conditions there will be a static extension to the given Bartnik data.

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Barak Weiss  

      Title: New bounds on lattice covering volumes, and nearly uniform covers

      Abstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK, such that L+rK = R^n, normalized by the covolume of L. Pairs (L,K) with small covering volume correspond to efficient coverings of space by translates of K, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE, Hebrew University) and Oded Regev (CS, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.

    • Math Science Literature Lecture Series
      12:00 pm-1:30 pm
      12/01/2024

      Ralph Cohen (Stanford University)

      Title: Immersions of manifolds and homotopy theory

      Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest dimension Euclidean space into which every n-manifold embeds or immerses. The embedding question is still very much unsolved, and the immersion question was solved in the 1980’s. I will discuss the homotopy theoretic techniques involved in the solution of this problem, and contributions in the 60’s, 70’s and 80’s of Massey, Brown, Peterson, and myself. I will also discuss questions regarding the best embedding and immersion dimensions of specific manifolds, such has projective spaces. Finally, I will end by discussing more modern approaches to studying spaces of embeddings due to Goodwillie, Weiss, and others. This talk will be geared toward a general mathematical audience.

      Talk chair: Michael Hopkins

      Video

    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Quantum Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Condensed Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/30/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4-17-2018 Special Algebraic Geometry Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Puskar Mondal

      Title: Recent progress on coupled Einstein-Yang-Mills dynamics

      Abstract: I will discuss my recent work with prof. S.T. Yau on Einstein-Yang-Mills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gauge-gravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a double-null framework play an important role. I’ll sketch how the special structure of the Einstein and Yang-Mills nonlinearities play a crucial role in obtaining the stability result of non-expanding spacetimes in particular AF spacetimes.

    • Seminars
      Seminars Colloquia & Seminar
      9/16/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/20/2020 Math Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/6/2019 Math Physics
      12:00 pm-1:00 pm
      12/01/2024
    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      12/2/2020 Strongly Correlated Quantum Materials
      12:00 pm-1:30 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-5-2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/27/2020 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Puskar Mondal (CMSA)

      Title: On the Breakdown of Einstein’s Gravity

      Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-26-2018 Math Physics Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/3/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Aghil Alaee

      Title: A quasi-local mass in general relativity

      Abstract: One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime, which can include a star, black hole, or galaxy. We define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition.  Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau.

       

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Chuck Doran

      Title: Motivic Geometry of Two-Loop Feynman Integrals

      Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/19/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Gabriel Wong

      Title: Quantum information and extended topological quantum field theory

      Abstract: Recently, ideas from quantum information theory have played an important role in condensed matter and quantum gravity research. Most of these applications focus on the entanglement structure of quantum states, and the computation of entanglement measures such as entanglement entropy has been an essential part of the story. In this talk, we will address some subtleties that arise when trying to define entanglement entropy in quantum field theory and quantum gravity. In particular, we will explain why extended topological field theory provides a useful framework to define and compute entanglement entropy in a continuous system. Time permitting, we will explain some recent applications of these ideas in low dimensional quantum gravity and to topological string theory.

       

       

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-2-2018 Mathematical Physics Seminar
      12:00 pm-1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/28/2019 Math Physics
      12:00 pm-1:00 pm
      12/01/2024
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11/26/2018 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Aghil Alaee

      Title: Toroidal Positive Mass Theorem

      Abstract: In this talk, we review the positive mass conjecture in general relativity and prove a toroidal version of this conjecture in an asymptotically hyperbolic setting.

    • Seminars
      Seminars Colloquia & Seminar
      10/7/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Iacopo Brivio (CMSA)

      Title: Extension of pluricanonical forms in positive and mixed characteristics

      Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{times m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring.

       

    • Seminars
      Seminars Colloquia & Seminar
      9/9/2019 Math-Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Michael Simkin

      Title: Randomized algorithms in combinatorics

      Abstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples:

      1. Enumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other?
      2. Constructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In 1973 Erdos conjectured that there exist STSs with arbitrary large girth (informally, no small set of vertices spans many triples). I will discuss the use of randomized algorithms to prove this conjecture. Joint work with Kwan, Sah, and Sawhney.
      3. Thresholds in random graphs and hypergraphs: I will discuss how randomized algorithms can be combined with the recent resolution of the Kahn–Kalai conjecture to determine thresholds in random (hyper) graph theory. Joint work with Pham, Sah, and Sawhney.
    • Seminars
      Seminars Colloquia & Seminar
      3/25/2019 Mathematical Physics Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Quantum Matter
      12:00 pm-1:30 pm
      12/01/2024
    • Seminars
      12:00 pm-1:00 pm
      12/01/2024
      Raymarching and the Thurston Geometries

      On Wednesday, December 16 at 12:00 p.m. EST, WAM and CMSA will host a holiday seminar featuring Sabetta Matsumoto, Georgia Institute of Technology who will present The Inside View: Raymarching and the Thurston Geometries.

      The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon, Henry Segerman and Steve Trettel.

      Visit the event page

      Register to access this event here

       

    • Quantum Matter
      12:00 pm-1:00 pm
      12/01/2024

      Speaker: Eric Sharpe (Virginia Tech)

      Title: Anomaly resolution via decomposition

      Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples.  After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.

    • Quantum Matter
      12:00 pm-1:00 pm
      12/01/2024

      Speaker: Biao Lian (Princeton)

      Title: Integrability and chaos of 1+1d chiral edge states

      Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.

    • General Relativity Seminar
      12:00 pm-1:00 pm
      12/01/2024

      The Seminar on General Relativity will take place every Wednesday from 12pm – 1pm in CMSA Building, 20 Garden Street, G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      04-06-2016Mihalis Dafermos (Princeton)The black hole stability problem: the inside story
      04-13-2016Felix Finster, University of RegensburgLinear stability of Kerr black holes
      04-20-2016Paul Chesler, Harvard PhysicsNumerical relativity in asymptotically anti-de Sitter spacetime
      04-27-2016Andy Strominger (Harvard Physics) & Mihalis Dafermos (Princeton University)The Scattering Problem in General Relativity
      05-04-2016Robert Penna, MITBMS invariance and the membrane paradigm
      05-11-2016Piotr T. Chruściel, University of ViennaGluing things in general relativity
      05-18-2016Achilleas Porfyriadis, Harvard PhysicsGravitational waves from the Kerr/CFT correspondence
      05-25-2016Scott Hughes, MITThe gravitational-wave event GW150914: What we learned, and how we learned it
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Juven Wang

      Title: Open Problems in Physics and Novel Solutions from Math

       

      Abstract: (1) How do neutrinos obtain tiny mass and oscillate between e, \mu, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis?

      (2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions?

      (3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry?

      (4) Family/Generation problem: Why are there three families/generations of quarks and leptons?

      In my talk, I will sketch and propose novel solutions to these challenging open problems in physics based on my own work (available on arXiv, some jointly with my collaborators).

      I will show that the eclectic cross-disciplinary fertilization of ideas between the Math-Physics geometry and topology, Quantum Condensed Matter, and High-Energy Physics (theory, pheno, lattice) can help solving these big problems.

      The (1) answer relates to Ultra Unification: a Z_{16} class Atiyah-Patodi-Singer eta invariant (Baryon – Lepton)-protected topological superconductor and a symmetry-extended anomalous topological quantum field theory.

      The (2) and (3) answers relate to a trivial cobordism class and Symmetric Mass Generation, and disordering and removing the Pecci-Quinn axions.

      The (4) answer has to do with the Hirzebruch signature and Atiyah-Singer index theorem, gravitational Chern-Simons theory, and 3 E8 quantum Hall states.

       

    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Title: Duality in Einstein’s Gravity

      Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      4/8/2021 Interdisciplinary Science Seminar
      12:00 pm-1:00 pm
      12/01/2024
    • Member Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Member Seminar

      Speaker: Alejandro Poveda

      Title: On compactness phenomena

      Abstract: In this presentation I shall be preoccupied with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behavior. This phenomenon is intrinsic to the very architecture of the mathematical universe and manifests to us in a cornucopia of forms. Over the past fifty years, the study of compactness phenomena has been a cornerstone of research in set theory. This talk will present recent discoveries regarding compactness principles, spanning classical themes like the tree property and stationary reflection, while also forging novel connections with other topics, such as Woodin’s HOD Conjecture.

    • Active Matter Seminar
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 10.20.22
      Active Matter Seminar
      Speaker: Sharad Ramanathan, Harvard
      Title: Attempts at understanding human axial elongation and patterning
      Abstract: Some of the most dramatic events during human development is the axial elongation of the embryo with concomitant changes in the geometry and composition of the underlying tissues. The posterior part of the embryo gives rise to the spinal cord, vertebral column, ribcage, back muscles, and dermis.  In this talk, I will present our attempts at coaxing human embryonic stem cells to form these structures of the early human embryo that closely recapitulate the geometry, relative arrangements, composition, and dynamics of development of the early spinal cord flanked progenitors of the musculoskeletal system. Our goal was to do so, such that we could build hundreds of these organoids at a time. I will also present preliminary results for the use of this system to understand key events during early human development through imaging and genetic perturbations.
    • Colloquium
      12:00 pm-1:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      colloquium

      Colloquium

      Speaker: Yannai Gonczarowski (Harvard)

      Title: Strategyproof-Exposing Mechanisms Descriptions

      Abstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.

      By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.

      Joint work with Ori Heffetz and Clayton Thomas.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-22-2017 Random Matrix & Probability Theory Seminar
      12:01 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:03 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Cosmic Road to New Physics
      12:04 pm
      12/01/2024
      The colourful star cluster NGC 3532

      The CMSA will host a 3-day workshop on cosmological signatures of fundamental physics. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

      The next decade will see a wealth of new cosmological data, which can lead to new insights for fundamental physics. This upcoming data will span the entire history of the cosmos, from the era prior to big-bang nucleosynthesis to the inner Galactic structure today, including the intervening eras of recombination and cosmic dawn. Often, beyond-standard-model (BSM) physics will leave imprints in more than one of these eras. Thus, it is timely to gather experts in BSM physics across the entire cosmic history to exchange ideas and develop joint and powerful probes of new physics. For this program, it will be crucial to have an overlap of particle physicists, astrophysicists and cosmologists. There are a number of tools and techniques being actively developed across these disciplines. The workshop aims to provide a platform for efficient exchange of these new ideas.

      The first day we will discuss sub-Galactic probes, including Gaia data and gravitational waves. The second day we will cover cosmological probes, such as the cosmic microwave background and the 21-cm line. The third day we will discuss early Universe probes, such as inflation and phase transitions. Every day the meeting will begin with a pedagogical blackboard talk plus an overview talk, followed by about 4 talks on more specific topics.

      Organizers:

      Scientific Advisory:

      Speakers: 

      CosmicRoad_Poster

    • Colloquium
      12:05 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:06 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:08 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:09 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      12:10 pm-1:10 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

       

      Speaker: Man-Wai Cheung

      Title: Compactification for cluster varieties without frozen variables of finite type

      Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

    • CMSA EVENT: 2019 Ding Shum Lecture
      12:11 pm
      12/01/2024
      DingShum-2019

      DSC_0468-e1568985499370

      On October 22, 2019, the CMSA will be hosting our third annual Ding Shum lecture. This year’s lecture will be a talk on “Election Security” by Ronald L. Rivest (MIT). The lecture will take place from 4:30-5:30pm in Science Center, Hall A.

      Ronald L. Rivest is an Institute Professor at the Massachusetts Institute of Technology. He is a member of the Electrical Engineering and Computer Science Department and the Computer Science and Artificial Intelligence Laboratory (CSAIL) and a founder of the Cryptography and Information Security research group within CSAIL. His research has been in the areas of algorithms, machine learning, cryptography, and election security, for which he has received multiple awards, including: the ACM Turing Award (with Adleman and Shamir), the BBVA Frontiers of Knowledge Award, National Inventor’s Hall of Fame membership, and the Marconi Prize.

      Prof. Rivest is also well-known as a co-author of the textbook “Introduction to Algorithms” (with Cormen, Leiserson, and Stein), and as a co-inventor of the RSA public-key cryptosystem (with Adleman and Shamir). He is a co-founder of RSA and of Verisign.He has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), in charge of the Security subcommittee. He is a member of the CalTech/MIT Voting Technology Project, on the Board of Verified Voting, and an advisor to the Electronic Privacy Information Center. Additionally, he has served on the Technical Guidelines Development Committee (advisory to the Election Assistance Commission), as a member of the CalTech/MIT Voting Technology Project, and as an advisor to the Electronic Privacy Information Center.

      Last year featured Eric Maskin, who spoke on “How to Improve Presidential Elections: the Mathematics of Voting.” The first Ding Shum lecture took place on October 10, 2017, featuring Leslie Valiant on “Learning as a Theory of Everything.”

      This event is made possible by the generous funding of Ding Lei and Harry Shum.

      DingShum-2019

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-1-2017 Random Matrix & Probability Seminar
      12:11 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Special Lecture Series on Donaldson-Thomas and Gromov-Witten Theories
      12:11 pm
      12/01/2024-04/19/2017

      From March 8 to April 19, the Center of Mathematical Sciences and Applications will be hosting a special lecture series on Donaldson-Thomas and Gromov-Witten Theories. Artan Sheshmani (QGM Aarhus and CMSA Harvard) will give eight talks on the topic on Wednesdays and Fridays from 9:00-10:30 am, which will be recorded and promptly available on CMSA’s Youtube Channel.

    • Colloquium
      12:12 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:13 pm-12:14 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-27-2017 Mathematical Physics Seminar
      12:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-7-2017 Social Science Applications Forum
      12:15 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:15 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/13/2019 Special Seminar
      12:15 pm-1:05 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3-8-2017 CMSA Special Lecture Series
      12:16 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Noncommutative Analysis, Computational Complexity, and Quantum Information
      12:19 pm
      12/01/2024-10/18/2019
      Noncommutative-Analysis-Poster-3

      On October 16-18, 2019 the CMSA will be hosting a workshop on Noncommutative Analysis, Computational Complexity, and Quantum Information.

      This workshop will focus on  linking three different rapidly developing areas: noncommutative real algebraic geometry (RAG), theory of computation and quantum information theory. This mix of overlapping but independently developing topics should lead to a stimulating flow of tools and important problems into several disciplines.  Given the different communities there will be an emphasis on tutorials and making the lectures broadly understandable.

      The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by Boaz Barak, Bill Helton, Pablo Parrilo, Tselil Schramm.

      Please register here

      Speakers:

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-8-2017 Random Matrix & Probability Theory Seminar
      12:21 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-6-2017 Mathematical Physics Seminar
      12:24 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      12:25 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-10-2017 Special Lecture Series
      12:27 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-21-2017 Social Science Applications Forum
      12:28 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
      12:28 pm
      12/01/2024-05/05/2019
      1 Oxford Street, Cambridge MA 02138
      Differential Geometry, Calabi-Yau theory and General Relativity

      Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau

      On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the  Science Center, Lecture Hall C. 

      Organizers:

      • Horng-Tzer Yau (Harvard)
      • Wilfried Schmid (Harvard)
      • Clifford Taubes (Harvard)
      • Cumrun Vafa (Harvard)

      Speakers:

      • Lydia Bieri, University of Michigan
      • Tristan Collins, MIT
      • Simon Donaldson, Imperial College
      • Fan Chung Graham, UC San Diego
      • Nigel Hitchin, Oxford University
      • Jun Li, Stanford University
      • Kefeng Liu, UCLA
      • Chiu-Chu Melissa Liu, Columbia University
      • Alina Marian, Northeastern University
      • Xenia de la Ossa, Oxford University
      • Duong H. Phong, Columbia University
      • Richard Schoen, UC Irvine
      • Andrew Strominger, Harvard University
      • Nike Sun, MIT
      • Clifford Taubes, Harvard University
      • Chuu-Lian Terng, UC Irvine
      • Valentino Tosatti, Northwestern University
      • Karen Uhlenbeck, University of Texas
      • Cumrun Vafa, Harvard University
      • Mu Tao Wang, Columbia University
      • Edward Witten, IAS
      • Stephen Yau, Tsinghua University, P.R. China
    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 03.22.2023

      Speaker: Mete Soner (Princeton University)

      Title: Synchronization in a Kuramoto Mean Field Game

      Abstract:  Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a  key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  We explore this system in the mean field formalism.  We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium.  The mean field game also exhibits a bifurcation from incoherence to self-organization.  This approach has found interesting applications including circadian rhythms and jet-lag recovery.  This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Tim Adamo, University of Edinburgh

      Title: An invitation to strong-field scattering

      Abstract: Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to all-multiplicity twistor and string methods.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Xi Yin (Harvard Physics) and Peter Kronheimer (Harvard Math)
      Topics:
      Xi Yin: What is string field theory?
      Peter Kronheimer: What is Seiberg-Witten theory?
    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Four-dimensional topology
      12:30 pm-1:30 pm
      12/01/2024
      Lecture_Manolescu-pdf

      Ciprian Manolescu (Stanford)

      Title: Four-dimensional topology

      Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to four-manifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience.

      Video

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 05.03.2023

      Speaker: Xin Guo, UC Berkeley

      Title: Generative Adversarial Networks (GANs): An Analytical Perspective

      Abstract: Generative models have attracted intense interests recently. In this talk, I will discuss one class of generative models, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis.

       

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)
      Topics:
      Dan Freed: What is framing anomaly? How is it different from other anomalies?
      Dan Berwick-Evans: What is Atiyah-Singer index theorem?
    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      Speakers: Dan Freed (Harvard Math and CMSA), Denis Auroux (Harvard Math)

    • Math Science Literature Lecture Series
      12:30 pm-2:00 pm
      12/01/2024
      Lecture_Freedman-1-pdf

      Michael Freedman (Microsoft – Station Q)

      Title: A personal story of the 4D Poincare conjecture

      Abstract:  The proof of PC4 involved the convergence of several historical streams.  To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.

      Talk Chair: Peter Kronheimer

      Video

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 03.08.2023

      Speaker: Ning Su, University of Pisa

      Title: Conformal symmetry, Optimization algorithms and the Critical Phenomena

      Abstract: In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid phase transition and Heisenberg magnet to very high precision.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 03.29.2023

      Speaker: Ruth Britto (Trinity College Dublin)

      Title: Scattering amplitudes in quantum field theory

      Abstract: Particle collider experiments require a detailed description of scattering events, traditionally computed through sums of Feynman diagrams. However, it is not practical to evaluate Feynman diagrams directly for all significant scattering processes. Moreover, adding all diagrams reveals many cancellations: scattering amplitudes in theories such as QCD take remarkably simple forms. This simplicity is a clue that the perturbative theory is perhaps best understood without reference to Feynman diagrams. In fact, it has recently become possible to explain some of this simplicity. I will show how to derive many amplitudes efficiently and elegantly, and propose taming the remaining complexity with ideas drawn from combinatorics and geometry.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 04.26.2023.rev2

      Speaker: Max Metlitski (MIT)

      Title: Boundary behavior at classical and quantum phase transitions

      Abstract: There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter, where exotic protected boundary states are ubiquitous. In this talk, I’ll ask: what happens at a boundary of a system, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field, as well as some extensions to quantum phase transitions.

       

    • Colloquium
      12:30 pm
      12/01/2024

      No additional detail for this event.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University)

      Topics:

      Michael Douglas: “What is non-commutative field theory?”
      Mayuko Yamashita: “What is differential cohomology?”
    • Topological Quantum Matter Seminar
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Hart Goldman, University of Chicago

      Title: Composite fermions and the fractional quantum anomalous Hall effect

      Abstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk, I will argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new zero-field context. In particular, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end, I will present exact diagonalization evidence for such composite Fermi liquid states at zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs), I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 04.12.2023
      Speaker: James Halverson (Northeastern University)
       
      Title: Unexpected Uses of Neural Networks: Field Theory and Metric Flows

      Abstract:  We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics, sometimes leading to rigorous results. In this talk, however, I will argue that breakthroughs in deep learning theory are also useful for making progress, focusing on applications to field theory and metric flows. Specifically, I will introduce a neural network approach to field theory with a different statistical origin, that exhibits generalized free field behavior at infinite width and interactions at finite width, and that allows for the study of symmetries via the study of correlation functions in a different duality frame. Then, I will review recent progress in approximating Calabi-Yau metrics as neural networks and cast that story into the language of neural tangent kernel theory, yielding a theoretical understanding of neural network metric flows induced by gradient descent and recovering famous metric flows, such as Perelman’s formulation of Ricci flow, in particular limits.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 11.16.22 - 2

      Colloquium

      Speaker: Hidenori Tanaka (NTT Research at Harvard)

      Title: Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks

      Abstract: In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle, but the role of symmetry breaking is not well understood. Here, we develop a Lagrangian formulation to study the geometry of learning dynamics in neural networks and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. Then, we generalize Noether’s theorem known in physics to describe a unique symmetry breaking mechanism in learning and derive the resulting motion of the Noether charge: Noether’s Learning Dynamics (NLD). Finally, we apply NLD to neural networks with normalization layers and discuss practical insights. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      A tale of two balloons
      12:30 pm-1:30 pm
      12/01/2024
      CMSA-Combinatorics-Physics-and-Probability-Seminar-11.16.21

      Abstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law, and generalize bounds on independent sets that are factors of IID on trees.
      Joint work with Omer Angel and Gourab Ray.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-20-2017 Mathematical Physics Seminar
      12:30 pm
      12/01/2024

      No additional detail for this event.

    • Math Science Literature Lecture Series
      12:30 pm-1:30 pm
      12/01/2024
      Lecture_Lian-pdf

      Bong Lian (Brandeis)

      Title: From string theory and Moonshine to vertex algebras

      Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed at a general audience.

      Slides | Video

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium
      Colloquium
      Speaker: Melody Chan
      Title: Moduli spaces of graphs
      Abstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.
    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.13.2023

      Title: Complete Calabi-Yau metrics: Recent progress and open problems

      Abstract: Complete Calabi-Yau metrics are fundamental objects in Kahler geometry arising as singularity models or “bubbles” in degenerations of compact Calabi-Yau manifolds.  The existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to Yau and Tian-Yau. I will describe some recent progress towards the question of existence, and explain some future directions, highlighting connections with notions of algebro-geometric stability.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Mike Douglas (Harvard CMSA) and Anurag Anshu (Harvard Computer Science)

      Topics:

      Mike Douglas: What are scaling laws in deep learning?

      Anurag Anshu: What’s the difference between classical information theory and quantum information theory (or classical computation vs quantum computation)?

       

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.02.2023

      Speaker: Max Reppen (Boston University)

      Title: Neural Optimal Stopping Boundary

      Abstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.12.22 (1)

      Colloquium

      Title: Complete disorder is impossible: Some topics in Ramsey theory

      Speaker: James Cummings, Carnegie Mellon University

      Abstract: The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory, which touches on many areas of mathematics including graph theory, set theory and dynamics. I will give an overview of Ramsey theory, emphasizing the diverse ideas which are at play in this area.

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA)

      Topics:

      Dan Freed: What is Dijkgraaf-Witten theory?

      Sunghyuk Park: What happened at the Clay Math Institute Workshop?

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.19.22

      Colloquium

      Speaker: Patrick Lopatto (Brown)

      Title: The Mobility Edge of Lévy Matrices

      Abstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness, these models have been broadly applied in physics, finance, and statistics. When the entries have infinite mean, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.

    • Strongly Correlated Quantum Materials and High-Temperature Superconductors
      Strongly Correlated Quantum Materials and High-Temperature Superconductors
      11/6/2020 Strongly Correlated Quantum Materials Lecture
      12:30 pm-3:00 pm
      12/01/2024
    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.08.2023

      Speaker: David Gamarnik (MIT)

      Title: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property

      Abstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph, the problem of finding a near ground state in a spin glass model, the problem of finding a satisfying assignment in a random constraint satisfaction problem, and many many more. Unfortunately, at the same time no formal computational hardness results exist which  explains this persistent algorithmic gap.

      In the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms which exhibit a form of stability/noise insensitivity.

      We will specifically show how to use this property to obtain stronger (stretched exponential) than the state of the art (quasi-polynomial) lower bounds on the size of constant depth Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph, and the problem of finding a near ground state of a p-spin model.

      Joint work with Aukosh Jagannath and Alex Wein

    • CMSA Q&A Seminar
      12:30 pm-1:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      CMSA Q and A Seminar

      Speakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math)

      Topics:

      Mike Hopkins: What are topological modular forms?

      Mihnea Popa: What is the abundance conjecture and why should it to be true?

       

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 09.28.22

      Colloquium

      Speaker: Dima Sinapova (Rutgers University)

      Title: The Tree Property and uncountable cardinals

      Abstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes.

      We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.

       

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.26.22

      Speaker: Virginia Vassilevska Williams (MIT)

      Title: Clique listing algorithms

      Abstract: A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history.

      A fundamental question, with many applications, is “How fast can one list all k-cliques in a given graph?”.

      Even just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant, such as 3 or 4 (independent of n), even the brute-force algorithm runs in polynomial time, O(n^k), and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k), the brute-force algorithm is in some sense optimal, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques, with running times depending on the number of vertices n, the number of edges m, the number of k-cliques T and more. We will focus on the case when k=3, but we will note some extensions.

      (Based on joint work with Andreas Bjorklund, Rasmus Pagh, Uri Zwick, Mina Dalirrooyfard, Surya Mathialagan and Yinzhan Xu)

    • Colloquium
      12:30 pm-1:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 02.22.2023

      Speaker: Netta Engelhardt (MIT)

      Title: The Black Hole Information Paradox: A Resolution on the Horizon?

      Abstract: The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary, and in particular its application to entanglement and complexity, however, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-5-2017 Random Matrix & Probability Theory Seminar
      12:31 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:32 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Conference on Algebraic Geometry, Representation theory and Mathematical Physics
      12:33 pm
      12/01/2024-05/01/2019

      From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.  

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Videos

      Speakers: 

       

      Monday, April 29

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amWei Zhang, MITTitle: The arithmetic fundamental lemma for diagonal cycles

      Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions.  The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

      10:00 – 10:30amBreak
      10:30 – 11:30amYuri Tschinkel, NYUTitle: Equivariant birational geometry and modular symbols

      Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

      11:30 – 1:30pmLunch
      1:30 – 2:30pmAlexander Efimov, MoscowTitle: Torsionness for regulators of canonical extensions

      Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

      2:30 – 3:00pmBreak
      3:00 – 4:00pmAmin Gholampour, MarylandTitle: Euler Characteristics of punctual quot schemes on threefolds

      Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

      4:00 – 4:30pmBreak
      4:30 – 5:30pmMaksym Fedorchuck, BCTitle:  Stability of one-parameter families of weighted hypersurfaces

      Abstract:  We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space.  The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties.  Joint work with Hamid Ahmadinezhad and Igor Krylov.

       

      Tuesday, April 30

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amBrendan Hassett, BrownTitle: Rationality for geometrically rational threefolds

      Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics.  (joint with Tschinkel)

      10:00 – 10:30amBreak
      10:30 – 11:30amDennis Gaitsgory, HarvardTitle: The Fundamental Local Equivalence in quantum geometric Langlands

      Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted  Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its  dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

      11:30 – 1:00pmLunch
      1:00- 2:00pmAndrei Negut, MITTitle: AGT relations in geometric representation theory

      Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

      2:00 – 2:15pmBreak
      2:15 – 3:15pmDan Abramovich, BrownTitle: Resolution in characteristic 0 using weighted blowing up

      Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.

      Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.

      We show that there is a functorial way to resolve varieties using \emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X \subset Y$ one functorially assigns an invariant $(a_1,\ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , \ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.

      This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

      3:15 – 3:30pmBreak
      3:30 – 4:30pmFedor Bogomolov, NYUTitle: On the base of a Lagrangian fibration for a compact hyperkahler manifold.

      Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of  Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

      4:30 – 4:45pmBreak
      4:45 – 5:45pmDawei Chen, BCTitle: Volumes and intersection theory on moduli spaces of Abelian differentials

      Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

       

      Wednesday, May 1

      TimeSpeakerTitle/Abstract
      8:30 – 9:00amBreakfast
      9:00 – 10:00amPavel Etingof, MITTitle: Short star-products for filtered quantizations

      Abstract: PDF

      This is joint work with Eric Rains and Douglas Stryker.

      10:00 – 10:30amBreak
      10:30 – 11:30amRoman Bezrukavnikov, MITTitle: Stability conditions and representation theory

      Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
      and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
      to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

      11:30 – 11:45amBreak
      11:45 – 12:45pmQile Chen, BCTitle: Counting curves in critical locus via logarithmic compactification

      Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.

      In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.

      This is a joint work with Felix Janda and Yongbin Ruan.

      12:45 – 2:30pmLunch
      2:30 – 3:30pmSi Li, TsinghuaTitle: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry

      Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

      3:30 – 4:00pmBreak
      4:00 – 5:00pmLudmil Katzarkov, MoscowTitle: PDE’s non commutative  motives and HMS.

      Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir.  Geometry will be discussed.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-29-2017 Random Matrix & Probability Theory Seminar
      12:35 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3-24-2017 Random Matrix & Probability Theory Seminar
      12:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3-30-2017 CMSA Special Seminar
      12:38 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-27-2017 Mathematical Physics Seminar
      12:40 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:41 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-5-2017 Special Lecture Series
      12:42 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-7-2017 Special Lecture Series
      12:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Special Lecture Series
      12:44 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:45 pm-1:45 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 11.02.22

      Speaker: Liang Fu (MIT)

      Title: Doping and inverting Mott insulators on semiconductor moire superlattices

      Abstract: Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First, in an intermediate range of magnetic fields, doping this Mott insulator gives rise to a dilute gas of spin polarons, which form a pseudogap metal. Second, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.

    • Colloquium
      12:45 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-14-2017 Special Lecture Series
      12:46 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-3-2017 Mathematical Physics Seminar
      12:50 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      12:51 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      4-12-2017 Social Science Applications Forum
      12:53 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Mirror Symmetry and Stability
      12:55 pm
      12/01/2024-03/20/2019
      HMS-2019-1

      This three-day workshop will take place at Harvard University on March 18-20, 2019 in Science Center room 507. The main topic will be stability conditions in homological mirror symmetry. This workshop is funded by the Simons Collaboration in Homological Mirror Symmetry.

      Organizers: Denis Auroux, Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau, Bong Lian, Shing-Tung Yau, Jingyu Zhao

      Speakers:

      Dylan Allegretti (Sheffield)
      Tristan Collins (MIT)
      Naoki Koseki (Tokyo)
      Chunyi Li (Warwick)
      Jason Lo (CSU Northridge)
      Emanuele Macrì (NEU & IHES)
      Genki Ouchi (Riken iTHEMS)
      Pranav Pandit (ICTS)
      Laura Pertusi (Edinburgh)
      Jacopo Stoppa (SISSA)
      Alex Takeda (UC Berkeley)
      Xiaolei Zhao (UC Santa Barbara)

      More details will be added later.

      Visit the event page for more information. 

       

      HMS-2019-1

    • Colloquium
      12:55 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      12:57 pm
      12/01/2024

      No additional detail for this event.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Active crystals are highly ordered structures that emerge from the nonequilibrium self-organization of motile objects, and have been widely studied in synthetic and bacterial active matter. In this talk, I will describe how swimming sea star embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiment, hydrodynamic theory, and simulations, we demonstrate that the formation, dynamics, and dissolution of these living crystals are controlled by the natural development of the embryos. Remarkably, due to nonreciprocal force and torque exchange between the embryos, the living chiral crystals exhibit self-sustained oscillations with dynamic signatures recently predicted to emerge in materials with odd elasticity.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character \theta of G, and a G-invariant function w on V.  This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient.  GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM, very few computations of these invariants have been carried out.  In this talk I will describe a new method for computing generating functions of GLSM invariants.  I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.

    • Math Science Literature Lecture Series
      1:00 pm-2:00 pm
      12/01/2024
      Lecture_Harris_updated-pdf

      Joe Harris (Harvard)

      Title: Rationality questions in algebraic geometry

      Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension two) and Hodge theory (dimension 3). But there remained much we didn’t understand about the condition of rationality, such as how it behaves in families. However, there has been recent progress: work of Hassett, Tschinkel, Pirutka and others, working with examples in dimension 4, showed that it is in general neither an open condition nor a closed one, but does behave well with respect to specialization. In this talk I’ll try to give an overview of the history of rationality and the current state of our knowledge.

      Video

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack), there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk, we first show that these three definitions are equivalent. Second, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third, we apply these results to various moduli situations, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      No additional detail for this event.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-01.27.2022

      Abstract: Fluids pervade complex systems, ranging from fish schools, to bacterial colonies and nanoparticles in drug delivery. Despite its importance, little is known about the role of fluid mechanics in such applications. Is schooling the result of vortex dynamics synthesized by individual fish wakes or the result of behavioral traits? Is fish schooling energetically favorable?  I will present multifidelity computational studies of collective swimming in 2D and 3D flows. Our studies demonstrate that classical models of collective swimming (like the Reynolds model) fail to maintain coherence in the presence of long-range hydrodynamic interactions. We demonstrate in turn that collective swimming can be achieved through reinforcement learning. We extend these studies to 2D and 3D viscous flows governed by the Navier Stokes equations. We examine various hydrodynamic benefits with a progressive increase of the school size and demonstrate the importance of controlling the vorticity field generated by up to 300 synchronized swimmers.

    • Seminars
      Seminars Colloquia & Seminar
      11/13/2019 General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024
    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar
      Speaker: Herbert Levine (Northeastern)
      Title: Frustration-free states of cell fate networks: the case of the epithelial-mesenchymal transition

      Abstract: Cell fate decisions are made by allowing external signals to govern the steady-state pattern adopted by networks of interacting regulatory factors governing transcription and translation. One of these decisions, of importance for both developmental processes and for cancer metastasis, is the epithelial-mesenchymal transition (EMT). In this talk, we will argue that these biological networks have highly non-generic interaction structures such that they allow for phenotypic states with very low frustration, i.e. where most interactions are satisfied. This property has important consequences for the allowed dynamics of these systems.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA-GR-Seminar-03.10.22

      Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Gromov-Witten invariants count pseudo-holomorphic curves on a symplectic manifold passing through some fixed points and submanifolds. Similarly, open Gromov-Witten invariants are supposed to count disks with boundary on a Lagrangian, but in most cases such counts are not independent of some choices as we would wish. Motivated by Fukaya’11, J. Solomon and S. Tukachinsky constructed open Gromov-Witten invariants in their 2016 papers from an algebraic perspective of $A_{\infty}$-algebras of differential forms, utilizing the idea of bounding chains in Fukaya-Oh-Ohta-Ono’06. On the other hand, Welschinger defined open invariants on sixfolds in 2012 that count multi-disks weighted by the linking numbers between their boundaries. We present a geometric translation of Solomon-Tukachinsky’s construction. From this geometric perspective, their invariants readily reduce to Welschinger’s.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Max Lavrentovich, Worcester State University

      Title: Strongly driven mixtures and membranes: Out of equilibrium surprises

      Abstract: The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phase-separating colloidal mixture and a lipid membrane, which demonstrate counterintuitive properties when driven out of equilibrium. We will see that the phase separating mixture, when driven by a uniform force, develops (in simulations) an intriguing pattern with a characteristic length scale set by the magnitude of the drive. We will look at some theoretical approaches to understanding the pattern formation and possible experimental realizations. The membrane, when driven by an oscillatory electric field, develops (in experiments) a long-lived metastable state with a decreased capacitance and increased dissipation. This state may have implications for neuronal processing and memory formation.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.

      1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.

      2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-02.24.22

      Abstract: The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological
      disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes: (i) to explain the tortoise & hare story in bacterial competition: how motility of Pseudomonas aeruginosa bacteria leads to a slower invasion of bacteria colonies, which are individually faster, and
      (ii) how self-propelled defects lead to finding an unanticipated mechanism for cell death.

      I will then discuss various strategies to tame, otherwise chaotic, active flows, showing how hydrodynamic screening of active flows can act as a robust way of controlling and guiding active particles into dynamically ordered coherent structures. I will also explain how combining hydrodynamics with topological constraints can lead to further control of exotic morphologies of active shells.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      No additional detail for this event.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.

    • Seminars
      Seminars Colloquia & Seminar
      12/6/2019 Special Seminar
      1:00 pm-2:00 pm
      12/01/2024
    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I will present a four-term exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations, the Hodge, weight, and perverse Leray filtrations, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the Clemens-Schmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran.

    • Combinatorics Physics and Probability
      Combinatorics Physics and Probability
      9/28/2021 Combinatorics, Physics and Probability Seminar
      1:00 pm
      12/01/2024

      Title: The hypersimplex and the m=2 amplituhedron

      Abstract: I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2k-dimensional subset of Gr(k, k+2), and the hypersimplex, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.

    • Math Science Literature Lecture Series
      1:00 pm-2:00 pm
      12/01/2024

      Robert Griess (University of Michigan)

      Title: My life and times with the sporadic simple groups

      Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad school at University of Chicago,  I became fascinated with the unfolding story of sporadic simple groups. It involved theory, detective work and experiments. During this lecture, I will describe some of the people, important ideas and evolution of thinking about sporadic simple groups. Most should be accessible to a general mathematical audience.

      Video | Slides

    • CMSA EVENT: Simons Collaboration Workshop, April 5-7, 2018
      1:00 pm-6:00 pm
      12/01/2024-04/07/2018
      banner-image-1

      The CMSA will be hosting a three-day Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 5-7, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      Please click here to register for this event.  We have space for up to 30 registrants on a first come, first serve basis.

      We may be able to provide some financial support for grad students and postdocs interested in this event.  If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.

      Confirmed Speakers:

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 11.17.22
      Active Matter Seminar

      Speaker: Max Prigozhin (Harvard)

      Title: Dynamic and multicolor electron microscopy

      Abstract: My lab is developing biophysical methods to achieve multicolor and dynamic biological imaging at the molecular scale. Our approach to capturing the dynamics of cellular processes involves cryo-vitrifying samples after known time delays following stimulation using custom cryo- plunging and high-pressure freezing instruments. To achieve multicolor electron imaging, we are exploring the property of cathodoluminescence—optical emission induced by the electron beam. We are developing nanoprobes (“cathodophores”) that will be used as luminescent protein tags in electron microscopy. We are applying these new methods to study G-protein- coupled receptor signaling and to visualize the formation of biomolecular condensates.

    • Algebraic Geometry in String Theory Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem, and new results in this direction, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-02.10.22

      Abstract: My lab is interested in the active and adaptive materials that underlie control of cell shape.  This has centered around understanding force transmission and sensing within the actin cytoskeleton.  I will first review our current understanding of the types of active matter that can be constructed by actin polymers.  I will then turn to our recent experiments to understand how Cell shape changes in epithelial tissue.  I will describe the two sources of active stresses within these tissues, one driven by the cell cycle and controlling cell-cell stresses and the other controlled by cell-matrix signaling controlling motility.  I will then briefly describe how we are using optogenetics to locally control active stresses to reveal adaptive and force-sensitive mechanics of the cytoskeletal machinery. Hopefully, I will convince you that recent experimental and theoretical advances make this a very promising time to study this quite complicated form of active matter.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: During development, organisms interact with their natural habitats while undergoing morphological changes, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria, a basal animal lineage that includes sea anemones, corals, hydras, and jellyfish, offers unique insight into the development and evolution of morphological complexity.  In my talk, I will introduce our research on “ethology of morphogenesis,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels, opening new perspectives about the design principle of soft-bodied animals. In addition, I will discuss a fascinating feature of cnidarian biology. For humans, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule.

      References
      Anniek Stokkermans, Aditi Chakrabarti, Ling Wang, Prachiti Moghe, Kaushikaram Subramanian, Petrus Steenbergen, Gregor Mönke, Takashi Hiiragi, Robert Prevedel, L. Mahadevan, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976

      Ikmi A, Steenbergen P, Anzo M, McMullen M, Stokkermans M, Ellington L, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensisNature communications, Sept 02; 11:4399

      He S, Del Viso F, Chen C, Ikmi A, Kroesen A, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensisScience, Vol. 361, Issue 6409, pp. 1377-1380.
      Ikmi A, McKinney SA, Delventhal KM, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensisNature communications. Nov 24; 5:5486.

    • Seminars
      Seminars Colloquia & Seminar
      Combinatorics & Complexity Seminar, Fridays
      1:00 pm-4:00 pm
      12/01/2024

      The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

      Additional information on CMSA’s Combinatorics and Complexity program can be found here.

       

      DateNameTitle/Abstract
      09-08-17TBA
      09-15-2017TBA
      09-22-17TBA
      09-29-17TBA
      10-06-17 TBA
      10-13-2017TBA
      10-20-2017TBA
      10-27-2017TBA
      11-03-2017TBA
      11-10-2017TBA
      11-17-2017TBA
      11-24-2017TBA
      12-01-2017TBA
      12-08-2017 TBA
    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 11.03.22

      Active Matter Seminar

      Speaker: Siavash Monfared, Niels Bohr Institute, Copenhagen

      Title: Force transmission informs the collective behavior of active cell layers

      Abstract: Collective cell migration drives numerous physiological processes such as tissue morphogenesis, wound healing, tumor progression and cancer invasion. However, how the interplay of mechanical interactions and the modes of collective self-organization among cells informs such processes is yet to be established. In this talk, I will focus on the role of three-dimensional force transmission, from a theoretical and computational perspective, on two phenomena: (1) cell extrusion from a cellular monolayer and (2) density-independent solid-like to fluid-like transition of active cell layers. For the first topic, I will focus on how increasing cell-cell adhesion relative to cell-substrate adhesion enables cells to collectively exploit distinct mechanical pathways – leveraging defects in nematic and hexatic phases associated with cellular arrangement – to eliminate an unwanted cell. For the second topic, I will show how solid-like to fluid-like transition in active cell layers is linked to the percolation of isotropic stresses. This is achieved via two distinct and independent paths to model this transition by increasing (a) cell-cell adhesion and (b) active traction forces. Additionally, using finite-size scaling analyses, the phase transition associated with each path is mapped onto the 2D site percolation universality class. Our results highlight the importance of force transmission in informing the collective behavior of living cells and opens the door to new sets of questions for those interested in connecting the physics of cellular self-organization to the dynamics of biological systems.

       

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will illustrate how this challenge can be overcome by elucidating the probabilistic connections between models of different levels of detail. These connections explain how stochastic partial differential equations (SPDE) arise naturally from particle models.

      I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.

    • Colloquium
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The knot homology (defined by Khovavov, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details, using physics ideas of Kapustin-Rozansky-Saulina, in the joint work with Rozansky, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane. The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane, the symmetry is the geometric counter-part of the mentioned Poincare duality.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

       

       

      Speaker: Achilleas Porfyriadis, Harvard Black Hole Initiative

      Title: Extreme Black Holes: Anabasis and Accidental Symmetry

      Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of  AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Fred MacKintosh (Rice University)

      Title: Contractility, structure formation and fluctuations in active gels, with and without molecular motors

      Abstract: Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence, however, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified, reconstituted systems also point to contractility and structure formation in disordered, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this, as well as possible evidence for non-motor force generation.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Michael Shelley (Flatiron)

      Title: Active structures and flows in living cells

      Abstract: Flows in the fluidic interior of living cells can serve biological function or act as signatures of how intracellular forces are exerted. I’ll discuss examples of each. One is understanding the emergence of cell-spanning vortical flows in large developing egg cells, while the other arises in studying the nature of force transduction in single cell embryos moving towards their first cell division. Both involve the cytoskeleton, that set of polymers, cross-linkers, and molecular motors that underlie much of the active mechanics within cells, and has led to the development of new coarse-grained active matter models and novel instabilities.

    • Seminars
      Seminars Colloquia & Seminar
      4-11-2017 Social Science Applications Forum
      1:00 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture.

      In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes.

      This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?

    • Active Matter Seminar
      1:00 pm-2:26 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-04.07.22

      Abstract: The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.

    • Math Science Literature Lecture Series
      1:00 pm-2:30 pm
      12/01/2024
      Lecture_Ma-1-pdf
      Yi Ma
      Photo Copyright Noah Berger / 2019

       

      Yi Ma (University of California, Berkeley)

      Title: Deep Networks from First Principles

      Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation, both for optimizing the same objective. This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.

      Talk chair: Harry Shum

      Slides | Video

    • Quantum Matter
      1:00 pm-2:30 pm
      12/01/2024
    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review  another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024

      Abstract: Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a self-organizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.

    • Active Matter Seminar
      1:00 pm-2:20 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-03.24.22

      Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes and second layers within a base monolayer of M xanthus cells. We find that cells align with each other over the majority of the monolayer forming an active nematic liquid crystal with defect point where cell alignment is undefined. We find that new layers and holes form at positive and negative topological defects respectively. We model the cell layer using hydrodynamic modeling and find that this layer and hole formation process is driven by active nematic forces through cell motility and anisotropic substrate friction.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar
      Speaker: Alexander Grosberg (NYU)

      Title: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell

      Abstract: Nucleus of a living cell houses a cell genome – a polymer called chromatin, which is a functional form of DNA.  It is very long, e.g., 2 meters long for every human cell.  Nucleus is also an arena of incessant energy-driven activity.  Experiments show that chromatin undergoes large scale motions sustained over long times of order seconds.  In the talk, after reviewing the phenomenology, I will show how these flows may arise due to a phase transition in which chromatin-driving motors, such as RNA polymerase, form a polar (“ferromagnetic”) order controlled by hydrodynamic interactions.  The talk is based on the joint work with I.Eshghi and A.Zidovska.

    • Active Matter Seminar
      1:00 pm-2:30 pm
      12/01/2024
      CMSA-Active-Matter-Seminar-04.28.22
      Speaker: Guillaume Duclos (Brandeis)
      Title: Building active nematic and active polar liquids out of biological machines

      Abstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium, leading to emergent collective behaviors not found in passive materials. In this talk, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics, as well as shine light on the physical mechanisms that regulate self-organization in living matter.

       

      Video (Youtube)

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Active Matter Seminar

       

      Speaker:  Jonathan Bauermann, Max Planck Institute for the Physics of Complex Systems

      Title: Active chemical reactions in phase-separating systems

      Abstract: Motivated by the existence of membrane-less compartments in the chemically active environment of living cells, I will discuss the dynamics of droplets in the presence of active chemical reactions. Therefore, I will first introduce the underlying interplay between phase separation and active reactions, which can alter the droplet dynamics compared to equilibrium systems. A key feature of such systems is the emergence of concentration gradients even at steady states. In the second part of this talk, I will discuss how these gradients can trigger instabilities in the core of chemically active droplets, giving rise to a new non-equilibrium steady state of liquid spherical shells. Finally, I will present experimental and theoretical results discussing the existence and energetic cost of this non-equilibrium steady state in a coacervate system.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Shane McInally, Brandeis

      Title: Control of actin cable length by decelerated growth and network geometry

      Abstract: The sizes of many subcellular structures are coordinated with cell size to ensure that these structures meet the functional demands of the cell. In eukaryotic cells, these subcellular structures are often membrane-bound organelles, whose volume is the physiologically important aspect of their size. Scaling organelle volume with cell volume can be explained by limiting pool mechanisms, wherein a constant concentration of molecular building blocks enables subcellular structures to increase in size proportionally with cell volume. However, limiting pool mechanisms cannot explain how the size of linear subcellular structures, such as cytoskeletal filaments, scale with the linear dimensions of the cell. Recently, we discovered that the length of actin cables in budding yeast (used for intracellular transport) precisely matches the length of the cell in which they are assembled. Using mathematical modeling and quantitative imaging of actin cable growth dynamics, we found that as the actin cables grow longer, their extension rates slow (or decelerate), enabling cable length to match cell length. Importantly, this deceleration behavior is cell-length dependent, allowing cables in longer cells to grow faster, and therefore reach a longer length before growth stops at the back of the cell. In addition, we have unexpectedly found that cable length is specified by cable shape. Our imaging analysis reveals that cables progressively taper as they extend from the bud neck into the mother cell, and further, this tapering scales with cell length. Integrating observations made for tapering actin networks in other systems, we have developed a novel mathematical model for cable length control that recapitulates our quantitative experimental observations. Unlike other models of size control, this model does not require length-dependent rates of assembly or disassembly. Instead, feedback control over the length of the cable is an emergent property due to the cross-linked and bundled architecture of the actin filaments within the cable. This work reveals a new strategy that cells use to coordinate the size of their internal parts with their linear dimensions. Similar design principles may control the size and scaling of other subcellular structures whose physiologically important dimension is their length.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Open mic Swampland Discussion

      Topic: Cobordism

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Nicolas Romeo (UChicago)

      Title: Scaling behavior and control of nuclear wrinkling

      Abstract: The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. We characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behaviour. A spectral analysis of three-dimensional high-resolution live-imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing the mechanical properties of the nuclear envelope, highlighting in passing the importance of nonlinear response to biological robustness.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Mehran Kardar, MIT

      Title: Competition at the front of expanding populations

      Abstract: When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations, we present a model that  integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness, as well as fixation time upon differentiation, are shown to belong to distinct universality classes depending on limits to gain of fitness.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar

      Speaker: Josef Käs, Leipzig University

      Title: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

      Abstract: Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.

      Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.

      We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.

      Video (Youtube)

    • Quantum Matter
      1:00 pm-2:30 pm
      12/01/2024
    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Open Mic Discussion
      Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 02.02.23
      Active Matter Seminar

      Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen

      Title: Interacting Active Matter

      Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      Jefferson Hal Room 256, 17 Oxford Street, Cambridge MA 02138
      Active Matter Seminar
      Speaker: Sahand Hormoz, Harvard Medical School, Dana-Farber Cancer Institute
      Title: Insights from single cell lineage trees
      Abstract: In this talk, I will discuss two recent projects from my lab that involve lineage trees of cells (the branching diagram that represents the ancestry and division history of individual cells). In the first project, we reconstructed the lineage trees of individual cancer cells from the patterns of randomly occurring mutations in these cells. We then inferred the age at which the cancer mutation first occurred and the rate of expansion of the population of cancer cells within each patient. To our surprise, we discovered that the cancer mutation occurs decades before diagnosis. For the second project, we developed microfluidic ‘mother machines’ that allow us to observe mammalian cells dividing across tens of generations. Using our observations, we calculated the correlation between the duration of cell cycle phases in pairs of cells, as a function of their lineage distance. These correlations revealed many surprises that we are trying to understand using hidden Markov models on trees. For both projects, I will discuss the mathematical challenges that we have faced and open problems related to inference from lineage trees.
    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.

    • Seminars
      Seminars Colloquia & Seminar
      5/15/2020 Math Physics Seminar
      1:00 pm-2:00 pm
      12/01/2024
    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Active Matter Seminar

      Speaker: Mark Bowick, Kavli Institute for Theoretical Physics, UCSB

      Title: The Role of Orientational Order in Development

      Abstract: Morphogenesis, the process through which genes generate form, establishes tissue scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fueled by cell proliferation, which, naively, should disrupt order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order remains an outstanding question in animal development. I will review the statistical mechanics of orientational order and discuss the observation of a fourfold orientationally ordered phase (tetratic) in the model organism Parhyale hawaiensis. I will also discuss theoretical mechanisms for the formation of orientational order that require both motility and cell division, with support from self-propelled vertex models of tissue. The aim is to uncover a robust, active mechanism for generating global orientational order in a non-equilibrium system that then sets the stage for the development of shape and form.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be “Swampland constraints, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.

    • Swampland Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.

    • General Relativity Seminar
      1:00 pm-2:00 pm
      12/01/2024

      Abstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      Lyman Lab, 17 Oxford Street, Cambridge MA 02138
      CMSA Active Matter Seminar 12.08.22
      Active Matter Seminar

      Speaker: Julien Tailleur (MIT)

      Title: Self-organization of motile cells by quorum-sensing or chemotactic interactions

      Abstract: Equilibrium statistical mechanics tells us how to control the self-assembly of passive materials by tuning the competition between energy and entropy to achieve desired states of organization. Out of equilibrium, no such principles apply and self-organization principles are scarce. Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Dissipation and injection of energy are then disconnected at the microscopic scale, hence driving the system strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases in the absence of cohesive attractive forces, but it also leaves us without guiding principles to understand the self-organization of active matter. In this talk, I will review the progress which has been made over the past ten years to control the organization of self-propelled agents using motility control, either externally or through interactions. I will show that generic principles apply and illustrate the theoretical developments presented in the talk using recent experiments on the motility-induced self-organization of bacterial mixtures.

    • Active Matter Seminar
      1:00 pm-2:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Active Matter Seminar 02.16.23
      Active Matter Seminar

      Speaker: Jörn Dunkel, MIT

      Title: Towards programmable living materials and quantitative models of active matter

      Abstract: Over the last two decades, major progress has been made in understanding the self-organization principles of active matter.  A wide variety of experimental model systems, from self-driven colloids to active elastic materials, has been established, and an extensive theoretical framework has been developed to explain many of the experimentally observed non-equilibrium pattern formation phenomena. Two key challenges for the coming years will be to translate this foundational knowledge into functional active materials, and to identify quantitative mathematical models that can inform and guide the design and production of such materials. Here, I will describe joint efforts with our experimental collaborators to realize self-growing bacterial materials [1], and to implement computational model inference schemes for active and living systems dynamics [2,3].

      [1] Nature 608: 324, 2022
      [2] PNAS 120: e2206994120, 2023
      [3] eLife 10: e68679, 2021

    • CMSA EVENT: Second Annual STAR Lab Conference
      1:01 pm-1:02 pm
      12/01/2024

      The second annual STAR Lab conference is running 10/29/-10/30/2015 at the Harvard Business School.  This event is co-sponsored by the Center of Mathematical Sciences and Applications.

      For more information, please consult the event’s website.

    • Colloquium
      1:02 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-10-2017 Mathematical Physics Seminar
      1:07 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:07 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:09 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      1:10 pm-3:00 pm
      12/01/2024
    • Colloquium
      1:10 pm-3:10 pm
      12/01/2024

      Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.

    • Colloquium
      1:10 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-31-2015 Mathematical Physics Seminar
      1:10 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:11 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Differential Geometry Seminar
      1:12 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-12-2017 Random Matrix & Probability Theory Seminar
      1:12 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-01-2015 Evolution Equation Seminar
      1:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-14-2015 Mathematical Physics Seminar
      1:14 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-17-2017 Mathematical Physics Seminar
      1:14 pm
      12/01/2024

      No additional detail for this event.

    • Active Matter Seminar
      1:15 pm-2:30 pm
      12/01/2024

      Abstract: In this talk I will review our ongoing theoretical and experimental efforts toward deciphering the hydrodynamic behavior of confluent epithelia. The ability of epithelial cells to collectively flow lies at the heart of a myriad of processes that are instrumental for life, such as embryonic morphogenesis and wound healing, but also of life-threatening conditions, such as metastatic cancer. Understanding the physical origin of these mechanisms requires going beyond the current hydrodynamic theories of complex fluids and introducing a new theoretical framework, able to account for biomechanical activity as well as for scale-dependent liquid crystalline order.

    • Quantum Matter
      1:15 pm-2:45 pm
      12/01/2024
      CMSA QMMP 1.24.23

      Quantum Matter Seminar

      Speakers: Jacob McNamara (Caltech) and Matthew Reece (Harvard)

      Title: Reflections on Parity Breaking

      Abstract: One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we will describe the formal meaning of parity as a gauge symmetry, and argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. We will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity, as well as their relationship with the Swampland Cobordism Conjecture.

       

      https://www.youtube.com/watch?v=hTeaVGRG3LA&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=19

    • Seminars
      Seminars Colloquia & Seminar
      4-18-2017 Social Science Applications Forum
      1:15 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-08-2015 Geometric Analysis Seminar
      1:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-06-2015 Geometric Analysis Seminar
      1:17 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-08-2015 Evolution Equations Seminar
      1:18 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:18 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:20 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:21 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      1:21 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:22 pm-2:22 pm
      12/01/2024

      Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
      entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
      Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4-19-2017 Random Matrix & Probability Theory Seminar
      1:22 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-13-2015 Geometric Analysis Seminar
      1:22 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-10-2015 Evolution Equations Seminar
      1:23 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: 2016 Big Data Conference & Workshop
      1:24 pm
      12/01/2024-08/23/2016
      1 Oxford Street, Cambridge MA 02138

      ! LOCATION CHANGE: The conference will be in Science Center Hall C on Tuesday, Aug.23, 2016.

      The Center of Mathematical Sciences and Applications will be hosting a workshop on Big Data from August 12 – 21, 2016 followed by a two-day conference on Big Data from August 22 – 23, 2016.

      Big Data Conference features many speakers from the Harvard Community as well as many scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the second conference on Big Data the Center will host as part of our annual events. The 2015 conference was a huge success.

      The conference will be hosted at Harvard Science Center Hall A (Monday, Aug.22) & Hall C (Tuesday, Aug.23): 1 Oxford Street, Cambridge, MA 02138.

      The 2016 Big Data conference is sponsored by the Center of Mathematical Sciences and Applications at Harvard University and the Alfred P. Sloan Foundation.

      Conference Speakers:

      1. Jörn Boehnke, Harvard CMSA
      2. Joan Bruna, UC Berkeley [Video]
      3. Tamara Broderick, MIT [Video]
      4. Justin Chen, MIT [Video]
      5. Yiling Chen, Harvard University [Video]
      6. Amir Farbin, UT Arlington [Video]
      7. Doug Finkbeiner, Harvard University [Video]
      8. Andrew Gelman, Columbia University [Video]
      9. Nina Holden, MIT [Video]
      10. Elchanan Mossel, MIT
      11. Alex Peysakhovich, Facebook
      12. Alexander Rakhlin, University of Pennsylvania [Video]
      13. Neal Wadhwa, MIT [Video]
      14. Jun Yin, University of Wisconsin
      15. Harry Zhou, Yale University [Video]

      Please click Conference Program for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Please click here for registration.

      Conference Schedule:

      August 22 – Day 1
      8:30amBreakfast
      8:55amOpening remarks
      9:00am – 9:50amYiling Chen, “Machine Learning with Strategic Data Sources” [Video]
      9:50am – 10:40amAndrew Gelman, “Taking Bayesian Inference Seriously” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmHarrison Zhou, “A General Framework for Bayes Structured Linear Models” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmDouglas Finkbeiner, “Mapping the Milky Way in 3D with star colors” [Video]
      2:20pm – 3:10pmNina Holden, “Sparse exchangeable graphs and their limits” [Video]
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmAlex Peysakhovich, “How social science methods inform personalization on Facebook News Feed” [Video]
      4:30pm – 5:20pmAmir Farbin, “Deep Learning in High Energy Physics” [Video]
      August 23 – Day 2
      8:45amBreakfast
      9:00am – 9:50amJoan Bruna Estrach, “Addressing Computational and Statistical Gaps with Deep Networks” [Video]
      9:50am – 10:40amJustin Chen & Neal Wadhwa, “Smaller Than the Eye Can See: Big Engineering from Tiny Motions in Video” [Video]
      10:40am – 11:10amBreak
      11:10am – 12:00pmAlexander Rakhlin, “How to Predict When Estimation is Hard: Algorithms for Learning on Graphs” [Video]
      12:00pm – 1:30pmLunch
      1:30pm – 2:20pmTamara Broderick, “Fast Quantification of Uncertainty and Robustness with Variational Bayes” [Video]
      2:20pm – 3:10pmElchanan Mossel, “Phylogenetic Reconstruction – a Rigorous Model of Deep Learning”
      3:10pm – 3:40pmBreak
      3:40pm – 4:30pmJörn Boehnke, “Amazon’s Price and Sales-rank Data: What can one billion prices on 150 thousand products tell us about the economy?”

      Workshop Participants:

      Richard Freeman’s Group:

      1. Sen Chai, ESSEC
      2. Brock Mendel, Harvard University
      3. Raviv Muriciano-Goroff, Stanford University
      4. Sifan Zhou, CMSA

      Scott Kominer’s Group:

      1. Bradly Stadie, UC Berkeley
      2. Neal Wadhwa, MIT [Video]
      3. Justin Chen

      Christopher Rogan’s Group:

      1. Amir Farbin, UT Arlington [Video]
      2. Paul Jackson, University of Adelaide

      For more information about the workshops, please reach out directly to the individual group leaders.

      This event is sponsored by CMSA Harvard University and the Alfred P. Sloan Foundation.

    • Seminars
      Seminars Colloquia & Seminar
      10-01-2015 Evolution Equations Seminar
      1:25 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-15-2015 Geometric Analysis Seminar
      1:26 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-16-2015 Random Matrix & Probability Theory Seminar
      1:27 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5-3-2017 Random Matrix & Probability Theory Seminar
      1:29 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-23-2015 Random Matrix & Probability Theory Seminar
      1:29 pm
      12/01/2024

      No additional detail for this event.

    • Computer Science for Mathematicians Seminar
      Computer Science for Mathematicians Seminar
      2/16/2021 Computer Science for Mathematicians
      1:30 pm-2:30 pm
      12/01/2024

      Speaker: Michael P. Kim (UC Berkeley)

      Title: Outcome Indistinguishability

      Abstract: Prediction algorithms assign numbers to individuals that are popularly understood as individual “probabilities” — e.g., what is the probability of 5-year survival after cancer diagnosis? — and which increasingly form the basis for life-altering decisions. The understanding of individual probabilities in the context of such unrepeatable events has been the focus of intense study for decades within probability theory, statistics, and philosophy. Building off of notions developed in complexity theory and cryptography, we introduce and study Outcome Indistinguishability (OI). OI predictors yield a model of probabilities that cannot be efficiently refuted on the basis of the real-life observations produced by Nature.

      We investigate a hierarchy of OI definitions, whose stringency increases with the degree to which distinguishers may access the predictor in question.  Our findings reveal that OI behaves qualitatively differently than previously studied notions of indistinguishability.  First, we provide constructions at all levels of the hierarchy.  Then, leveraging recently-developed machinery for proving average-case fine-grained hardness, we obtain lower bounds on the complexity of the more stringent forms of OI.  The hardness result provides scientific grounds for the political argument that, when inspecting algorithmic risk prediction instruments, auditors should be granted oracle access to the algorithm, not simply historical predictions.

      Joint work with Cynthia Dwork, Omer Reingold, Guy N. Rothblum, Gal Yona; to appear at STOC 2021.

    • Probability Seminar
      1:30 pm-2:30 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 05.11.23

      Probability Seminar

      Speaker: Giorgio Cipolloni (Princeton)

      Title: How do the eigenvalues of a large non-Hermitian random matrix behave?

      Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues. Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X.

      Location: Science Center Room 232

    • Seminars
      Seminars Colloquia & Seminar
      11/14/2018 Hodge Seminar
      1:30 pm
      12/01/2024
    • Probability Seminar
      1:30 pm-2:30 pm
      12/01/2024
      Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

      Probability Seminar

      Speaker: Arka Adhikari (Stanford)

      Title: Correlation decay for finite lattice gauge theories

      Abstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.

       

    • Seminars
      1:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5-2-2017 Social Sciences Application Forum
      1:30 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA GR Seminar 05.11.23

      General Relativity Seminar

      Speaker: Aghil Alaee, Clark University

      Title: Positivity of Static quasi-local Mass in general relativity

      Abstract: In this talk, we review results on the PMT of quasi-local masses and prove the positivity of static quasi-local masses with respect to the AdS and AdS Schwarzschild spacetimes.

    • Seminars
      1:30 pm-3:00 pm
      12/01/2024
    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 04.24.23 (1)

      General Relativity Seminar

      Speaker: Tin Yau Tsang, University of California Irvine

      Title: Recent advances in scalar curvature and positive mass theorems
      Abstract:  First, we have a review of classical tools for studying scalar curvature and positive mass theorem. Then we are going to discuss some advances and new perspectives on these tools which lead to a deeper understanding of geometry and initial data sets.
    • CMSA EVENT: Current Developments in Mathematics 2019
      1:30 pm-5:00 pm
      12/01/2024-11/23/2019
      CDM-POSTER-2019.email_-662x1024

       

      cdmFriday, Nov. 22, 2019 1:30 pm – 5:20 pm

      Saturday, Nov. 23, 2019  9:00 am – 5:00 pm

      Harvard University Science Center, Hall C

      Speakers:

      ·      Svetlana Jitomirskaya (UC Irvine)

      ·      Subash Khot (NYU)

      ·      Jun Li (Stanford)

      ·      André Neves (Chicago)

      ·      Geordie Williamson (U Sidney)

      Free and open to the public – registration is required.
      Please register in advance online at www.math.harvard.edu/cdm

      CDM_2019-agenda-791x1024

    • Special Seminar
      Special Seminar
      4/30/2018 Special Seminar
      1:30 pm-2:30 pm
      12/01/2024
    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 02.09.23

      General Relativity Seminar

      Speaker: Maciej Zworski, UC Berkeley

      Title: Quasinormal modes and Ruelle resonances: mathematician’s perspective

      Abstract: Quasinormal modes of gravitational waves and Ruelle resonances in hyperbolic classical dynamics share many general properties and can be considered “scattering resonances”: they appear in expansions of correlations, as poles of Green functions and are associated to trapping of trajectories (and are both notoriously hard to observe in nature, unlike, say, quantum resonances in chemistry or scattering poles in acoustical scattering). I will present a mathematical perspective that also includes zeros of the Riemann zeta function (scattering resonances for the Hamiltonian given by the Laplacian on the modular surface) and stresses the importance of different kinds of trapping phenomena, resulting, for instance, in fractal counting laws for resonances.

    • Seminars
      Seminars Colloquia & Seminar
      11/21/2018 Hodge Seminar
      1:30 pm
      12/01/2024
    • Special Seminar
      1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/23/2019 Hodge Seminar
      1:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      12/5/2018 Hodge Seminar
      1:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/28/2018 Hodge Lecture
      1:30 pm
      12/01/2024
    • Special Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Random Matrix & Probability Theory Seminar
      Speaker: Minh-Binh TRAN (SMU & MIT)

      Location: CMSA, Room G02

      Title: On the wave turbulence theory for a stochastic KdV type equation

      Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic  Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave  kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is  $d\ge 2$, the smallness of the nonlinearity $\lambda$ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation.  Unlike the cubic nonlinear Schrodinger equation, for which such a general result is commonly expected without the noise, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen  as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.

    • Seminars
      Seminars Colloquia & Seminar
      5/27/2020 Quantum Matter Seminar
      1:30 pm-3:00 pm
      12/01/2024
    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 02.16.23

      General Relativity Seminar

      Speaker: Kwinten Fransen (UC Santa Barbara)

      Title: Quasinormal Modes from Penrose Limits

      Abstract: In this talk, I will explain how to describe quasinormal modes with large real frequencies using Penrose limits. To do so, I first recall relevant aspects of the Penrose limit, and its resulting plane wave spacetimes, as well as quasinormal modes to subsequently tie these together. Having established the main principle, I will illustrate the usefulness of this point of view with the geometric realization of the emergent symmetry algebra underlying the quasinormal modes in the large real frequency limit and present its application to the astrophysically important example of Kerr black holes. Based on arXiv:2301.06999.

    • Colloquium
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 04.20.2023

      Speaker: Julio Parra Martinez, Caltech

      Title: Black hole collider physics

      Abstract: Despite more than a century since the development of Einstein’s theory, the general relativistic two-body problem remains unsolved. A precise description of its solution is now essential, as it is necessary for understanding the strong-gravity dynamics of compact binaries observed at LIGO/VIRGO/KAGRA and in future gravitational wave observatories. In this talk, I will describe how considering the scattering of black holes and gravitons can shed new light on this problem. I will explain how using modern ideas from collider and particle physics we can calculate scattering observables in classical gravity, and extract the basic ingredients that describe the bound binary dynamics. Such calculations have produced state-of-art predictions for current and future gravitational wave observatories, which open the door for further discovery as we enter this new era of precision gravitational physics.

    • General Relativity Seminar
      1:30 pm-2:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA GR Seminar 03.23.23

      General Relativity Seminar

      Speaker: Prahar Mitra (University of Cambridge)

      Title: New Phases of N=4 SYM

      Abstract: We construct new static solutions to gauged supergravity that, via the AdS/CFT correspondence, are dual to thermal phases in N=4 SYM at finite chemical potential. These solutions dominate the micro-canonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. These are constructed in two distinct truncations of gauged supergravity and can be uplifted to solutions of type IIB supergravity. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials. We will also discuss the status of hairy supersymmetric black hole solutions in this theory.

      Based on: https://arxiv.org/pdf/2207.07134.pdf [hep-th]

    • Seminars
      Seminars Colloquia & Seminar
      09-28-2015 Mathematical Physics Seminar
      1:31 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-24-2017 Mathematical Physics Seminar
      1:31 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:31 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      1:32 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:33 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Concluding Conference of the Special Program on Nonlinear Equations, April 8 – 10, 2016
      1:34 pm
      12/01/2024-04/10/2016

      The Center of Mathematical Sciences and Applications will be hosting a concluding conference on April 8-10, 2016 to accompany the year-long program on nonlinear equations. The conference will have 15 speakers and will be hosted at Harvard CMSA Building: Room G10 20 Garden Street, Cambridge, MA 02138

      Speakers:

      1. Lydia Bieri (University of Michigan)
      2. Luis Caffarelli (University of Texas at Austin)
      3. Mihalis Dafermos (Princeton University)
      4. Camillo De Lellis (Universität Zürich)
      5. Pengfei Guan (McGill University)
      6. Slawomir Kolodziej (Jagiellonian University)
      7. Melissa Liu (Columbia University)
      8. Duong H. Phong (Columbia University)
      9. Richard Schoen (UC Irvine)
      10. Cliff Taubes (Harvard University)
      11. Blake Temple (UC Davis)
      12. Valentino Tosatti (Northwestern University)
      13. Tai-Peng Tsai (University of British Columbia)
      14. Mu-Tao Wang (Columbia University)
      15. Xu-jia Wang (Australian National University)

      Please click NLE Conference Schedule with Abstracts for a downloadable schedule with talk abstracts.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Resturants.

      Schedule:

      April 8 – Day 1
      8:30amBreakfast
      8:45amOpening remarks
      9:00am – 10:00amCamillo De Lellis, “A Nash Kuiper theorem for $C^{1,1:5}$ isometric immersions of disks
      10:00am – 10:15amBreak
      10:15am – 11:15amXu-Jia Wang, “Monge’s mass transport problem
      11:15am – 11:30amBreak
      11:30am – 12:30pmPeng-Fei Guan, “The Weyl isometric embedding problem in general $3$ d Riemannian manifolds
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmBlake Temple, “An instability in the Standard Model of Cosmology
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmLydia Bieri, “The Einstein Equations and Gravitational Radiation
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmValentino Tosatti, “Adiabatic limits of Ricci flat Kahler metrics
      April 9 – Day 2
      8:45amBreakfast
      9:00am – 10:00amD.H. Phong, “On Strominger systems and Fu-Yau equations”
      10:00am – 10:15amBreak
      10:15am – 11:15amSlawomir Kolodziej, “Stability of weak solutions of the complex Monge-Ampère equation on compact Hermitian manifolds”
      11:15am – 11:30amBreak
      11:30am – 12:30pmLuis Caffarelli, “Non local minimal surfaces and their interactions”
      12:30pm – 2:00pmLunch
      2:00pm – 3:00pmMihalis Dafermos, “The interior of dynamical vacuum black holes and the strong cosmic censorship conjecture in general relativity”
      3:00pm – 3:15pmBreak
      3:15pm – 4:15pmMu-Tao Wang, “The stability of Lagrangian curvature flows”
      4:15pm – 4:30pmBreak
      4:30pm – 5:30pmMelissa Liu, “Counting curves in a quintic threefold”
      April 10 – Day 3
      8:45amBreakfast
      9:00am – 10:00amRick Schoen, “Metrics of fixed area on high genus surfaces with largest first eigenvalue”
      10:00am – 10:15amBreak
      10:15am – 11:15amCliff Taubes, “The zero loci of Z/2 harmonic spinors in dimensions 2, 3 and 4”
      11:15am – 11:30amBreak
      11:30am – 12:30pmTai-Peng Tsai, “Forward Self-Similar and Discretely Self-Similar Solutions of the 3D incompressible Navier-Stokes Equations”

      * This event is sponsored by National Science Foundation (NSF) and CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      10-22-2015 Evolution Equations Seminar
      1:37 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/11/2017 Mathematical Physics Seminar
      1:38 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-18-17 Mathematical Physics Seminar
      1:39 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-17-2015 Evolution Equations Seminar
      1:39 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      9-27-17 RM&PT Seminar
      1:41 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9-27-17 Mathematical Physics Seminar
      1:42 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-23-17 Mathematical Physics Seminar
      1:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/11/2019 Random Matrix
      1:45 pm-2:45 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-25-17 RMPT Seminars
      1:45 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:47 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-10-2017 RM & PT Seminar
      1:48 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:51 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-22-2015 Geometric Analysis Seminar
      1:52 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:52 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-30-2015 Random Matrix & Probability Theory Seminar
      1:53 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-13-2017 Mathematical Physics Seminar
      1:53 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-21-2015 Mathematical Physics Seminar
      1:54 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:54 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-15-17 RM & PT Seminar
      1:55 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      1:56 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      1:58 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      9/9/2020 RMPT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/18/2020 RMPT
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02/26/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • CMSA EVENT: Topological Insulators and Mathematical Science – Conference and Program
      2:00 pm-7:00 pm
      12/01/2024-09/17/2014

      The CMSA will be hosting a conference on the subject of topological insulators and mathematical science on September 15-17.  Seminars will take place each day from 2:00-7:00pm in Science Center Hall D, 1 Oxford Street, Cambridge, MA.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      12.07.2022

      New Technologies in Mathematics Seminar

      Speaker: Cyril Zhang, Microsoft Research

      Title: How do Transformers reason? First principles via automata, semigroups, and circuits

      Abstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models, leading to dramatic advances in natural language understanding, program synthesis, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses, given that they resist interpretation? In this work, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure.

      Specifically, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory, we characterize shortcut solutions, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore, in synthetic experiments, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness, and discuss mitigations.

      Joint work with Bingbin Liu, Jordan Ash, Surbhi Goel, and Akshay Krishnamurthy.

    • Seminars
      2:00 pm-4:00 pm
      12/01/2024

      References: 

      • D. Auroux, A beginner’s introduction to Fukaya categories. arXiv:1301.7056
      • I. Smith, A symplectic prolegomenon. arXiv:1401.0269
      • D. Auroux, “Topics in geometry: mirror symmetry”, Fall 2009 (MIT Math 18.969)
      • Nick Sheridan’s IAS and Jussieu lectures. 
      • Sheel Gantara “Topics in symplectic topology”, Spring 2016 (Stanford Math 257B)
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA NTM Seminar 10.26.2022

      New Technologies in Mathematics Seminar

      Speakers: João Araújo, Mathematics Department, Universidade Nova de Lisboa and Michael Kinyon, Department of Mathematics, University of Denver

      Title: From Engine to Auto

      Abstract: Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type, etc.
      In this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups, loops, semigroups, logic algebras, lattices and generalizations, quandles, and many more.
    • Seminars
      Seminars Colloquia & Seminar
      Homological Mirror Symmetry Seminar
      2:00 pm-4:00 pm
      12/01/2024-09/15/2017

      The seminar series, Homological Mirror Symmetry, will be held on selected Thursdays from 2PM – 4pm in CMSA Building, 20 Garden Street, Room G10.

      The list of speakers is below and will be updated as details are confirmed.

      DateNameTitle
      09-15-16
      09-22-16Netanel Blaier, Brandeis  “Intro to HMS.”

      Abstract: This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants.

      Lecture Slides

      09-29-16Netanel Blaier, Brandeisblaier4“Intro to HMS 2.”

      Abstract: In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya’s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory ‘toy model’.

      Lecture Slides

      10-06-16

      Hansol Hong, CMSAhong

      Title: Homological mirror symmetry for elliptic curves

      Abstract:
      We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also,
      which use homological algebra techniques and formal deformation theory of Lagrangians etc.

      Notes

      Notes (Baris)

      10-13-16

      Yu-Wei Fan, Harvard

      s_yuwei_fan

      Title: Semi-flat mirror symmetry and Fourier-Mukai transform

      Abstract: We will review the semi-flat mirror symmetry setting in Strominger-Yau-Zaslow, and discuss the correspondence between special Lagrangian sections on the A-side and deformed Hermitian-Yang-Mills connections on the B-side using real Fourier-Mukai transform, following Leung-Yau-Zaslow.

       10-20-16

      Tim Large, MIT

      Title: “Symplectic cohomology and wrapped Fukaya categories”

      Abstract: While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential.

      Notes

       10-27-16

      Philip Engel, Columbia

      picture

      Title: Mirror symmetry in the complement of an anticanonical divisor”

      According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This “superpotential” depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 “walls” consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to “quantum correct” the complex structure on the moduli space to undo the discontinuity introduced by these discs.

      Notes

      11-03-16

      Yusuf Baris Kartal, MIT

      HMS for Del Pezzo surfaces

      I will present Auroux-Katzarkov-Orlov’s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc.

      11-10-16No seminar this week
       12-08-16

      Lino Amorim, Boston University

      Title: The Fukaya category of a compact toric manifold

      Abstract: In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror.

      Video

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      12/2/2020 Random Matrix and Probability Theory
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024

      New Technologies in Mathematics Seminar

      Speaker: Timo Schick, Meta AI

      Title: Toolformer: Language Models Can Teach Themselves to Use Tools

      Abstract: Language models exhibit remarkable abilities to solve new tasks from just a few examples or textual instructions, especially at scale. They also, paradoxically, struggle with basic functionality, such as arithmetic or factual lookup, where much simpler and smaller models excel. In this talk, we show how these limitations can be overcome by letting language models teach themselves to use external tools via simple APIs. We discuss Toolformer, a model trained to independently decide which APIs to call, when to call them, what arguments to pass, and how to best incorporate the results into future token prediction. Through this, it achieves substantially improved zero-shot performance across a variety of downstream tasks without sacrificing its core language modeling abilities.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5/20/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024

      New Technologies in Mathematics Seminar

      Speaker: Dmitry Krotov, IBM Research – Cambridge

      Title: Modern Hopfield Networks for Novel Transformer Architectures

      Abstract: Modern Hopfield Networks or Dense Associative Memories are recurrent neural networks with fixed point attractor states that are described by an energy function. In contrast to conventional Hopfield Networks, which were popular in the 1980s, their modern versions have a very large memory storage capacity, which makes them appealing tools for many problems in machine learning and cognitive and neurosciences. In this talk, I will introduce an intuition and a mathematical formulation of this class of models and will give examples of problems in AI that can be tackled using these new ideas. Particularly, I will introduce an architecture called Energy Transformer, which replaces the conventional attention mechanism with a recurrent Dense Associative Memory model. I will explain the theoretical principles behind this architectural choice and show promising empirical results on challenging computer vision and graph network tasks.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speakers: Katherine Collins and Albert Jiang, Department of Computer Science and Technology, University of Cambridge

      Title: Evaluating Language Models for Mathematics through Interactions

      Abstract: There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs based on static pairs of inputs and outputs is insufficient to be able to make an informed decision about which LLMs, and under what assistive settings they can be sensibly utilised. Static assessment fails to take into account the essential interactive element in their deployment, and therefore limits how we understand language model capabilities. In this talk, we present our recent work introducing CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We discuss our study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we identify useful scenarios and existing issues of GPT-4 in mathematical reasoning through a series of case studies contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models which communicate uncertainty, respond well to user corrections, and are more interpretable and concise may constitute better assistants; interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models’ algebraic fallibility and discern where they are appropriate to use.

       

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Jimmy Ba, University of Toronto

      Title: How to steer foundation models?

      Abstract: By conditioning on natural language instructions, foundation models and large language models (LLMs) have displayed impressive capabilities as general-purpose computers. However, task performance depends significantly on the quality of the prompt used to steer the model. Due to the lack of knowledge of how foundation models work, most effective prompts have been handcrafted by humans through a demanding trial-and-error process. To reduce the human effort in this alignment process, I will discuss a few approaches to steer these powerful models to excel in various downstream language and image tasks.

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/21/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/04/2020 RMPT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/16/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/14/2020 RM&PT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/8/2019 Topology Seminar
      2:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/7/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/22/2019 Social Science Applications Forum
      2:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Johan Commelin, Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

      Title: Breaking the one-mind-barrier in mathematics using formal verification

      Abstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.

      I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.

      Video
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024

      Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

      In the 2020-2021 AY, the Random Matrix and Probability Theory Seminar will take place on select Wednesdays from 2:00 – 3:00pm virtually. This seminar is organized by Christian Brennecke (brennecke@math.harvard.edu ).

      To learn how to attend this seminar, please fill out this form.

      The schedule below will be updated as the details are confirmed.

      Spring 2021:

      DateSpeakerTitle/Abstract
      3/31/2021Philippe Sosoe, Cornell UniversityTitle:  Fluctuation bounds for O’Connell-Yor type systems

      Abstract: The O’Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about this model thanks to remarkable algebraic structure uncovered by O’Connell, Yor and others, basic estimates for the behavior of the tails of the centered partition function for finite N that are available for zero temperature models are missing. I will present an iterative estimate to obtain strong concentration and localization bounds  for the O’Connell-Yor polymer on an almost optimal scale N^{1/3+\epsilon}.

      In the second part of the talk, I will introduce a system of interacting diffusions describing the successive increments of partition functions of different sizes. For this system, the N^{2/3} variance upper bound known for the OY polymer can be proved for a general class of interactions which are not expected to correspond to integrable models.

      Joint work with Christian Noack and Benjamin Landon.

      4/7/2021Yue M. Lu, HarvardTitleHouseholder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Random Matrices

      Abstract: In many problems in statistical learning, random matrix theory, and statistical physics, one needs to simulate dynamics on random matrix ensembles. A classical example is to use iterative methods to compute the extremal eigenvalues/eigenvectors of a (spiked) random matrix. Other examples include approximate message passing on dense random graphs, and gradient descent algorithms for solving learning and estimation problems with random initialization. We will show that all such dynamics can be simulated by an efficient matrix-free scheme, if the random matrix is drawn from an ensemble with translation-invariant properties. Examples of such ensembles include the i.i.d. Gaussian (i.e. the rectangular Ginibre) ensemble, the Haar-distributed random orthogonal ensemble, the Gaussian orthogonal ensemble, and their complex-valued counterparts.A “direct” approach to the simulation, where one first generates a dense n × n matrix from the ensemble, requires at least O(n^2) resource in space and time. The new algorithm, named Householder Dice (HD), overcomes this O(n^2) bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are O(nT) and O(n T^2), respectively, with T being the number of iterations. When T ≪ n, which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint.Finally, the HD algorithm is not just a computational trick. I will show how its construction can serve as a simple proof technique for several problems in high-dimensional estimation
      4/14/2021Canceled
      4/16/2021
      Friday
      Patrick Lopatto (IAS)Title: Fluctuations in local quantum unique ergodicity for generalized Wigner matrices

      Abstract: In a disordered quantum system, delocalization can be understood in many ways. One of these is quantum unique ergodicity, which was proven in the random matrix context by Bourgade and Yau. It states that for a given eigenvector and set of coordinates J, the mass placed on J by the eigenvector tends to N^{-1}|J|, the mass placed on those coordinates by the uniform distribution. Notably, this convergence holds for any size of J, showing that the eigenvectors distribute evenly on all scales.

      I will present a result which establishes that the fluctuations of these averages are Gaussian on scales where |J| is asymptotically less than N, for generalized Wigner matrices with smooth entries. The proof uses new eigenvector observables, which are analyzed dynamically using the eigenvector moment flow and the maximum principle.

      This is joint work with Lucas Benigni.

      4/21/2021Jean-Christophe Mourrat, Courant Institute, NYUTitleMean-field spin glasses: beyond Parisi’s formula?

      Abstract: Spin glasses are models of statistical mechanics encoding disordered interactions between many simple units. One of the fundamental quantities of interest is the free energy of the model, in the limit when the number of units tends to infinity. For a restricted class of models, this limit was predicted by Parisi, and later rigorously proved by Guerra and Talagrand. I will first show how to rephrase this result using an infinite-dimensional Hamilton-Jacobi equation. I will then present partial results suggesting that this new point of view may allow to understand limit free energies for a larger class of models, focusing in particular on the case in which the units are organized over two layers, and only interact across layers.

      Fall 2020:

      DateSpeakerTitle/Abstract
      9/9/2020Yukun He (Zurich)Title: Single eigenvalue fluctuations of sparse Erdős–Rényi graphs

      Abstract: I discuss the fluctuations of individual eigenvalues of the adjacency matrix of the Erdös-Rényi graph $G(N,p)$. I show that if $N^{-1}\ll p \ll N^{-2/3}, then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. The main technical tool of the proof is a rigidity bound of accuracy $N^{-1-\varepsilon}p^{-1/2}$ for the extreme eigenvalues, which avoids the $(Np)^{-1}$-expansions from previous works. Joint work with Antti Knowles.

      10/14/2020David Belius (University of Basel)TitleThe TAP approach to mean field spin glasses

      Abstract: The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated methods  in theoretical physics and mathematics, such as the replica method, which are largely orthogonal to the TAP approach. The TAP approach has the advantage of being interpretable as a variational principle optimizing an energy/entropy trade-off, as commonly encountered in statistical physics and large deviations theory, and potentially allowing for a more direct characterization of the Gibbs measure and its “pure states”. In this talk I will recall the TAP approach, and present preliminary steps towards a solution of mean field spin glass models entirely within a TAP framework.

      10/28/2020Giuseppe Genovese (University of Basel)TitleNon-convex variational principles for the RS free energy of restricted Boltzmann machines

      Abstract: From the viewpoint of spin glass theory, restricted Boltzmann machines represent a veritable challenge, as to the lack of convexity prevents us to use Guerra’s bounds. Therefore even the replica symmetric approximation for the free energy presents some challenges. I will present old and new results around the topic along with some open problems.

      11/4/2020Benjamin Landon (MIT)Title:  Fluctuations of the spherical Sherrington-Kirkpatrick model

      Abstract:  The SSK model was introduced by Kosterlitz, Thouless and Jones as a simplification of the usual SK model with Ising spins. Fluctuations of its observables may be related to quantities from random matrix theory using integral representations.  In this informal talk we discuss some results on fluctuations of this model at critical temperature and with a magnetic field

      11/11/2020
      3:00 – 4:00pm
      Lucas Benigni (University of Chicago)Title:  Optimal delocalization for generalized Wigner matrices

      Abstract: We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result, known as delocalization, to more general entry distributions. After giving a brief overview of the previous results going in this direction, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.

      11/18/2020Simone Warzel (Technical University of Munich)Title:  Hierarchical quantum spin glasses

      Abstract: Hierarchical spin glasses such as the generalised random energy model are known to faithfully model typical energy landscapes in the classical theory of mean-field spin glasses. Their built-in hierarchical structure is known to emerge spontaneously in the spin-glass phase of, e.g., the Sherrington-Kirkpatrick model. In this talk, I will review recent results on the effects of a transversal magnetic field on such hierarchical quantum spin glasses.
      In particular, I will present a formula of Parisi-type for their free energy which allows to make predictions about the phase diagram.
      12/2/2020Sabine Jansen (LMU Munich)TitleThermodynamics of a hierarchical mixture of cubes

      Abstract: The talk discusses a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes of side-lengths 2^j, j\in \N_0. Cubes belong to an admissible set such that if two cubes overlap, then one cube is contained in the other, a picture reminiscent of Mandelbrot’s fractal percolation model. I will present exact formulas for the entropy and pressure, discuss phase transitions from a fluid phase with small cubes towards a condensed phase with a macroscopic cube, and briefly sketch some broader questions on renormalization and cluster expansions that motivate the model. Based on arXiv:1909.09546 (J. Stat. Phys. 179 (2020), 309-340).

      For information on previous seminars, click here

      The schedule will be updated as details are confirmed.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Gabriel Poesia, Dept. of Computer Science, Stanford University

      Title: Peano: Learning Formal Mathematical Reasoning Without Human Data

      Abstract: Peano is a theorem proving environment in which a computational agent can start tabula rasa in a new domain, learn to solve problems through curiosity-driven exploration, and create its own higher level actions. Gabriel will describe the system, present case studies on learning to solve simple algebra problems from the Khan Academy platform, and describe work on progress on learning the Natural Number Game, a popular introduction to theorem proving in Lean for mathematicians.

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      10.19.2022

      New Technologies in Mathematics Seminar

      Speaker: Antonia Creswell, DeepMind

      Title: Towards Faithful Reasoning Using Language Models

      Abstract: Language models are showing impressive performance on many natural language tasks, including question-answering. However, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this, we will introduce Selection-Inference, a faithful reasoning model, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy.

       

       

    • New Technologies in Mathematics Seminar
      2:00 pm-4:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      10.05.2022

      New Technologies in Mathematics Seminar

      Speaker: Guy Gur-Ari, Google Research

      Title: Minerva: Solving Quantitative Reasoning Problems with Language Models

      Abstract: Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA NTM Seminar 09.28.2022

      New Technologies in Mathematics

      Speaker: Surya Ganguli, Stanford University

      Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
      Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size, sometimes achieving exponential scaling, by collecting small carefully curated datasets rather than large random ones.
      References: Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
      Sorscher, Ben, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/31/2021 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/28/2020 RM&PT seminar
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Sean Welleck, CMU, Language Technologies Institute

      Title: Llemma: an open language model for mathematics

      Abstract: We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights, then trained on the Proof-Pile II, a 55 billion token dataset of mathematical web data, code, and scientific papers. The resulting models show improved mathematical capabilities, and can be adapted to various tasks. For instance, Llemma outperforms the unreleased Minerva model suite on an equi-parameter basis, and is capable of tool use and formal theorem proving without any further fine-tuning. We openly release all artifacts, including the Llemma models, the Proof-Pile II, and code to replicate our experiments. We hope that Llemma serves as a platform for new research and tools at the intersection of generative models and mathematics.

       

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/29/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5/13/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Quantum Matter
      2:00 pm-3:30 pm
      12/01/2024

      Speaker: Clay Cordova (U Chicago)

      Title: Non-Invertible Duality Defects in 3+1 Dimensions

      Abstract:  For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.

    • Topological Quantum Matter Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Ceren Dag, Harvard

      Title: Breaking ergodicity: quantum scars and regular eigenstates

      Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411, in peer review.

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Freddy Cachazo
      2:00 pm-5:00 pm
      12/01/2024-04/03/2018
      1 Oxford Street, Cambridge MA 02138
      Math Science Lectures in Honor of Raoul Bott

      DSC_0170-e1525711590120

      On April 2-3, the CMSA will be hosting two lectures by Freddy Cachazo (Perimeter Institute) on “Geometry and Combinatorics in Particle Interactions.”  This will be the first of the new annual Bott Math Science Lecture Series hosted by the CMSA.

      The lectures will take place from 4:30-5:30pm in Science Center, Hall D.

       

      Cachazo-e1519325938458

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-20-2017 RM & PT Seminar
      2:00 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Special Seminar

      Speaker: Mayuko Yamashita, Kyoto University

      Title: Topological modular forms and heretoric string theory

      Abstract: In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF.

      Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

       

    • Topological Quantum Matter Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker:  Ken K. W. Ma (Northeastern University)

      Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future

      Abstract: The discovery of fractional quantum Hall (FQH) states started a new chapter in modern physics. Nowadays, more than 70 FQH states at different filling factors have been observed. Among them, the FQH state at the filling factor ν=5/2 in GaAs (or the 5/2 state) remains one of the most special and attractive states. Since its discovery in 1987, different possible topological orders have been proposed to describe the 5/2 state. Some of them can host an exotic type of particles, known as non-Abelian anyons. Recent experiments have provided more insights into the understanding of the 5/2 state, but its underlying nature is still under debate.

      In this talk, I will review the basics of the 5/2 state [1] and a more unified theoretical description of different possible topological orders of the 5/2 state that we have recently proposed [2]. I will also review the groundbreaking thermal Hall conductance experiment [3] and the follow-up quantum Hall interface experiments by the Weizmann Institute group [4, 5], and discuss what possible lessons that we can learn from the experimental results. Lastly, I will talk about some possible directions and related topics for future investigations.

      References:

      [1] K. K. W. Ma, M. R. Peterson, V. W. Scarola, and K. Yang, “Fractional quantum Hall effect at the filling factor ν = 5/2” in Encyclopedia of Condensed Matter Physics (Second Edition), edited by T. Chakraborty, Academic Press (2024).
      [2] K. K. W. Ma and D. E. Feldman, “The sixteenfold way and the quantum Hall effect at half-integer filling factors”, Phys. Rev. B 100, 035302 (2019).
      [3] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern, “Observation of half-integer thermal Hall conductance”, Nature (London) 559, 205 (2018).
      [4] B. Dutta, W. Yang, R. Melcer, H. K. Kundu, M. Heiblum, V. Umansky, Y. Oreg, A. Stern, D. Mross, “Distinguishing between non-Abelian topological orders in a quantum Hall system”, Science 375, 193 (2021).
      [5] B. Dutta, V. Umansky, M. Banerjee, and M. Heiblum, “Isolated ballistic non-Abelian interface channel”, Science 377, 1198 (2022).

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Yuanzhi Li, CMU Dept. of Machine Learning and Microsoft Research

      Title: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation

      Abstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking results about this question. Using a synthetic biography dataset, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence, can mitigate this issue. Using linear probing, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations.

      We then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset, so that it could answer “What is the birthday of XXX” with 100% accuracy.  Even so, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly.  Even using Chain of Thought training data only helps the model answer such questions in a CoT manner, not directly.

      We will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example, is a 1B parameter language model enough to store all the knowledge of a middle school student?

       

       

    • Topological Quantum Matter Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Prashant Kumar, University of Chicago

      Title: Emergent composite-fermion Luttinger liquid at the half-filled Landau level

      Abstract: The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, I will present our numerical calculations of the excitation spectrum of this state on infinite cylinders. By comparing our results with a quasi-1D theory of CFs, we show compelling quantitative evidence for the emergence of a Luttinger liquid of composite-fermions at low energies, distinct from that of electrons. I will comment on some future directions.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      5/6/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Abhishek Panigrahi, Dept. of Computer Science, Princeton University

      Title: On the Power of Forward pass through Transformer Architectures

      Abstract: Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of study. This talk studies two interesting phenomena.

      In the first half, we explore how and why pre-trained language models, specifically BERT of moderate sizes, can effectively learn linguistic structures like parse trees during pre-training. Specifically, using synthetic data through PCFGs, we show how moderate-sized transformers can perform forward-backward parsing, also known as the inside-outside algorithm, during inference. We further understand the role of the pre-training loss for the model to learn to parse during pre-training.

      In the second half, we consider in-context learning of large language models, where they learn to reason on the fly. An ongoing hypothesis is that transformers simulate gradient descent at inference to perform in-context learning. We propose the Transformer in Transformer (TinT) framework, which creates explicit transformer architectures that can simulate and fine-tune a small pre-trained transformer model during inference. E.g. a 1.3B parameter TINT model can simulate and fine-tune a 125 million parameter model in a single forward pass. This framework suggests that large transformers might execute intricate sub-routines during inference, and provides insights for enhancing their capabilities through intelligent design considerations.

       

    • Math Science Literature Lecture Series
      2:00 pm-3:00 pm
      12/01/2024

      Shing-Tung Yau (Harvard)

      Title: Shiing-Shen Chern as a Great Geometer of 20th Century

      Video | Slides | Article

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024

      New Technologies in Mathematics Seminar

      Speaker: Ronen Eldan, Microsoft Research

      Title: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent

      Abstract: While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity?

      In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4-year-olds typically understand, generated by GPT-3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the state-of-the-art models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for low-resource or specialized domains, and shed light on the emergence of language capabilities in LMs.

       

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: François Charton, Meta AI

      Title:  Transformers for maths, and maths for transformers

      Abstract: Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics.

      Problems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic, I show that model predictions can be explained, that trained models do not confabulate, and that carefully choosing the training distributions can help achieve better, and more robust, performance.

       

       

       

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/1/2020 Random Matrix and Probability Theory Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • General Relativity Seminar
      2:00 pm-3:00 pm
      12/01/2024
      17 Oxford St, Cambridge, MA 02138

      General Relativity Seminar

      Speaker: Suman Kundu (Weizmann Institute)

      Title: ‘Grey Galaxy’ as the endpoint of the Kerr-AdS super radiant blackhole

      Abstract: Kerr AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses near extremality. We conjecture that these instabilities settle down into Grey Galaxies (GG)s – a new class of solutions to Einstein’s equations which we construct for $d=3$. Grey Galaxies consist of an $mega=1$ black hole in the `centre’ of $AdS$, surrounded by a uniformly thick and very large disk of thermal bulk matter that revolves around the centre of AdS at the speed of light. The parametrically low energy density and parametrically large radius of the gas disk are inversely related; as a consequence, the gas carries a finite fraction of the total energy. Grey Galaxy saddles exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr AdS black holes and the gas. In addition to a smooth piece, the boundary stress tensor of these solutions includes a contribution from a delta function localized at the `equator’ of the boundary sphere, a term which may be used as an order parameter that sharply distinguishes GG solutions from ordinary Kerr-Black hole saddles. We also construct `Revolving Black Hole (RBH) saddles’,  macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, that describe black holes revolving around the centre of $AdS$, at the fixed radial location but in a quantum wave function in the angular directions. RBH saddles turn out to be (marginally) entropically subdominant to GG saddles. We argue that supersymmetric versions of RBH saddles exist and have interesting consequences for the spectrum of SUSY states in, e.g.  ${\cal N}=4$ Yang-Mills theory.

    • New Technologies in Mathematics Seminar
      2:00 pm-3:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      New Technologies in Mathematics Seminar

      Speaker: Alex Gu, MIT Dept. of EE&CS

      Title: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models

      Abstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

       

    • Seminars
      Seminars Colloquia & Seminar
      4/22/2020 RM&PT Seminar
      2:00 pm-3:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-29-17 RM & PT Seminar
      2:03 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      09-24-2015 Evolution Equations Seminar
      2:03 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2015 Special Random Matrix & Probability Theory Seminar
      2:05 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-18-2015 Random Matrix & Probability Theory Seminar
      2:07 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:08 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 RM&PT Seminar
      2:08 pm
      12/01/2024
    • Colloquium
      2:10 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      11-29-2017 Mathematical Physics Seminar
      2:11 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      2:11 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      09-29-2015 Geometric Analysis Seminar
      2:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-28-2015 CMSA Special Seminar
      2:15 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:15 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12-6-2017 RM & PT Seminar
      2:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-05-2015 Mathematical Physics Seminar
      2:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-15-2015 Evolution Equations Seminar
      2:17 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12-6-2017 Mathematical Physics Seminar
      2:17 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-07-2015 Random Matrix & Probability Theory Seminar
      2:19 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:20 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-29-2015 Evolution Equations Seminar
      2:20 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-14-2015 Random Matrix & Probability Theory Seminar
      2:21 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:21 pm
      12/01/2024-03/06/2018

      During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

      You can watch Prof. Sheshmani describe the series here.

      The Syllabus is as follows:

      Date………..TopicVideo/Audio
      1-25-2018Gromov-Witten invariants 

      Definition, examples via algebraic geometry I

      Video / Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture.

       2-01-2018Gromov-Witten invariants 

      Virtual Fundamental Class I (definition)

      Video Audio / Combined 


      *due to technical difficulties the audio and video are split for this lecture

      2-13-2018Gromov-Witten invariants 

      Virtual Fundamental Class II (computation in some cases)

       2-15-2018Computing GW invariants 

      Three level GW classes

      Genus zero invariants of the projective plane

       2-20-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) I

      2-22-2018Quantum Cohomology 

      Small Quantum Cohomology (Definition and Properties) II

      2-27-2018Quantum Cohomology 

      Big Quantum Cohomology I

       3-1-2018Quantum Cohomology 

      Big Quantum Cohomology II

      GW potential

      WDVV equation

      3-6-2018GW invariants via Quantum Cohomology 

      The Quintic threefold case

      The P^2 case

      GW invariants via Quantum Cohomology 

      Dubrovin (quantum) connection

      Nakajima varieties 

      -Algebraic and symplectic reduction

      Nakajima varieties 

      Quasi maps to Nakajima varieties

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) I

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Small Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) I

       
      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) II

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) III

      Quantum cohomology of Nakajima varieties 

      Big Quantum Cohomology of Hilb^n (C2) IV

       
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      11/11/21 Interdisciplinary Science Seminar
      2:22 pm-3:22 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-11.11.21

      Title: The Kervaire conjecture and the minimal complexity of surfaces

      Abstract: We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture.
      The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/<<w>> is still nontrivial. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of surfaces in HNN extensions. This gives a conceptually simple proof of Klyachko’s theorem that confirms the Kervaire conjecture for any G torsion-free. I will also explain new results obtained using this approach.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-21-2015 Random Matrix & Probability Theory Seminar
      2:22 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Existence of Canonical Metrics on Non-Kähler Geometry
      2:23 pm-2:24 pm
      12/01/2024

      On Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on “Existence of Canonical Metrics on Non-Kähler Geometry.

      In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses works by Jun Li of Fudan University in Shanghai, Ji-Xiang Fu of Fudan University, Ivan Smith of the University of Cambridge, Richard P. Thomas of Imperial College London, Tristan C. Collins of the Massachusetts Institute of Technology, French mathematician Émile Picard, Teng Fei of Rutgers University in Newark, New Jersey, Adam Jacob of the University of California, Davis, and Duong H. Phong of Columbia University.

      More information about this talk can be found on the Simons Foundation website.

    • Colloquium
      2:23 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:24 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      11/18/2021 Interdisciplinary Science Seminar
      2:25 pm-3:25 pm
      12/01/2024

      Title: Amplituhedra, Scattering Amplitudes and Triangulations

      Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      12/2/2021 Interdisciplinary Science Seminar
      2:28 pm-3:28 pm
      12/01/2024

      Title: Polyhomogeneous expansions and Z/2-harmonic spinors branching along graphs

      Abstract: In this talk, we will first reformulate the linearization of the moduli space of Z/2-harmonic spinorsv branching along a knot. This formula tells us that the kernel and cokernel of the linearization are isomorphic to the kernel and cokernel of the Dirac equation with a polyhomogeneous boundary condition. In the second part of this talk, I will describe the polyhomogenous expansions for the Z/2-harmonic spinors branching along graphs and formulate the Dirac equation with a suitable boundary condition that can describe the perturbation of graphs with some restrictions. This is joint work with Andriy Haydys and Rafe Mazzeo.

    • Colloquium
      2:29 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      12/9/21 Interdisciplinary Science Seminar
      2:29 pm-3:29 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-12.09.21-1583x2048

      Title: Numerical Higher Dimensional Geometry

      Abstract: In 1977, Yau proved that a Kahler manifold with zero first Chern class admits a Ricci flat metric, which is uniquely determined by certain “moduli” data. These metrics have been very important in mathematics and in theoretical physics, but despite much subsequent work we have no analytical expressions for them. But significant progress has been made on computing numerical approximations. We give an introduction (not assuming knowledge of complex geometry) to these problems and describe these methods.

    • Seminars
      Seminars Colloquia & Seminar
      9/26/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-Quantum-Matter-in-Mathematics-and-Physics-11.18.21-1583x2048

      Speaker: B. Andrei Bernevig (Princeton University)

      Title: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH

      Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.

    • Seminars
      Seminars Colloquia & Seminar
      9/19/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/12/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-28-2015 Random Matrix & Probability Theory Seminar
      2:30 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      2:30 pm-3:30 pm
      12/01/2024-04/26/2020
    • Seminars
      Seminars Colloquia & Seminar
      12/10/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-QMMP-1.18.22-1544x2048-1

      Speaker: Aavishkar Patel (UC Berkeley)

      Title: Metals with strongly correlated electrons: quantum criticality, disordered interactions, Planckian dissipation, and scale invariance

      Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.

    • Seminars
      Seminars Colloquia & Seminar
      11/26/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024

      Speaker: Jeongwan Haah (Microsoft)

      Title: A degeneracy bound for homogeneous topological order

    • Seminars
      Seminars Colloquia & Seminar
      11/21/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      2/27/2019 Colloquium
      2:30 pm-4:00 pm
      12/01/2024
    • Quantum Matter
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-QMMP-1.28.2022-1544x2048-1

      Speaker: Maria Tikhanovskaya (Harvard)

      Title: Maximal quantum chaos of the critical Fermi surface

      Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.

    • Seminars
      Seminars Colloquia & Seminar
      11/14/2019 Spacetime Seminar
      2:30 pm
      12/01/2024
    • Colloquium
      2:30 pm-3:00 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      4/10/2019 Colloquium
      2:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/3/2019 Colloquium
      2:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/31/2019 Spacetime Seminar
      2:30 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Social Science Applications Forum
      2:30 pm-4:00 pm
      12/01/2024
    • Quantum Matter
      2:30 pm-4:00 pm
      12/01/2024
      CMSA-QMMP-12.10.21-1544x2048

      Speaker: Lukasz Fidkowski (U Washington)

      Title: Gravitational anomaly of 3 + 1 dimensional Z2 toric code with fermionic charges and ferionic loop self-statistics

      Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.

    • Seminars
      Seminars Colloquia & Seminar
      3/7/2019 Social Science Applications Forum
      2:30 pm-3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/18/2019 Spacetime Seminar
      2:30 pm-3:00 pm
      12/01/2024
    • Colloquium
      2:32 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-19-2015 Mathematical Physics Seminar
      2:33 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-20-2015 Geometric Analysis Seminar
      2:35 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10-26-2015 Mathematical Physics Seminar
      2:36 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-02-2015 Mathematical Physics Seminar
      2:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      01-26-2018 Mirror Symmetry Seminar
      2:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-03-2015 Geometric Analysis Seminar
      2:39 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-04-2015 Random Matrix & Probability Theory Seminar
      2:40 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      1-29-2018 Mathematical Physics Seminar
      2:42 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      Special Seminar
      1-30-2018 Special Seminar
      2:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2-2-2018 Mirror Symmetry Seminar
      2:44 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:44 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:45 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      12/16/2021 Interdisciplinary Science Seminar
      2:46 pm-3:46 pm
      12/01/2024

      Title: Quadratic reciprocity from a family of adelic conformal field theories

      Abstract: We consider a deformation of the 2d free scalar field action by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it’s no longer invariant under the local conformal symmetry algebra. Furthermore, there is an adelic version of this family of global conformal field theories, parametrized by the choice of a number field, together with a Hecke character. Tate’s thesis plays an important role here in calculating Green’s functions of these theories, and in ensuring the adelic compatibility of these theories. In particular, the local L-factors contribute to prefactors of these Green’s functions. We shall try to see quadratic reciprocity from this context, as a consequence of an adelic version of holomorphic factorization of these theories. This is work in progress with B. Stoica and X. Zhong.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/6/2022 Interdisciplinary Science Seminar
      2:47 pm-3:47 pm
      12/01/2024

      Title: The smooth closing lemma for area-preserving surface diffeomorphisms

      Abstract: In this talk, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing result of twisted Seiberg- Witten Floer homology. This is joint work with Dan Cristofaro-Gardiner and Rohil Prasad.

    • Colloquium
      2:47 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:48 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/13/2022 Interdisciplinary Science Seminar
      2:48 pm-3:48 pm
      12/01/2024

      Title: A universal triangulation for flat tori

      Abstract: A celebrated theorem of Nash completed by Kuiper implies that every smooth Riemannian surface has a C¹ isometric embedding in the Euclidean 3-space E³. An analogous result, due to Burago and Zalgaller, states that every polyhedral surface, obtained by gluing Euclidean triangles, has an isometric PL embedding in E³. In particular, this provides PL isometric embeddings for every flat torus (a quotient of E² by a rank 2 lattice). However, the proof of Burago and Zalgaller is partially constructive, relying on the Nash-Kuiper theorem. In practice, it produces PL embeddings with a huge number of vertices, moreover distinct for every flat torus. Based on a construction of Zalgaller and on recent works by Arnoux et al. we exhibit a universal triangulation with less than 10.000 vertices, admitting for any flat torus an isometric embedding that is linear on each triangle. Based on joint work with Florent Tallerie.

    • Seminars
      Seminars Colloquia & Seminar
      11-19-2015 Evolution Equations Seminar
      2:50 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 CMSA Special Lecture
      2:51 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/20/2022 – Interdisciplinary Science Seminar
      2:52 pm-4:52 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-01.20.22-1577x2048

      Title: Markov chains, optimal control, and reinforcement learning

      Abstract: Markov decision processes are a model for several artificial intelligence problems, such as games (chess, Go…) or robotics. At each timestep, an agent has to choose an action, then receives a reward, and then the agent’s environment changes (deterministically or stochastically) in response to the agent’s action. The agent’s goal is to adjust its actions to maximize its total reward. In principle, the optimal behavior can be obtained by dynamic programming or optimal control techniques, although practice is another story.

      Here we consider a more complex problem: learn all optimal behaviors for all possible reward functions in a given environment. Ideally, such a “controllable agent” could be given a description of a task (reward function, such as “you get +10 for reaching here but -1 for going through there”) and immediately perform the optimal behavior for that task. This requires a good understanding of the mapping from a reward function to the associated optimal behavior.

      We prove that there exists a particular “map” of a Markov decision process, on which near-optimal behaviors for all reward functions can be read directly by an algebraic formula. Moreover, this “map” is learnable by standard deep learning techniques from random interactions with the environment. We will present our recent theoretical and empirical results in this direction.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      1/27/2022 – Interdisciplinary Science Seminar
      2:54 pm-4:54 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-1.27.2022-1583x2048

      Title: Polynomials vanishing at lattice points in convex sets

      Abstract: Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number, which we compute for many (but maybe not all) triangles P.

    • Seminars
      Seminars Colloquia & Seminar
      11-09-2015 Mathematical Physics Seminar
      2:54 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:54 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      2:55 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:56 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-19-2015 Random Matrix and Probability Theory Seminar
      2:57 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      2:57 pm
      12/01/2024

      Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      2/3/2022 – Interdisciplinary Science Seminar
      2:57 pm-4:57 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.03.2022-1583x2048-1

      Title:Quasiperiodic prints from triply periodic blocks

      Abstract: Slice a triply periodic wooden sculpture along an irrational plane. If you ink the cut surface and press it against a page, the pattern you print will be quasiperiodic. Patterns like these help physicists see how metals conduct electricity in strong magnetic fields. I’ll show you some block prints that imitate the printing process described above, and I’ll point out the visual features that reveal conductivity properties.

      Interactive slides:https://www.ihes.fr/~fenyes/seeing/slices/

    • Colloquium
      2:59 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      11-16-2015 Mathematical Physics Seminar
      2:59 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/31/2020 Quantum Matter Seminar
      3:00 pm-4:30 pm
      12/01/2024
    • Special Seminar
      Special Seminar
      3-28-2018 Special Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11-17-2015 Geometric Analysis Seminar
      3:00 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      2/25/2020 Fluid Dynamics
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2-27-2018 HMS Lecture
      3:00 pm-4:00 pm
      12/01/2024-03/01/2018
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024

      Speaker: Jason Rute, CIBO Technologies

      Title: Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models

      Abstract: Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.

    • New Technologies in Mathematics Seminar
    • Seminars
      Seminars Colloquia & Seminar
      Algebraic Geometry Seminar, Thursdays
      3:00 pm-4:00 pm
      12/01/2024

      This seminar will not be held in the Spring 2018 Semester.

      The Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated as details are confirmed.

       

       

      DateNameTitle/Abstract
      09-14-17 Yu-Wei Fan (Harvard Math)

      Entropy of an autoequivalence on Calami-Yau manifolds

      Abstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi.

      11-1-17

      *5:00pm, G10*

       Shamil Shakirov, Harvard Math

      Undulation invariants of plane curves

      Abstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5

      11-2-17

       

      Alexander Moll, IHES

      Hilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves

      ABSTRACT: By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence.

      11-9-17  TBD  TBD
      11-16-17 TBD TBD
      11-23-17  TBD  TBD
      11-30-17  TBD  TBD
      12-7-17  TBD  TBD
      12-15-17  TBD  TBD
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/4/2019 Special Seminar
      3:00 pm
      12/01/2024
    • Math Science Literature Lecture Series
      3:00 pm-4:00 pm
      12/01/2024
      Lecture_Donaldson-pdf

      Simon Donaldson (Stony Brook)

      Title: The ADHM construction of Yang-Mills instantons

      Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the Yang-Mills instanton equations over the 4-sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics,  and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof,  using Penrose’s twistor theory and results on algebraic vector bundles over projective 3-space. As time permits, we will also discuss some further developments, for example, the work of Nahm on monopoles and connections to Mukai duality for bundles over complex tori.

      Video | Slides

    • Math Science Literature Lecture Series
      Math Science Literature Lecture Series Event
      CMSA Math-Science Literature Lecture: Quantum Groups
      3:00 pm-4:00 pm
      12/01/2024-05/05/2020
      Lecture_Etingof-pdf

      Pavel Etingof (MIT)

      Title: Quantum Groups

      Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum Yang-Baxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as representation theory, the Langlands program, low-dimensional topology, category theory, enumerative geometry, quantum computation, algebraic combinatorics, conformal field theory, integrable systems, integrable probability, and others. I will review some of the main ideas and examples of quantum groups and try to briefly describe some of the applications.

      Video | Slides

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      10/9/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Probability Seminar
      3:00 pm-4:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 04.10.23

      Probability Seminar

      *Please note room change: Science Center 232*

      Speaker: Ron Peled (Tel Aviv University)

      Title: Localization for random band matrices

      Abstract: I will explain an approach via “an adaptive Mermin-Wagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}.

      Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/03/2018 RMPT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Dmytro Shklyrov HMS Focused Lecture Series
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/25/2019 Math Physics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Fluid Dynamics Seminar
      3:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • CMSA EVENT: 2018 Ding Shum Lecture
      3:00 pm-4:00 pm
      12/01/2024
      ding-shum-2018

       

      Screen-Shot-2018-06-14-at-1.41.25-PM

      On October 24, 2018, the CMSA will be hosting our second annual Ding Shum lecture. This event was made possible by the generous funding of Ding Lei and Harry Shum. Last year featured Leslie Valiant, who spoke on “learning as a Theory of Everything.”

      This year will feature Eric Maskin, who will speak on “How to Improve Presidential Elections: the Mathematics of Voting.” This lecture will take place from 5:00-6:00pm in Science Center, Hall D. 

      Pictures of the event can be found here.

    • Seminars
      Seminars Colloquia & Seminar
      2/14/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/17/2019 Fluid Dynamics Seminar
      3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/31/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Special Seminar
      3:00 pm-4:30 pm
      12/01/2024-05/09/2019

      In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on Derived algebraic/differential geometry run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

      Click here for reference material

      Click here for a syllabus

      Schedule:

      Section 1: Basic setting of derived geometry

      The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

      2/05/2019Lecture 1: Model and с-categoriesVideo
      2/07/2019Lecture 2: Grothendieck topologies and homotopy descentVideo
      2/12/2019Lecture 3: Derived Artin stacksVideo 
      2/14/2019Lecture 4: Cotangent complexes

      Section 2: Loop spaces and differential forms

      The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

      2/19/2019Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces)Video
      2/21/2019Lecture 6: Chern characterVideo
      2/26/2019

      Room G02

      Lecture 7: Local structure of closed differential forms in the derived sense Part IVideo
      2/28/2019Lecture 8: Local structure of closed differential forms in the derived sense Part IIVideo
      3/05/2019Lecture 9: Cyclic homologyVideo

      Section 3: Shifted symplectic structures
      Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

      3/07/2019Lecture 10: Definition and existence resultsVideo
      3/12/2019Lecture 11: Lagrangians and Lagrangian fibrationsVideo
      3/14/2019

      Room G02

      Lecture 12: Lagrangians and Lagrangian fibrationsVideo
      3/26/2019Lecture 13: Intersections of LagrangiansVideo
      3/28/2019

      Room G02

      Lecture 14: Examples and applications 2 (Part I)Video
      4/02/2019Lecture 15: Examples and applications 2 (Part II)Video

      Section 4: Uhlenbeck–Yau construction and correspondence

      4/04/2019Lecture 16: Examples and applications 2 (Part III)Video
      4/09/2019

      Room G02

      Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)Video
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/7/2019 General Relativity Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/11/2020 RM&PT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      2/13/2019 Special Algebraic Geometry Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Quantum Matter
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/24/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Quantum Matter
      3:00 pm-4:30 pm
      12/01/2024

      Speaker: Jie Wang (Simons Foundation)

      Title: Quantum Geometric Aspects of Chiral Twisted Graphene Models

      Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:

      [1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155)
      [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL)
      [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)

    • Seminars
      Seminars Colloquia & Seminar
      2/20/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Probability Seminar
      3:00 pm-4:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 11.30.22

      Probability Seminar

      Title: Lipschitz properties of transport maps under a log-Lipschitz condition

      Abstract: Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting, for applications, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition.

      I will present a construction of a transport map, constructed infinitesimally along the Langevin flow, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds, and which, at the moment, seem to be out of reach of the classically studied optimal transport theory.

      Joint work with Max Fathi and Yair Shenfeld.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/6/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/8/2019 Special Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024

      Speaker: Josef Urban, Czech Technical University

      Title: AI and Theorem Proving

      Abstract: The talk will discuss the main approaches that combine machine learning with automated theorem proving and automated formalization. This includes learning to choose relevant facts for “hammer” systems, guiding the proof search of tableaux and superposition automated provers by interleaving learning and proving (reinforcement learning) over large ITP libraries, guiding the application of tactics in interactive tactical systems, and various forms of lemmatization and conjecturing. I will also show some demos of the systems, and discuss autoformalization approaches such as learning probabilistic grammars from aligned informal/formal corpora, combining them with semantic pruning, and using neural methods to learn direct translation from Latex to formal mathematics.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/28/2018 Random Matrix and Probability Theory Seminar
      3:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/7/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024

      Speaker: Thomas Hales, Univ. of Pittsburgh Dept. of Mathematics

      Title: A Mathematical Language

      Abstract: A controlled natural language for mathematics is an artificial language that is designed in an explicit way with precise computer-readable syntax and semantics.  It is based on a single natural language (which for us is English) and can be broadly understood by mathematically literate English speakers.  This talk will describe the design of a controlled natural language for mathematics that has been influenced by the Lean theorem prover, by TeX, and by earlier controlled natural languages. The semantics are provided by dependent type theory.

    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/14/2018 RM & PT Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/22/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      12/5/2018 Random Matrix and Probability Theory Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/15/2019 Fluid Dynamics
      3:00 pm-4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      5/1/2019 Fluid Dynamics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
      3:00 pm-4:00 pm
      12/01/2024
    • New Technologies in Mathematics Seminar
    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      2/10/2022 – Interdisciplinary Science Seminar
      3:00 pm-4:00 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.10.2022-1

      Title: Metric Algebraic Geometry

      Abstract: A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a distance metric. In this talk, we introduce metric algebraic geometry through a discussion of Voronoi cells, bottlenecks, and the reach of an algebraic variety. We also show applications to the computational study of the geometry of data with nonlinear models.

    • Seminars
      Seminars Colloquia & Seminar
      11-23-2015 Mathematical Physics Seminar
      3:01 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar (2016-2017)
      3:01 pm
      12/01/2024-12/14/2017
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      DSC_0025-768x512

      The random matrix and probability theory will be every Wednesday from 3pm-4pm in CMSA Building, 20 Garden Street, Room G10.

    • Member Seminar
      3:02 pm
      12/01/2024-01/01/2021

      The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below.

      Previous seminars can be found here.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/29/2021Cancelled
      2/5/2021Itamar ShamirTitle: Boundary CFT and conformal anomalies

      Abstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.

      2/12/2021Louis FanTitle:  Joint distribution of Busemann functions in corner growth models

      Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.

      2/19/2021Daniel JunghansTitle: Control issues of the KKLT scenario in string theory

      Abstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular, we show that, generically, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.

      2/26/2021Tsung-Ju LeeTitle: SYZ fibrations and complex affine structures

      Abstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.

      3/5/2021Cancelled
      3/11/2021

      9:00pm ET

      Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification

      Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

      3/18/2021

      9:00pm ET

      Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification
      Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.
      3/26/2021

      8:30am ET

      Aghil AlaeeTitle:  Rich extra dimensions are hidden inside black holes

      Abstract: In this talk, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.

      4/2/2021
      8:30am ET
      Enno KeßlerTitle: Super Stable Maps of Genus Zero

      Abstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.

      4/9/2021Juven Wang

      Video

      Title: Ultra Unification

      Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate more on the nonperturbative global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.

      4/16/2021Sergiy VerstyukTitle: Deep learning methods for economics

      Abstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way, interpretability of neural networks features prominently.

      4/23/2021Yifan WangTitle: Virtues of Defects in Quantum Field Theories

      Abstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra, precision studies of defect observables, and the implications thereof for strongly coupled dynamics. In this talk, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics, and that open new windows to nonperturbative effects in quantum gravity.

      4/30/2021Yun ShiTitle: D-critical locus structure for local toric Calabi-Yau 3-fold

      Abstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.

      5/7/2021Thérèse Yingying WuTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2

      Abstract: In this talk, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.

      5/14/2021Du PeiTitle: Three applications of TQFTs

      Abstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds, and 3) smooth structures on 4-manifolds.

      5/21/2021Farzan VafaTitle: Active nematic defects and epithelial morphogenesis

      Abstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/11/2020Moran KorenTitle:  Observational Learning and Inefficiencies in Waitlists

      Abstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents, upon receiving an offer, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.

      9/18/2020Michael DouglasTitle: A talk in two parts, on strings and on computers and math

      Abstract: I am dividing my time between two broad topics. The first is string theory, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert,GPT) which have led to breakthroughs on natural language processing, describe their potential for helping us do math, and sketch some related theoretical problems.

      9/25/2020Cancelled – Math Science Lecture
      10/2/2020Cancelled – Math Science Lecture
      10/9/2020Wai Tong (Louis) FanTitle: Stochastic PDE as scaling limits of interacting particle systems

      Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
      In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.

      10/16/2020Tianqi WuTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

      Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.

      10/23/2020Changji XuTitle: Random Walk Among Bernoulli Obstacles

      Abstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk, we will discuss some recent results about the behaviors of the conditional random walk, in quenched, annealed, and biased settings.

      10/30/2020Michael SimkinTitle: The differential equation method in Banach spaces and the $n$-queens problem

      Abstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
      We apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.

      11/6/2020Kenji KawaguchiTitle: Deep learning: theoretical results on optimization and mixup

      Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization, robustness, and generalization, during the optimization process of a neural network. In this talk, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.

      11/13/2020Omri Ben-EliezerTitle: Sampling in an adversarial environment

      Abstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations, the existing statistical literature does not apply.

      We propose a new sequential adversarial model capturing these situations, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results, techniques, and applications reveal close connections to various areas in mathematics and computer science, including VC theory, discrepancy theory, online learning, streaming algorithms, and computational geometry.

      Based on joint works with Noga Alon, Yuval Dagan, Shay Moran, Moni Naor, and Eylon Yogev.

      11/20/2020Charles DoranTitle: The Calabi-Yau Geometry of Feynman Integrals

      Abstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.

      Colloquia & Seminars,Seminars

    • CMSA EVENT: Working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017
      3:02 pm-3:03 pm
      12/01/2024-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis, January 9-13, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Participants:

      Gerard Ben Arous, Courant Institute of Mathematical Sciences

      Alex Bloemendal, Broad Institute

      Arup Chakraburty, MIT

      Zhou Fan, Stanford University

      Alpha Lee, Harvard University

      Matthew R. McKay, Hong Kong University of Science and Technology (HKUST)

      David R. Nelson, Harvard University

      Nick Patterson, Broad Institute

      Marc Potters, Capital Fund management

      Yasser Roudi, IAS

      Tom Trogdon, UC Irvine

      Organizers:

      Michael Brenner, Lucy Colwell, Govind Menon, Horng-Tzer Yau

      Please click Program for a downloadable schedule with talk abstracts.

      Please note that breakfast & lunch will be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants should you need recommendations for dinner.

      Schedule:

      January 9 – Day 1
      9:30am – 10:00amBreakfast & Opening remarks
      10:00am – 11:00amMarc Potters, “Eigenvector overlaps and the estimation of large noisy matrices”
      11:00am – 12:00pmYasser Roudi
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 10 – Day 2
      8:30am – 9:00amBreakfast
      9:00am – 10:00amArup Chakraburty, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”
      10:00am – 11:00amTom Trogdon, “On the average behavior of numerical algorithms”
      11:00am – 12:00pmDavid R. Nelson, “Non-Hermitian Localization in Neural Networks”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 11 – Day 3
      8:30am – 9:00amBreakfast
      9:00am – 10:00amNick Patterson
      10:00am – 11:00amLucy Colwell
      11:00am – 12:00pmAlpha Lee
      12:00pm – 2:00pmLunch
      2:00pm-4:00pmAfternoon Discussion
      4:00pmGerard Ben Arous (Public Talk), “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms
      January 12 – Day 4
      8:30am – 9:00amBreakfast
      9:00am – 10:00amGovind Menon
      10:00am – 11:00amAlex Bloemendal
      11:00am – 12:00pmZhou Fan, “Free probability, random matrices, and statistics”
      12:00pm – 2:00pmLunch
      2:00pmAfternoon Discussion
      January 13 – Day 5
      8:30am – 9:00amBreakfast
      9:00am – 12:00pmFree for Working
      12:00pm – 2:00pmLunch
      2:00pmFree for Working

      * This event is sponsored by CMSA Harvard University.

    • Colloquium
      3:03 pm-4:00 pm
      12/01/2024

      Abstract: I will discuss a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.

    • Colloquium
      3:03 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      3:03 pm-4:03 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.11.22-1583x2048

      Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.

    • Seminars
      Seminars Colloquia & Seminar
      11-24-2015 Geometric Analysis Seminar
      3:03 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-04-2016 Evolution Equations Seminar
      3:04 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      3:05 pm-4:05 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.12.22-1583x2048-1

      Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Sparse Markov Models for High-dimensional Inference
      3:05 pm-4:05 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.17.2022-1-1583x2048-1

      Abstract: Finite order Markov models are theoretically well-studied models for dependent data.  Despite their generality, application in empirical work when the order is larger than one is quite rare.  Practitioners avoid using higher order Markov models because (1) the number of parameters grow exponentially with the order, (2) the interpretation is often difficult. Mixture of transition distribution models (MTD)  were introduced to overcome both limitations. MTD represent higher order Markov models as a convex mixture of single step Markov chains, reducing the number of parameters and increasing the interpretability. Nevertheless, in practice, estimation of MTD models with large orders are still limited because of curse of dimensionality and high algorithm complexity. Here, we prove that if only few lags are relevant we can consistently and efficiently recover the lags and estimate the transition probabilities of high order MTD models. Furthermore, we show that using the selected lags we can construct non-asymptotic confidence intervals for the transition probabilities of the model. The key innovation is a recursive procedure for the selection of the relevant lags of the model.  Our results are  based on (1) a new structural result of the MTD and (2) an improved martingale concentration inequality. Our theoretical results are illustrated through simulations.

    • Colloquium
      3:06 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-02-2016 Geometric Analysis Seminar
      3:06 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Hodge and Noether-Lefschetz Loci Seminar
      3:06 pm
      12/01/2024

      In the Fall 2018 Semester the CMSA will be hosting a seminar on Hodge and Noether-Lefschetz loci, with lectures given by Hossein Movasati (IMPA). The seminar will occur weekly on Wednesday at 1:30 in room G10 of the CMSA.

      The schedule below will be updated as talks are confirmed.

      DateTitle/Abstract
      11/7/2018

      Video

      Title: Hodge and Noether-Lefschetz loci

      Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligne’s absolute Hodge cycle theorem for abelian varieties etc.

      In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome.

      11/14/2018

      Video

      Title:  Integral Hodge conjecture for Fermat varieties

      Abstract: We describe an algorithm which verifies whether  linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this  confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of  vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor.

      11/21/2018

      Video

      Title:  Periods of algebraic cycles

      Abstract: The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900’s wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space.  As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space.

      11/28/2018

      Video

      Title: Periods of Complete Intersection Algebraic Cycles

      Speaker: Roberto Villaflor

      Abstract: In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space.

      12/05/2018

      Room G02

      Title: Some explicit Hodge cycles

      Abstract: Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known.

      12/12/2018

      Video

      Title: A conjectural Hodge locus for cubic tenfold

      Abstract: In this talk we will consider the difference  of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold,  for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces.

      1/16/2019Title: Algebraic BCOV anomaly equation

      Abstract: We introduce the moduli space T of  non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau).  We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus.

      1/23/2019

      Video

      Title: A new model for modular curves

      Abstract: One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model.

      The talk is based on the article arXiv:1808.01689.

      1/30/2019

      Video

      Title: Constant Yukawa couplings

      Abstract: In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants.

      2/6/2019

      Video

      Title: Integrality properties of CY modular forms

      Abstract: The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated  by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method.  In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients.

      We also  give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri.

      2/13/2019Title: Foliations and Hodge loci

      Abstract: In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves,  we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin.

       

      References:

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Singular Set in Obstacle Problems
      3:08 pm-4:08 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-2.24.2022-1583x2048

      Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.

    • Colloquium
      3:09 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Data Analysis Workshop, April 4 – 8, 2016
      3:09 pm-3:10 pm
      12/01/2024-04/08/2016

      The Center of Mathematical Sciences and Applications will be hosting a 5-day workshop on Data Analysis and related areas on April 4 – 8, 2016.

      Workshop Locations:

      April 4 – 7 (Monday ~ Thursday)

      Room G10,
      20 Garden Street, Cambridge, MA 02138 

      April 8 (Friday)

      EPS Faculty Lounge, Room 409, 4th floor, Hoffman Lab
      20 Oxford Street, Cambridge, MA 02138

       Participants:

      • Peter Hubyers (Harvard University)
      • Eli Tziperman (Harvard University)
      • Andrew Rhines (University of Washington)
      • Karen McKinnon (UCAR)
      • Douglas MacMartin (Caltech)
      • Thomas Laepple (Alfred Wegener Institute)
      • Yossi Ashkenazy (Ben-Gurion University)
      • Marlene Kretschamer (Potsdam Institute for Climate Impact Research)
      • Natesh Pillai (Harvard University)
      • Judah Cohen (Atmospheric and Environmental Research)
      • Cristian Proistosescu (Harvard University)

      Please click Workshop Agenda for a downloadable agenda.

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      02-11-2016 Evolution Equations Seminar
      3:09 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-16-2018 RM & PT Seminar
      3:09 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Colloquium
      3:11 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-03-2016 Random Matrix & Probability Theory Seminar
      3:11 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:11 pm-4:11 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.03.2022-1583x2048-1

      Abstract: While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573.

      Bio: Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research, New England. In 2019, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text, images, and other forms of data, using techniques such as non-convex optimization and tensor decompositions.

    • Colloquium
      3:12 pm-4:12 pm
      12/01/2024

      Abstract: Not so long ago, the relations between algebraic geometry and combinatorics were strictly governed by the former party, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry, specifically Hodge Theory. And so, while we proved analogues for these results, combinatorics felt subjugated to inspirations from outside of it.
      In recent years, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature, we use intuitions from the Hall marriage theorem, translated to algebra: once there, they are statements about self-pairings, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry, which in turn established solutions to long-standing conjectures in combinatorics.

      I will survey this theory, called biased pairing theory, and new developments within it, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki, Vasiliki Petrotou and Johanna Steinmeyer.

    • Interdisciplinary Science Seminar
      3:13 pm-4:13 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.10.2022-1583x2048-1

      Abstract: The gig economy provides workers with the benefits of autonomy and flexibility, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms, an unexplored aspect is the organization identity. In a series of studies, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach, combining methodologies from randomized field experiments, recommender systems, and counterfactual machine learning. Together, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy.

      Bio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning, causal inference, and field experiments in his research, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences, including PNAS, ACM TOIS, WWW, and ICWSM.

    • Colloquium
      3:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 RM & PT Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 RM & PT Seminar
      3:15 pm
      12/01/2024
    • Colloquium
      3:15 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2019 Random Matrix and Probability Theory Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Interdisciplinary Science Seminar
      3:15 pm-4:15 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048

      Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization, during the optimization process. In this talk, I will discuss some mathematical properties of optimization and generalization for deep neural networks.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11/6/2019 Random Matrix and Probability Theory Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/23/2019 RMPT Seminar
      3:15 pm-4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-16-2016 Geometric Analysis Seminar
      3:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      02-15-2016 Mathematical Physics Seminar
      3:17 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      An operadic structure on supermoduli spaces
      3:17 pm-5:17 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048 (1)

      Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin. Based joint work with Yu. I. Manin and Y. Wu. https://arxiv.org/abs/2202.10321

    • Seminars
      Seminars Colloquia & Seminar
      02-18-2016 Evolution Equations Seminar
      3:19 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:20 pm-5:20 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-03.231.2022-1583x2048-1

      Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space.  Many fundamental questions have been open for these classical objects.  We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry.  Key objects involve compactifications of embedded vector spaces, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector bundles and the cohomology ring of stellahedral varieties.

    • Seminars
      Seminars Colloquia & Seminar
      02-22-2016 Mathematical Physics Seminar
      3:20 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:22 pm-5:22 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.07.2022-1583x2048-1

      Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson, as well as joint work with (separately) Larson and Jim Bryan.

    • Seminars
      Seminars Colloquia & Seminar
      02-23-2016 Geometric Analysis Seminar
      3:22 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      02-24-2016 Random Matrix & Probability Theory
      3:23 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Mini-workshop on SYZ and Homological Mirror Symmetry
      3:23 pm
      12/01/2024-12/02/2016

      The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2, 2016 at Harvard CMSA Building: Room G10, 20 Garden Street, Cambridge, MA 02138.

      Organizers:

      Bong Lian (Brandeis University), Siu-Cheong Lau (Boston University), Shing-Tung Yau (Harvard University)

      Speakers:

      1. Conan Leung, Chinese University of Hong Kong
      2. Junwu Tu, University of Missouri
      3. Jingyu Zhao, Columbia University
      4. David Treumann, Boston College
      5. Hiro Lee Tanaka, Harvard University
      6. Fabian Haiden, Harvard University
      7. Hansol Hong, Harvard CMSA/Brandeis University
      8. Netanel Blaier, Harvard CMSA/Brandeis University
      9. Garret Alston, The University of Oklahoma

      Please click Workshop Program for a downloadable schedule with talk abstracts.

      Conference Schedule:

      Monday, November 28 – Day 1
      10:30am –11:30amHiro Lee Tanaka“Floer theory through spectra”
      Lunch
      1:00pm – 2:30pmFabian Haiden“Categorical Kahler Geometry”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmFabian Haiden“Categorical Kahler Geometry”
      4:30pm – 5:15pmGarret Alston“Potential Functions of Non-exact fillings”
      Tuesday, November 29 – Day 2
      10:30am –11:30amConan Leung, “Remarks on SYZ”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30pm-2:45pm Break
      2:45pm – 4:15pmHiro Lee Tanaka“Floer theory through spectra”
      4:30pm – 5:15pmHansol Hong, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”
      Wednesday, November 30 – Day 3
      10:30am –11:30amJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
      Lunch
      1:00pm – 2:30pmJingyu Zhao, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”
       2:30-2:45pm Break
      2:45pm – 4:15pmDavid Treumann, “Invariants of Lagrangians via microlocal sheaf theory”
      Thursday, December 1 – Day 4
      10:30am –11:30amDavid Treumann“Some examples in three dimensions”
      Lunch
      1:00pm – 2:30pmJunwu Tu“Homotopy L-infinity spaces and mirror symmetry”
       2:30-2:45pm Break
      2:45pm – 3:30pmNetanel Blaier, “The quantum Johnson homomorphism, and the symplectic mapping class group of 3-folds”

      * This event is sponsored by the Simons Foundation and CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      02-25-2016 Evolution Equations Seminar
      3:25 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      3:25 pm
      12/01/2024

      During the Spring 2021 semester, and until further notice, all seminars will take place virtually.

      The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

      To learn how to attend, please fill out this form.

      Information on previous colloquia can be found here.

      Spring 2021:

      DateSpeakerTitle/Abstract
      1/27/2021Evelyn Tang (Max Planck Institute for Dynamics and Self-Organization)

      Slides

      Video

      Title: Topology protects chiral edge currents in stochastic systems

      Abstract: Living systems can exhibit time-scales much longer than those of the underlying components, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, stochastic growth and shrinkage, and synchronization.

      2/3/2021André Luiz de Gouvêa (Northwestern)

      Video

      Title: The Brave Nu World

      Abstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos, concentrating on the observation of neutrino oscillations and neutrino masses, along with all the open questions that came of these discoveries from the end of the 20th century.

      2/10/2021Mykhaylo Shkolnikov (Princeton)

      Video

      Title: Probabilistic approach to free boundary problems and applications

      Abstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems, such as the supercooled Stefan problem. The approach is based on a new notion of solution, referred to as probabilistic, which arises naturally in the context of large system limits of interacting particle systems. In the talk, I will give an example of how such interacting particle systems arise in applications (e.g., finance), then obtain a solution of a free boundary problem in the large system limit, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy, Francois Delarue, Jiacheng Zhang and Xiling Zhang

      2/17/2021
      9:00 – 10:00PM ET
      C. Seshadhri (UC Santa Cruz)

      Video

      Title: Studying the (in)effectiveness of low dimensional graph embeddings

      Abstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph, the basic idea is to produce a low-dimensional vector for each vertex, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks, such as link prediction, community labeling, recommendations, etc. Despite many results emerging in this area over the past few years, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. Empirically, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel, Caleb Levy, Aneesh Sharma, and Andrew Stolman.)

      2/24/2021David Ben-Zvi (U Texas)

      Video

      Title: Electric-Magnetic Duality for Periods and L-functions

      Abstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.
      A fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.
      We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

      3/3/2021

      9:00pm ET

      Omer Tamuz (Caltech)Title: Monotone Additive Statistics

      Abstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z?

      (Joint work with Tobias Fritz, Xiaosheng Mu, Luciano Pomatto and Philipp Strack.)

      3/10/2021

      9:00pm ET

      Piotr Indyk (MIT)Title: Learning-Based Sampling and Streaming

      Abstract: Classical algorithms typically provide “one size fits all” performance, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type, in the context of streaming and sampling algorithms. In particular, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19), and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that, given a data item, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden, CY Hsu, D Katabi, S Narayanan, R Rubinfeld, S Silwal, T Wagner and A Vakilian.

      3/17/2021
      9:00pm ET
      Chiu-Chu Melissa Liu (Columbia)Title: Topological Recursion and Crepant Transformation Conjecture

      Abstract: The Crepant Transformation Conjecture (CTC), first proposed by Yongbin Ruan and later refined/generalized by others, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.

      3/24/2021Weinan E (Princeton)

      Video

      Title: Machine Learning and PDEs

      Abstract: I will discuss two topics:
      (1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;
      (2) Formulating machine learning as PDE (more precisely, integral-differental equation) problems.

      3/31/2021Thore Graepel (DeepMind/UCL)

      Video

      Title: From AlphaGo to MuZero – Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model

      Abstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

      4/7/2021Kui Ren (Columbia)Title: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems

      Abstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.

      4/14/2021Siu-Cheong Lau (Boston U)Title: An algebro-geometric formulation of computing machines

      Abstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical, Euclidean and hyperbolic moduli.

      4/21/2021Vasco Carvalho (Cambridge)Title: The Economy as a Complex Production Network
      Abstract: A modern economy is an intricately linked web of specialized production units, each relying on the flow of inputs from their suppliers to produce their own output, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.
      4/28/2021

      9:00 – 10:00pm ET

      Shamit Kachru (Stanford)

      Slides

      Title: K3 Metrics from String Theory

      Abstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously, they admit Ricci flat metrics — but the proof of that fact is not constructive, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk, I describe two different methods of constructing (smooth, Ricci flat) K3 metrics, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction, which can be practically implemented.


      Fall 2020:

      DateSpeakerTitle/Abstract
      9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry

      Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

      10/7/2020

      10:00am

      Mariangela Lisanti (Princeton University)

      Video

      Title: Mapping the Milky Way’s Dark Matter Halo with Gaia

      Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.

      10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

      Video

      Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers

      Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
      a) My general argument “against” quantum computers,
      b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
      Relevant papers:
      Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.
      wordpress.com/2019/11/stat-quantum2.pdf

      Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.
      wordpress.com/2020/08/laws-blog2.pdf

      Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.
      wordpress.com/2019/09/main-pr.pdf

      10/21/2020Marta Lewicka (University of Pittsburgh)

      Video

      Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

      Abstract: We propose results that relate the following two contexts:
      (i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
      (ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
      For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
      geometry and mechanics of materials in the prediction of patterns and shape formation.

      10/28/2020Jonathan Heckman (University of Pennsylvania)

      Video

      Title: Top Down Approach to Quantum Fields

      Abstract: Quantum Field theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions, as well as in spacetimes with four or fewer spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems

      11/4/2020
      9:00pm ET
      Surya Ganguli (Stanford)

      Video

      Title: Weaving together machine learning, theoretical physics, and neuroscience through mathematics

      Abstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning, theoretical physics, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate the design principles governing neural systems, both biological and artificial, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy, speed and accuracy with which non-equilibrium sensors can detect signals
      Selected References:
      M. Advani and S. Ganguli, Statistical mechanics of optimal convex inference in high dimensions, Physical Review X, 6, 031034, 2016.
      M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation, NeurIPS, 2016.
      A.K. Lampinen and S. Ganguli, An analytic theory of generalization dynamics and transfer learning in deep linear networks, International Conference on Learning Representations (ICLR), 2019.
      H. Tanaka, A. Nayebi, N. Maheswaranathan, L.M. McIntosh, S. Baccus, S. Ganguli, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction, NeurIPS 2019.
      S. Deny, J. Lindsey, S. Ganguli, S. Ocko, The emergence of multiple retinal cell types through efficient coding of natural movies, Neural Information Processing Systems (NeurIPS) 2018.
      B. Sorscher, G. Mel, S. Ganguli, S. Ocko, A unified theory for the origin of grid cells through the lens of pattern formation, NeurIPS 2019.
      Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
      S.E. Harvey, S. Lahiri, and S. Ganguli, A universal energy accuracy tradeoff in nonequilibrium cellular sensing, https://arxiv.org/abs/2002.10567

      11/11/2020Kevin Buzzard (Imperial College London)

      Video

      Title: Teaching proofs to computers

      Abstract: A mathematical proof is a sequence of logical statements in a precise language, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this, these tools are not used in mathematics departments, perhaps because they are not yet capable of telling mathematicians *something new*.
      I will give an overview of the Lean theorem prover, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.

      11/18/2020Jose A. Scheinkman (Columbia)

      Video

      Title: Re-pricing avalanches

      Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations, in turn, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

      11/25/2020

      10:45am

      Eric J. Heller (Harvard)

      Video

      Title: Branched Flow

      Abstract: In classical and quantum  phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth, random, weakly deflecting  but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic  statistical flow much later, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal, but this has not been quantified.  Many questions arise, including the scale(s) of the random medium,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions

      12/2/2020Douglas Arnold (U of Minnesota)

      Video

      Title: Preserving geometry in numerical discretization

      Abstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric, topological, and algebraic structures of the original differential system.  For ordinary differential equations, such geometric integrators were developed at the end of the last century, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC, in which the structures to preserve are related to Hilbert complexes underlying the PDEs, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics, electromagnetism, and other applications which relate to the de Rham complex.  More recently, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex, leading to progress in discretizations of problems from solid mechanics, materials science, and general relativity.

      12/9/2020Manuel Blum and Lenore Blum (Carnegie Mellon)

      Video

      Title: What can Theoretical Computer Science Contribute to the Discussion of Consciousness?

      Abstract: The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. We give a precise formal definition of a Conscious Turing Machine (CTM), also called Conscious AI, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.
      After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the range of related concepts that the model explains easily and naturally, and the extent of the theory’s agreement with scientific evidence

    • Seminars
      Seminars Colloquia & Seminar
      03-03-2016 Evolution Equations Seminar
      3:26 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      3-5-2018 Mathematical Physics Seminar
      3:27 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Seminars
      Seminars Colloquia & Seminar
      03-29-2016 Geometric Analysis Seminar
      3:27 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      3:28 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: JDG 2017 Conference, April 28 – May 2, 2017
      3:29 pm
      12/01/2024-05/02/2017

      In celebration of the Journal of Differential Geometry’s 50th anniversary, the Harvard Math Department will be hosting the Tenth Conference on Geometry and Topology (JDG 2017) from April 28 – May 2, 2017.

      Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.

      Confirmed Speakers

      * This event is co-sponsored by Lehigh University and partially supported by the National Science Foundation.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Tomas Berggren (MIT)

      Title: Geometry of the doubly periodic Aztec dimer model

      Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions — known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.

       

       

    • Colloquium
      3:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 05.03.23

      Probability Seminar

      Speaker: Boris Hanin (Princeton)

      Title: Random Neural Networks

      Abstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially L) are large. The first set of results are for deep linear networks, which are simply products of L random matrices of size N x N. I’ll explain how the setting where the ratio L / N is fixed with both N and L large reveals a number of phenomena not present when only one of them is large. I will then state several results about non-linear networks in which this depth-to-width ratio L / N again plays a crucial role and gives an effective notion of depth for a random neural network.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 04.26.23

      Probability Seminar

      Speaker: Jimmy He (MIT)

      Title: Boundary current fluctuations for the half space ASEP

      Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

    • Seminars
      Seminars Colloquia & Seminar
      11/12/2019 Spacetime Seminar
      3:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/10/2019 Spacetime Seminar
      3:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      Harvard Science Center, 1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 04.19.23

      Probability Seminar

      Speaker: Evita Nestoridi (Stonybrook)

      Title: Diagonalizing Transition Matrices of Card Shuffles

      Abstract: In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 04.12.23

      Probability Seminar

      Speaker: Emma Bailey (CUNY)

      Title: Large deviations of Selberg’s central limit theorem

      Abstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance.  It is natural to investigate how far into the tails this Gaussianity persists, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials.  It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations, as well as certain maxima and moments. In this talk I will focus more on the techniques we apply to approach this problem and I will assume no number theoretic knowledge. This is joint work with Louis-Pierre Arguin.

    • Seminars
      Seminars Colloquia & Seminar
      7/29/2020 Quantum Matter Seminar
      3:30 pm-5:00 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 04.05.23

      Probability Seminar

      Speaker: Ahmed El Alaoui (Cornell)

      Title: Sampling from the SK and mixed p-spin measures with stochastic localization

      Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model. This is based on a joint work with Andrea Montanari and Mark Sellke.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/17/2018 RM & PT Seminar
      3:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA Probability Seminar 03.22.23

      Probability Seminar

      Speaker: Wei-Kuo Chen (Minnesota)

      Title: Some rigorous results on the Lévy spin glass model

      Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024

      Probability Seminar

      Speaker: Benjamin Landon (University of Toronto)

      Title: Tail estimates for stationary KPZ models

      Abstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size, including the stochastic six vertex model, the ASEP and a class of non-integrable interacting diffusions.

      Joint work with Christian Noack and Phil Sosoe.

       

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main)

      Title: Solving spin systems, the Babylonian way

      Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues, but quite astonishingly, evidence is mounting that Parisi’s ultrametricity assumption, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024

      Probability Seminar

      Speaker: Vishesh Jain (University of Illinois Chicago)
      Title: Thresholds for edge colorings
      Abstract: We show that if each edge of the complete bipartite graph K_{n,n} is given a random list of C(\log n) colors from [n], then with high probability, there is a proper edge coloring where the color of each edge comes from the corresponding list. We also prove analogous results for Latin squares and Steiner triple systems. This resolves several related conjectures of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-Osthus. I will discuss some of the main ingredients which go into the proof: the Kahn-Kalai conjecture, absorption, and the Lovasz Local Lemma distribution. Based on joint work with Huy Tuan Pham.
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 02.15.23

      Probability Seminar

      Speaker: Zhigang Yao (Harvard CMSA/National University of Singapore)

      Title: Manifold Fitting: An Invitation to Statistics

      Abstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference: https://arxiv.org/abs/1909.10228

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Youngtak Sohn (MIT)

      Title: Universality of max-margin classifiers

      Abstract: Many modern learning methods, such as deep neural networks, are so complex that they perfectly fit the training data. Despite this, they generalize well to the unseen data. Motivated by this phenomenon, we consider high-dimensional binary classification with linearly separable data. First, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule, namely the max-margin classification, has near-optimal prediction accuracy. Then, we discuss universality of max-margin classification. In particular, we characterize the prediction accuracy of the non-linear random features model, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally, we consider the wide-network limit, where the number of neurons tends to infinity, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective.

      Joint work with Andrea Montanari, Feng Ruan, Jun Yan, and Basil Saeed.

    • Quantum Matter
      3:30 pm-5:00 pm
      12/01/2024

      Title: Electric-magnetic duality and the Geometric Langlands duality

      Abstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      Virtual and in 20 Garden Street, Room G10
      CMSA Probability Seminar 02.08.23

      Probability Seminar

      Speaker: Roland Bauerschmidt (Cambridge)

      Title: Bakry-Emery theory and renormalisation

      Abstract: I will discuss an approach to log-Sobolev inequalities that
      combines the Bakry-Emery theory with renormalisation and present several
      applications. These include log-Sobolev inequalities with polynomial
      dependence for critical Ising models on Z^d when d>4 and singular SPDEs
      with uniform dependence of the log-Sobolev constant on both the
      regularisation and the volume. The talk is based on joint works with
      Thierry Bodineau and Benoit Dagallier.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024

      Probability Seminar

      Speaker: Antoine Maillard (ETH Zürich)

      Title: Fitting ellipsoids to random points

      Abstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science, and is conjectured to undergo a sharp transition: with high probability, it has a solution if n < d^2/4, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture, and highlight some recent progress, in three different directions:

      • A proof that the problem is feasible for n < d^2 / C, for some (large) constant C, significantly improving over previously-known bounds.
      • A non-rigorous characterization of the conjecture, as well as significant generalizations, using analytical methods of statistical physics.
      • A rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.

      This talk is based on the three manuscripts: arXiv:2307.01181, arXiv:2310.01169, arXiv:2310.05787, which are joint works with A. Bandeira, Tim Kunisky, Shahar Mendelson and Elliot Paquette.

    • Seminars
      Seminars Colloquia & Seminar
      4/4/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      12/01/2024
    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      CMSA Probability Seminar 12.07.22

      Probability Seminar

      Note location change: Science Center Room 300H

      Speaker: Lior Alon (MIT)

      Title: Fourier quasicrystals and stable polynomials

      Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A, such that the sum of exp(iat), over a in A, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial, and the measures associated with each irreducible factor is either supported on an arithmetic progression, or its support has a bounded intersection with any arithmetic progression. Finally, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix.

      Based on joint work with Pravesh Kothari.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 11.16.22

      Probability Seminar

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Probability Seminar 11.09.22 (1)

      Probability Seminar

      Speaker: Hugo Falconet (Courant Institute, NYU)

      Title: Liouville quantum gravity from random matrix dynamics

      Abstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary group at equilibrium, then the measures $|det(U_t – e^{i theta}|^gamma dt dtheta$ converge to the 2d LQG measure with parameter $gamma$, in the limit of large dimension. This extends results from Webb, Nikula and Saksman for fixed time. The proof relies on a new method for Fisher-Hartwig asymptotics of Toeplitz determinants with real symbols, which extends to multi-time settings. I will explain this method and how to obtain multi-time loop equations by stochastic analysis on Lie groups.

      Based on a joint work with Paul Bourgade.

       

    • Seminars
      Seminars Colloquia & Seminar
      3/14/2019 General Relativity Seminar
      3:30 pm-4:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Social Science Application Forum
      3:30 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2-23-2018 RM & PT Seminar
      3:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Quantum Matter
      3:30 pm-5:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-04.22.22-1583x2048-1

      Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Jinyoung Park (NYU)

      Title: Thresholds

      Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a “threshold.” Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

    • Probability Seminar
      3:30 pm-4:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Catherine Wolfram (MIT)

      Title: Large deviations for the 3D dimer model

      Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is different from two, explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.

       

    • Seminars
      Seminars Colloquia & Seminar
      10/15/2019 Spacetime Seminar
      3:30 pm-5:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02-29-2016 Mathematical Physics Seminar
      3:31 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-01-2016 Geometric Analysis Seminar
      3:32 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      3:33 pm-5:33 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-04.28.22-1583x2048-1

      Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole,  length of the shortest closed geodesic on X.

    • Seminars
      Seminars Colloquia & Seminar
      03-10-2016 Evolution Equations Seminar
      3:34 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Materials and Data Analysis, March 27-30, 2017
      3:34 pm
      12/01/2024-03/30/2017

      The Center of Mathematical Sciences and Applications will be hosting a 5-day working Conference on Materials and Data Analysis and related areas, March 27-30, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Photos of the event can be found on CMSA’s Blog.

       Participants:

      Organizers:

      * This event is sponsored by CMSA Harvard University.

      Schedule:

      Monday, March 27

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amKieron Burke, University of California, IrvineBackground in DFT and electronic structure calculations
      10:00am – 11:00amKieron Burke, University of California, Irvine

      The density functionals machines can learn

      11:00am – 12:00pmSadasivan Shankar, Harvard UniversityA few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives

      Tuesday, March 28

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amRyan Adams, HarvardTBA
      10:00am – 11:00amGábor Csányi, University of Cambridge

      Interatomic potentials using machine learning: accuracy, transferability and chemical diversity

      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmEvan Reed, Stanford UniversityTBA

       Wednesday, March 29 

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amPatrick Riley, GoogleThe Message Passing Neural Network framework and its application to molecular property prediction
      10:00am – 11:00amJörg Behler, University of GöttingenTBA
      11:00am – 12:00pmEkin Doğuş Çubuk, Stanford UniversTBA
      4:00pmLeslie Greengard, Courant InstituteInverse problems in acoustic scattering and cryo-electron microscopy

      CMSA Colloquium

      Thursday, March 30

      TimeSpeakerTitle
      8:30am – 9:00amBreakfast
      9:00am – 10:00amMatthias Rupp, Fitz Haber Institute of the Max Planck SocietyTBA
      10:00am – 11:00amPetros Koumoutsakos, Radcliffe Institute for Advanced Study, HarvardTBA
      11:00am – 1:00pmLunch Break
      1:00pm – 2:00pmDennis Sheberla, Harvard UniversityRapid discovery of functional molecules by a high-throughput virtual screening
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-09-2016 Random Matrix & Probability Theory
      3:35 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      3:35 pm-4:35 pm
      12/01/2024

      Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Fluid Dynamics Seminar
      3:35 pm
      12/01/2024
    • CMSA EVENT: Workshop on Discrete and Topological Models for Effective Field Theories, January 9-13, 2017
      3:35 pm-3:36 pm
      12/01/2024-01/13/2017

      The Center of Mathematical Sciences and Applications will be hosting a Workshop on “Discrete and Topological Models for Effective Field Theories,” January 9-13, 2017.  The workshop will be hosted in G02 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      Titles, abstracts and schedule will be provided nearer to the event.

      Participants:

      Dan Freed, UT Austin

      Anton Kapustin, California Institute of Technology

      Alexei Y. Kitaev, California Institute of Technology

      Greg Moore, Rutgers University

      Constantin Teleman, University of Oxford

      Organizers:

      Mike Hopkins, Shing-Tung Yau

      * This event is sponsored by CMSA Harvard University.

    • Interdisciplinary Science Seminar
      3:36 pm-5:36 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.05.2022-1583x2048

      Abstract: Although everyone talks about AI + healthcare, many people were unaware of the fact that there are two possible outcomes of the collaboration, due to the inherent dissimilarity between the two giant subjects. The first possibility is healthcare-leads, and AI is for building new tools to make steps in healthcare easier, better, more effective or more accurate. The other possibility is AI-leads, and therefore the protocols of healthcare can be redesigned or redefined to make sure that the whole infrastructure and pipelines are ideal for running AI algorithms.

      Our system Qianfang belongs to the second category. We have designed a new kind of clinic for the doctors and patients, so that it will be able to collect high quality data for AI algorithms. Interestingly, the clinic is based on Traditional Chinese Medicine (TCM) instead of modern medicine, because we believe that TCM is more suitable for AI algorithms as the starting point.

      In this talk, I will elaborate on how we convert TCM knowledge into a modern type-safe large-scale system, the mini-language that we have designed for the doctors and patients, the interpretability of AI decisions, and our feedback loop for collecting data.

      Our project is still on-going, not finished yet.Bio: Yang Yuan is now an assistant professor at IIIS, Tsinghua. He finished his undergraduate study at Peking University in 2012. Afterwards, he received his PhD at Cornell University in 2018, advised by Professor Robert Kleinberg. During his PhD, he was a visiting student at MIT/Microsoft New England (2014-2015) and Princeton University (2016 Fall). Before joining Tsinghua, he spent one year at MIT Institute for Foundations of Data Science (MIFODS) as a postdoc researcher. He now works on AI+Healthcare, AI Interpretability and AI system.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-23-2016 Random Matrix & Probability Theory
      3:37 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Geometric Models for Sets of Probability Measures
      3:38 pm-5:38 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-05.12.22-1583x2048

      Abstract: Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models.  In this setting, we often are unable to match individual data points but rather need to deduce relationships between entire weighted and unweighted point sets. In this talk, I will summarize our team’s recent efforts to apply geometric techniques to problems in this space, using tools from optimal transport and spectral geometry. Motivated by applications in dataset comparison, time series analysis, and robust learning, our work reveals how to apply geometric reasoning to data expressed as probability measures without sacrificing computational efficiency.

    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Social Science Applications Forum
      3:38 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Working Conference on Covariance Analysis in Biology, May 1-4, 2017
      3:40 pm-3:41 pm
      12/01/2024-05/02/2017

      The Center of Mathematical Sciences and Applications will be hosting a working Conference on Covariance Analysis in Biology, May 1-4, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street, Cambridge, MA 02138.

      This event is open and free.  If you would like to attend, please register here to help us keep a headcount. A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Speakers:

      Orr Ashenberg, Fred Hutchinson Cancer Research Center

      John Barton, Massachusetts Institute of Technology

      Simona Cocco, Laboratoire de Physique Statistique de l’ENS

      Sean Eddy, Harvard University

      Efthimios Kaxiras, Harvard University

      Michael Laub, Massachusetts Institute of Technology

      Debora S. Marks, Harvard University

      Govind Menon, Brown University

      Rémi Monasson, Laboratoire de Physique Théorique de l’ENS

      Andrew Murray, Harvard University

      Ilya Nemenman, Emory College

      Chris Sander, Dana-Farber Cancer Institute, Harvard Medical School

      Dave Thirumalai, University of Texas at Austin

      Martin Weigt, IBPS, Université Pierre et Marie Curie

      Matthieu Wyart, EPFL

      More speakers will be confirmed soon.

       

      Schedule:

      (Please click here for a downloadable version of the schedule.)

      Please note that the schedule for both days is currently tentative and is subject to change.

      May 1, Monday

      TimeSpeakerTopic
      9:00-10:00amSean EddyTBA
      10:00-11:00amMike LaubTBA
      11:00am-12:00pmIlya NemenmanTBA
      May 2, Tuesday
      TimeSpeakerTopic
      9:00-10:00amOrr AshenbergTBA
      10:00-11:00amDebora MarksTBA
      11:00am-12:00pmMartin WeigtTBA
      4:30pm-5:30pmSimona CoccoCMSA Colloquia

       

      May 3, Wednesday
      TimeSpeakerTopic
      9:00-10:00amAndrew MurrayTBA
      10:00-11:00amMatthieu WyartTBA
      11:00am-12:00pmRémi MonassonTBA

       

      May 4, Thursday
      TimeSpeakerTopic
      9:00-10:00amDavid ThirumalaiTBA
      10:00-11:00amChris SanderTBA
      11:00am-12:00pmJohn BartonTBA

       

      Organizers:

      Michael Brenner, Lucy Colwell, Elena Rivas, Eugene Shakhnovich

      * This event is sponsored by CMSA Harvard University.

    • Seminars
      Seminars Colloquia & Seminar
      03-07-2016 Mathematical Physics Seminar
      3:41 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      2-26-2018 Mathematical Physics Seminar
      3:42 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-11-2016 Random Matrix & Probability Theory
      3:42 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-08-2016 Geometric Analysis Seminar
      3:44 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017
      3:44 pm
      12/01/2024-05/04/2017

      In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

      To register for this event, please click here.

      Confirmed speakers:

      The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

      For a list of lodging options convenient to the Center, please see our recommended lodgings page.

      Schedule:

      The schedule for both days is currently tentative and is subject to change. A pdf version of the schedule can also be downloaded here.

      June 5, Monday (Full day)

      TimeSpeakerTopic
      8:30am – 9:0amBreakfast
      9:00am – 10:00amJonathan WeitsmanTitle: On the geometric quantization of (some) Poisson manifolds
      10:30am – 11:30amEckhard MeinrenkenTitle: On Hamiltonian loop group spaces

      Abstract: Let G be a compact Lie group. We explain a construction of an LG-equivariant spinor module over any Hamiltonian loop group space with proper moment map. It may be regarded as its `canonical spin-c structure’. We show how to reduce to finite dimensions, resulting in actual spin-s structure on transversals, as well as twisted spin-c structures for the associated quasi-hamiltonian space. This is based on joint work with Yiannis Loizides and Yanli Song.

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmAna Rita PiresTitle: Infinite staircases in symplectic embedding problems

      Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

      Video

      3:00pm – 4:00pmSobhan SeyfaddiniTitle: Rigidity of conjugacy classes in groups of area-preserving homeomorphisms

      Abstract: Motivated by understanding the algebraic structure of groups of area-preserving homeomorphims F. Beguin, S. Crvoisier, and F. Le Roux were lead to the following question: Can the conjugacy class of a Hamiltonian homeomorphism be dense? We will show that one can rule out existence of dense conjugacy classes by simply counting fixed points. This is joint work with Le Roux and Viterbo.

      4:30pm – 5:30pmRoger CasalsTitle: Differential Algebra of Cubic Graphs
      Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.Video

      June 6, Tuesday (Full day)

      TimeSpeakerTopic
      8:30am – 9:00amBreakfast
      9:00am – 10:00amAlejandro UribeTitle: Semi-classical wave functions associated with isotropic submanifolds of phase space

      Abstract: After reviewing fundamental ideas on the quantum-classical correspondence, I will describe how to associate spaces of semi-classical wave functions to isotropic submanifolds of phase space satisfying a Bohr-Sommerfeld condition. Such functions have symbols that are symplectic spinors, and they satisfy a symbol calculus under the action of quantum observables. This is the semi-classical version of the Hermite distributions of Boutet the Monvel and Guillemin, and it is joint work with Victor Guillemin and Zuoqin Wang. I will inlcude applications and open questions.

      Video

      10:30am – 11:30amAlisa KeatingTitle: Symplectomorphisms of exotic discs

      Abstract: It is a theorem of Gromov that the group of compactly supported symplectomorphisms of R^4, equipped with the standard symplectic form, is contractible. While nothing is known in higher dimensions for the standard symplectic form, we show that for some exotic symplectic forms on R^{4n}, for all but finitely n, there exist compactly supported symplectomorphisms that are smoothly non-trivial. The principal ingredients are constructions of Milnor and Munkres, a symplectic and contact version of the Gromoll filtration, and Borman, Eliashberg and Murphy’s work on existence of over-twisted contact structures. Joint work with Roger Casals and Ivan Smith.

      Video

      11:30am – 1:30pmBreak
      1:30pm – 2:30pmChen HeTitle: Morse theory on b-symplectic manifolds

      Abstract: b-symplectic (or log-symplectic) manifolds are Poisson manifolds equipped with symplectic forms of logarithmic singularity. Following Guillemin, Miranda, Pires and Scott’s introduction of Hamiltonian group actions on b-symplectic manifolds, we will survey those classical results of Hamiltonian geometry to the b-symplectic case.

      Video

      3:00pm – 4:00pmYael KarshonTitle: Geometric quantization with metaplectic-c structures

      Abstract: I will present a variant of the Kostant-Souriau geometric quantization procedure that uses metaplectic-c structures to incorporate the “half form correction” into the prequantization stage. This goes back to the late 1970s but it is not widely known and it has the potential to generalize and improve upon recent works on geometric quantization.

      Video


    • Seminars
      Seminars Colloquia & Seminar
      03-21-2016 Mathematical Physics Seminar
      3:46 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-24-2016 Evolution Equations Seminar
      3:47 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: 2017 Big Data Conference
      3:47 pm
      12/01/2024-08/19/2017
      1 Oxford Street, Cambridge MA 02138

      The Center of Mathematical Sciences and Applications will be hosting a conference on Big Data from August 18 – 19, 2017, in Hall D of the Science Center at Harvard University.

      The Big Data Conference features many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. This is the third conference on Big Data the Center will host as part of our annual events, and is co-organized by Richard Freeman, Scott Kominers, Jun Liu, Horng-Tzer Yau and Shing-Tung Yau.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      Please note that lunch will not be provided during the conference, but a map of Harvard Square with a list of local restaurants can be found by clicking Map & Restaurants.

      Confirmed Speakers:

       

      Following the conference, there will be a two-day workshop from August 20-21. The workshop is organized by Scott Kominers, and will feature:

      • Jörn Boehnke, Harvard University
      • Nikhil Naik, Harvard University
      • Bradly Stadie, Open AI, University of California, Berkeley

       

      Conference Schedule

      A PDF version of the schedule below can also be downloaded here.

      August 18, Friday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amMohammad Akbarpour

      Video

      Title: Information aggregation in overlapping generations and the emergence of experts

      Abstract: We study a model of social learning with “overlapping generations”, where agents meet others and share data about an underlying state over time. We examine under what conditions the society will produce individuals with precise knowledge about the state of the world. There are two information sharing regimes in our model: Under the full information sharing technology, individuals exchange the information about their point estimates of an underlying state, as well as their sources (or the precision of their signals) and update their beliefs by taking a weighted average. Under the limited information sharing technology, agents only observe the information about the point estimates of those they meet, and update their beliefs by taking a weighted average, where weights can depend on the sequence of meetings, as well as the labels. Our main result shows that, unlike most social learning settings, using such linear learning rules do not guide the society (or even a fraction of its members) to learn the truth, and having access to, and exploiting knowledge of the precision of a source signal are essential for efficient social learning (joint with Amin Saberi & Ali Shameli).

      9:40 am – 10:20 amLucas Janson

      Video

      Title: Model-Free Knockoffs For High-Dimensional Controlled Variable Selection

      Abstract: Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of model-free knockoffs, which reads from a different perspective the knockoff procedure (Barber and Candès, 2015) originally designed for controlling the false discovery rate in linear models. The key innovation of our method is to construct knockoff variables probabilistically instead of geometrically. This enables model-free knockoffs to deal with arbitrary (and unknown) conditional models and any dimensions, including when the dimensionality p exceeds the sample size n, while the original knockoffs procedure is constrained to homoscedastic linear models with n greater than or equal to p. Our approach requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. As we require no knowledge/assumptions about the conditional distribution of the response, we effectively shift the burden of knowledge from the response to the covariates, in contrast to the canonical model-based approach which assumes a parametric model for the response but very little about the covariates. To our knowledge, no other procedure solves the controlled variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn’s disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

      Slides

      10:20 am – 10:50 amBreak
      10:50 pm – 11:30 pmNoureddine El Karoui

      Video

      Title: Random matrices and high-dimensional statistics: beyond covariance matrices

      Abstract: Random matrices have played a central role in understanding very important statistical methods linked to covariance matrices (such as Principal Components Analysis, Canonical Correlation Analysis etc…) for several decades. In this talk, I’ll show that one can adopt a random-matrix-inspired point of view to understand the performance of other widely used tools in statistics, such as M-estimators, and very common methods such as the bootstrap. I will focus on the high-dimensional case, which captures well the situation of “moderately” difficult statistical problems, arguably one of the most relevant in practice. In this setting, I will show that random matrix ideas help upend conventional theoretical thinking (for instance about maximum likelihood methods) and highlight very serious practical problems with resampling methods.

      11:30 am – 12:10 pmNikhil Naik

      Video

      Title: Understanding Urban Change with Computer Vision and Street-level Imagery

      Abstract: Which neighborhoods experience physical improvements? In this work, we introduce a computer vision method to measure changes in the physical appearances of neighborhoods from time-series street-level imagery. We connect changes in the physical appearance of five US cities with economic and demographic data and find three factors that predict neighborhood improvement. First, neighborhoods that are densely populated by college-educated adults are more likely to experience physical improvements. Second, neighborhoods with better initial appearances experience, on average, larger positive improvements. Third, neighborhood improvement correlates positively with physical proximity to the central business district and to other physically attractive neighborhoods. Together, our results illustrate the value of using computer vision methods and street-level imagery to understand the physical dynamics of cities.

      (Joint work with Edward L. Glaeser, Cesar A. Hidalgo, Scott Duke Kominers, and Ramesh Raskar.)

      12:10 pm – 12:25 pmVideo #1

      Video #2

      Data Science Lightning Talks
      12:25 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmTracy Ke

      Video

      Title: A new SVD approach to optimal topic estimation

      Abstract: In the probabilistic topic models, the quantity of interest—a low-rank matrix consisting of topic vectors—is hidden in the text corpus matrix, masked by noise, and Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank matrix and the singular vectors of the text corpus matrix are usually complicated and hard to spell out, so how to use SVD for learning topic models faces challenges.

      We overcome the challenge by revealing a surprising insight: there is a low-dimensional simplex structure which can be viewed as a bridge between the low-rank matrix of interest and the SVD of the text corpus matrix, and which allows us to conveniently reconstruct the former using the latter. Such an insight motivates a new SVD-based approach to learning topic models.

      For asymptotic analysis, we show that under a popular topic model (Hofmann, 1999), the convergence rate of the l1-error of our method matches that of the minimax lower bound, up to a multi-logarithmic term. In showing these results, we have derived new element-wise bounds on the singular vectors and several large deviation bounds for weakly dependent multinomial data. Our results on the convergence rate and asymptotical minimaxity are new. We have applied our method to two data sets, Associated Process (AP) and Statistics Literature Abstract (SLA), with encouraging results. In particular, there is a clear simplex structure associated with the SVD of the data matrices, which largely validates our discovery.

      2:10 pm – 2:50 pmAlbert-László Barabási

      Video

      Title: Taming Complexity: From Network Science to Controlling Networks

      Abstract: The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. We apply these tools to several real networks, unveiling how the network topology determines its controllability. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems.

       

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmMarena Lin

      Video

      Title: Optimizing climate variables for human impact studies

      Abstract: Estimates of the relationship between climate variability and socio-economic outcomes are often limited by the spatial resolution of the data. As studies aim to generalize the connection between climate and socio-economic outcomes across countries, the best available socio-economic data is at the national level (e.g. food production quantities, the incidence of warfare, averages of crime incidence, gender birth ratios). While these statistics may be trusted from government censuses, the appropriate metric for the corresponding climate or weather for a given year in a country is less obvious. For example, how do we estimate the temperatures in a country relevant to national food production and therefore food security? We demonstrate that high-resolution spatiotemporal satellite data for vegetation can be used to estimate the weather variables that may be most relevant to food security and related socio-economic outcomes. In particular, satellite proxies for vegetation over the African continent reflect the seasonal movement of the Intertropical Convergence Zone, a band of intense convection and rainfall. We also show that agricultural sensitivity to climate variability differs significantly between countries. This work is an example of the ways in which in-situ and satellite-based observations are invaluable to both estimates of future climate variability and to continued monitoring of the earth-human system. We discuss the current state of these records and potential challenges to their continuity.

      4:00 pm – 4:40 pmAlex Peysakhovich Title: Building a cooperator

      Abstract: A major goal of modern AI is to construct agents that can perform complex tasks. Much of this work deals with single agent decision problems. However, agents are rarely alone in the world. In this talk I will discuss how to combine ideas from deep reinforcement learning and game theory to construct artificial agents that can communicate, collaborate and cooperate in productive positive sum interactions.

      4:40 pm – 5:20 pmTze Leung Lai

      Video

      Title: Gradient boosting: Its role in big data analytics, underlying mathematical theory, and recent refinements

      Abstract: We begin with a review of the history of gradient boosting, dating back to the LMS algorithm of Widrow and Hoff in 1960 and culminating in Freund and Schapire’s AdaBoost and Friedman’s gradient boosting and stochastic gradient boosting algorithms in the period 1999-2002 that heralded the big data era. The role played by gradient boosting in big data analytics, particularly with respect to deep learning, is then discussed. We also present some recent work on the mathematical theory of gradient boosting, which has led to some refinements that greatly improves the convergence properties and prediction performance of the methodology.

      August 19, Saturday (Full day)

      TimeSpeakerTopic
      8:30 am – 9:00 amBreakfast
      9:00 am – 9:40 amNatesh Pillai

      Video

      Title: Accelerating MCMC algorithms for Computationally Intensive Models via Local Approximations

      Abstract: We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler’s exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the exact posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this article: when the likelihood has some local regularity, the number of model evaluations per Markov chain Monte Carlo (MCMC) step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ordinary differential equation (ODE) and partial differential equation (PDE) inference problems, with both synthetic and real data.

      9:40 am – 10:20 amRavi Jagadeesan

      Video

      Title: Designs for estimating the treatment effect in networks with interference

      Abstract: In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring” on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

      10:20 am – 10:50 amBreak
      10:50 am – 11:30 amAnnie Liang

      Video

      Title: The Theory is Predictive, but is it Complete? An Application to Human Generation of Randomness

      Abstract: When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much “predictable variation” there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction.  We illustrate our methods on the task of predicting human-generated random sequences. Relative to a theoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness (joint with Jon Kleinberg and Sendhil Mullainathan).

      11:30 am – 12:10 pmZak Stone

      Video

      Title: TensorFlow: Machine Learning for Everyone

      Abstract: We’ve witnessed extraordinary breakthroughs in machine learning over the past several years. What kinds of things are possible now that weren’t possible before? How are open-source platforms like TensorFlow and hardware platforms like GPUs and Cloud TPUs accelerating machine learning progress? If these tools are new to you, how should you get started? In this session, you’ll hear about all of this and more from Zak Stone, the Product Manager for TensorFlow on the Google Brain team.

      12:10 pm – 1:30 pmLunch
      1:30 pm – 2:10 pmJann Spiess

      Video

      Title: (Machine) Learning to Control in Experiments

      Abstract: Machine learning focuses on high-quality prediction rather than on (unbiased) parameter estimation, limiting its direct use in typical program evaluation applications. Still, many estimation tasks have implicit prediction components. In this talk, I discuss accounting for controls in treatment effect estimation as a prediction problem. In a canonical linear regression framework with high-dimensional controls, I argue that OLS is dominated by a natural shrinkage estimator even for unbiased estimation when treatment is random; suggest a generalization that relaxes some parametric assumptions; and contrast my results with that for another implicit prediction problem, namely the first stage of an instrumental variables regression.

      2:10 pm – 2:50 pmBradly StadieTitle: Learning to Learn Quickly: One-Shot Imitation and Meta Learning

      Abstract: Many reinforcement learning algorithms are bottlenecked by data collection costs and the brittleness of their solutions when faced with novel scenarios.
      We will discuss two techniques for overcoming these shortcomings. In one-shot imitation, we train a module that encodes a single demonstration of a desired behavior into a vector containing the essence of the demo. This vector can subsequently be utilized to recover the demonstrated behavior. In meta-learning, we optimize a policy under the objective of learning to learn new tasks quickly. We show meta-learning methods can be accelerated with the use of auxiliary objectives. Results are presented on grid worlds, robotics tasks, and video game playing tasks.

      2:50 pm – 3:20 pmBreak
      3:20 pm – 4:00 pmHau-Tieng Wu

      Video

      Title: When Medical Challenges Meet Modern Data Science

      Abstract: Adaptive acquisition of correct features from massive datasets is at the core of modern data analysis. One particular interest in medicine is the extraction of hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. The mathematical and statistical problems are made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. In this talk, I will discuss recent progress in solving this kind of problem by combining the cepstrum-based nonlinear time-frequency analysis and manifold learning technique. A particular solution will be given along with its theoretical properties. I will also discuss the application of this method to two medical problems – (1) the extraction of a fetal ECG signal from a single lead maternal abdominal ECG signal; (2) the simultaneous extraction of the instantaneous heart/respiratory rate from a PPG signal during exercise; (3) (optional depending on time) an application to atrial fibrillation signals. If time permits, the clinical trial results will be discussed.

      4:00 pm – 4:40 pmSifan Zhou

      Video

      Title: Citing People Like Me: Homophily, Knowledge Spillovers, and Continuing a Career in Science

      Abstract: Forward citation is widely used to measure the scientific merits of articles. This research studies millions of journal article citation records in life sciences from MEDLINE and finds that authors of the same gender, the same ethnicity, sharing common collaborators, working in the same institution, or being geographically close are more likely (and quickly) to cite each other than predicted by their proportion among authors working on the same research topics. This phenomenon reveals how social and geographic distances influence the quantity and speed of knowledge spillovers. Given the importance of forward citations in academic evaluation system, citation homophily potentially put authors from minority group at a disadvantage. I then show how it influences scientists’ chances to survive in the academia and continue publishing. Based on joint work with Richard Freeman.

       

      To view photos and video interviews from the conference, please visit the CMSA blog.

       

    • Seminars
      Seminars Colloquia & Seminar
      12-07-2015 Mathematical Physics Seminar
      3:49 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      03-22-2016 Geometric Analysis Seminar
      3:51 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: CMSA/Math Fall Gathering
      4:00 pm-6:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA
      Friday, Sep 22, 2022
      4:00 pm
      All CMSA and Math affiliates are invited.
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Quantum cohomology as a deformation of symplectic cohomology
      4:00 pm-5:00 pm
      12/01/2024
      20211124_Nick-Sheridan_RESCHEDULED_poster

      Abstract: Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.

    • Math Science Lectures in Honor of Raoul Bott
      Math Science Lectures in Honor of Raoul Bott Event
      Math Science Lectures in Honor of Raoul Bott: Mina Aganagic
      4:00 pm
      12/01/2024-04/10/2019
      1 Oxford Street, Cambridge MA 02138

      On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley).  This was the second annual Math Science Lecture Series held in honor of Raoul Bott.

      The lectures took place in Science Center, Hall C

      “Two math lessons from string theory”

      Lecture 1:

       

       

       

       

       

      April 9, 2019

      Title: “Lesson on Integrability”

       

      Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.

      Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

      Lecture 2:

       

       

       

       

       

      April 10, 2019

      Title: “Lesson on Knot Categorification”

       

      Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.

      The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.

      This talk is mostly based on joint work with Andrei Okounkov.

       

      Information about last year’s Math Science Bott lecture can be found here. 

      Aganagic

    • Seminars
      4:00 pm-5:00 pm
      12/01/2024

    • Topological Quantum Matter Seminar
      4:00 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Yizhuang You, UC San Diego

      Title: Symmetric Mass Generation
      Abstract: Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Higher rank DT theory from rank 1
      4:00 pm-5:00 pm
      12/01/2024
      20211110_Richard-Thomas_poster

      Abstract: Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

    • Yip Lecture Series
      Yip Lecture Series Event
      Yip Annual Lecture
      4:00 pm-5:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).

      The lecture was held from 4:00-5:00pm in Science Center, Hall A.

      Credit:Bronzwaer/Davelaar/Moscibrodzka/Falcke/Radboud University
    • Math Science Lectures in Honor of Raoul Bott
      4:00 pm-5:30 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      Fibered ribbon knots vs. major 4D conjectures

      Location: Harvard University Science Center Hall A & via Zoom webinar

      Dates: Feb 20 & 22, 2024

      Time: 4:00-5:30 pm

      Directions and Recommended Lodging

      Registration is required.

      Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin and a Clay Research Fellow.

      This will be the fourth annual Math Science Lecture Series held in Honor of Raoul Bott.

      Talk topic:  Fibered ribbon knots vs. major 4D conjectures

      Feb. 20, 2024

      Title: Fibered ribbon knots and the Poincaré conjecture

      Abstract: A knot is “fibered” if its complement in S^3 is the total space of a bundle over the circle, and ribbon if it bounds a smooth disk into B^4 with no local maxima with respect to radial height. A theorem of Casson-Gordon from 1983 implies that if a fibered ribbon knot does not bound any fibered disk in B^4, then the smooth 4D Poincaré conjecture is false. I’ll show that unfortunately (?) many ribbon disks bounded by fibered knots are fibered, giving some criteria for extending fibrations and discuss how one might search for non-fibered examples.

      Feb. 22, 2024

      Title: Fibered knots and the slice-ribbon conjecture

      Abstract: The slice-ribbon conjecture (Fox, 1962) posits that if a knot bounds any smooth disk into B^4, it also bounds a ribbon disk. The previously discussed work of Casson-Gordon yields an obstruction to many fibered knots being ribbon, yielding many interesting potential counterexamples to this conjecture — if any happy to bound a non-ribbon disk. In 2022, Dai-Kong-Mallick-Park-Stoffregen showed that unfortunately( ?) many of these knots don’t bound a smooth disk into B^4 and thus can’t disprove the conjecture. I’ll show a simple alternate proof that a certain interesting knot (the (2,1)-cable of the figure eight) isn’t slice and discuss remaining open questions. This talk is joint with Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.

       

      Talk Chair: Cliff Taubes (Harvard Mathematics)

      Moderator: Freid Tong (Harvard CMSA)


      Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.

    • Probability Seminar
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Probability Seminar

      Speaker: Wei-Kuo Chen (University of Minnesota)

      Title: A Gaussian convexity for logarithmic moment generating function

      Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy.

       

    • Quantum Matter
      4:00 pm-5:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.18.22-1583x2048-1

      Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045

    • Seminars
      Seminars Colloquia & Seminar
      10/16/2019 Colloquium
      4:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      3/12/2020 Colloquium
      4:00 pm-5:00 pm
      12/01/2024
    • Colloquium
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      02CMSA Colloquium 03.02.2023

      Speaker: Erez Urbach, Weizmann Institute of Science

      Title: The string/black hole transition in anti de Sitter space

      Abstract: String stars, or Horowitz-Polchinski solutions, are string theory saddles with normalizable condensates of thermal-winding strings. In the past, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux), their possible connection to small black holes in AdS, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model, and their relation to the deconfined phase of 3+1 pure Yang-Mills.

    • Colloquium
      4:00 pm
      12/01/2024
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Lagrangians and mirror symmetry in the Higgs bundle moduli space
      4:00 pm-5:00 pm
      12/01/2024

      Abstract: The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed, but  also to open up new features involving finite-dimensional algebras which are deformations of cohomology algebras. Answering some of the questions raised  requires revisiting basic constructions of stable bundles on curves.

    • Probability Seminar
      4:00 pm-5:00 pm
      12/01/2024
      Harvard Science Center, 1 Oxford Street, Cambridge MA 02138

      Probability Seminar

      Speaker: Marius Lemm, University of Tuebingen

      Title: Light cones for open quantum systems
      Abstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely, if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound on the slope of this light cone (i.e., on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux, J. Faupin, D.H. Ou Yang, I.M. Sigal, and J. Zhang.

       

    • Topological Quantum Matter Seminar
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Roman Geiko, UCLA

      Title: Homotopy classes of loops of Clifford unitaries

      Abstract: We study Clifford locality-preserving unitaries and stabilizer Hamiltonians by means of Hermitian K-theory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two short-range entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu.  https://arxiv.org/abs/2306.09903.

    • Joint Harvard-CUHK-YMSC Differential Geometry
      4:00 pm-5:00 pm
      12/01/2024

      Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class S[A1]. I will describe the resulting geometric structures using a kind of complexified Hitchin system parameterising bundles on curves equipped with pencils of flat connections.

    • Topological Quantum Matter Seminar
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Daniele Guerci, Flatiron Institute

      Title: Chern Mosaic and ideal bands in helical trilayer graphene

      Abstract: In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat bands features the superposition of a Chern -1 and a Chern 2 bands described by the superposition of two lowest Landau level [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [3]. Building on this knowledge, I will discuss the properties of the zero-modes at higher magic angles.

      [1] Y.Mao,D.Guerci,C.Mora, PRB 107, 125423 (2023) [Editors’ Suggestion]

      [2] D.Guerci,Y.Mao,C.Mora, arXiv:2305.03702 (2023)

      [3] D.Guerci,Y.Mao,C.Mora, arXiv:2308.02638 (2023)

    • Colloquium
      4:00 pm-5:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      CMSA Colloquium 10.05.22 (1)

      Colloquium

      Please note this colloquium will be held at a special time:  4:00-5:00 pm.

      Speaker: Subir Sachdev (Harvard)

      Title: Quantum statistical mechanics of charged black holes and strange metals
      Abstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.
      Slides: cmsa22
    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      03-28-2016 Mathematical Physics Seminar
      4:08 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-06-2016 Random Matrix & Probability Theory
      4:10 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      03-30-2016 Random Matrix & Probability Theory Seminar
      4:11 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:12 pm-5:12 pm
      12/01/2024

      Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Fast Point Transformer
      4:13 pm-5:13 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-06.02.2022-1583x2048-1

      Abstract: The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine the local predictions together. However, this scheme inevitably involves additional stages for pre- and post-processing and may also degrade the final output due to predictions in a local perspective. This talk introduces Fast Point Transformer that consists of a new lightweight self-attention layer. Our approach encodes continuous 3D coordinates, and the voxel hashing-based architecture boosts computational efficiency. The proposed method is demonstrated with 3D semantic segmentation and 3D detection. The accuracy of our approach is competitive to the best voxel-based method, and our network achieves 129 times faster inference time than the state-of-the-art, Point Transformer, with a reasonable accuracy trade-off in 3D semantic segmentation on S3DIS dataset.

      Bio: Jaesik Park is an Assistant Professor at POSTECH. He received his Bachelor’s degree from Hanyang University in 2009, and he received his Master’s degree and Ph.D. degree from KAIST in 2011 and 2015, respectively. Before joining POSTECH, He worked at Intel as a research scientist, where he co-created the Open3D library. His research interests include image synthesis, scene understanding, and 3D reconstruction. He serves as a program committee at prestigious computer vision conferences, such as Area Chair for ICCV, CVPR, and ECCV.

    • Seminars
      Seminars Colloquia & Seminar
      04-14-2016 Evolution Equations Seminar
      4:13 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-12-2016 Geometric Analysis Seminar
      4:14 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/11/2019 Special Seminar
      4:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Duality String Seminar, Thursdays
      4:15 pm-6:00 pm
      12/01/2024-10/12/2016

      The Duality String  Seminar is held every Thursday at 4:15pm in Jefferson Lab, 453.

      For details, please visit the website.

      * The Duality String Seminar is sponsored by the Center of Mathematical Sciences and Applications’ Cheng Yu-Tong Fund, for Research at the Interface of Mathematics and Physics.

    • Seminars
      Seminars Colloquia & Seminar
      03-31-2016 Evolution Equations Seminar
      4:15 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      4:15 pm-5:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      04-04-2016 Mathematical Physics Seminar
      4:20 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-05-2016 Geometric Analysis Seminar
      4:21 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-11-2016 Mathematical Physics Seminar
      4:22 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      Entanglement and its key role in quantum information
      4:23 pm-5:23 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-06.30.22-1583x2048-1

      Abstract: Entanglement is a type of correlation found in composite quantum systems, connected with various non-classical phenomena. Currently, entanglement plays a key role in quantum information applications such as quantum computing, quantum communication, and quantum sensing. In this talk the concept of entanglement will be introduced along with various methods that have been proposed to detect and quantify it. The fundamental role of entanglement in both quantum theory and quantum technology will also be discussed.

      Bio: Spyros Tserkis is a postdoctoral researcher at Harvard University, working on quantum information theory. Before joining Harvard in Fall 2021, he was a postdoctoral researcher at MIT and the Australian National University. He received his PhD from the University of Queensland.

    • Seminars
      Seminars Colloquia & Seminar
      04-07-2016 Evolution Equations Seminar
      4:24 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-06-2016 Seminar on General Relativity
      4:25 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-11-2016 Random Matrix & Probability Theory Seminar
      4:28 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-13-2016 General Relativity Seminar
      4:29 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Colloquium

      Speaker: Justin Moore (Cornell University)

      Title: Homology, higher derived limits, and set theory

      Abstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the “shape” of the space and can give counterintuitive information about its dimension. One remedy of this is to develop a homology theory based on approximating spaces by polyhedra, computing their homologies, and then taking a limit. This is the approach taken by Steenrod-Sitnikov homology and Lisica and Mardesic’s strong homology. Even within the class of locally compact second countable spaces though, the properties of these homology theories — and the higher derived limits which underly them — are dependent on axioms of set theory beyond ZFC. Recently it was shown that it is consistent with (and therefore independent of) ZFC that strong homology and Steenrod Sitnikov homology coincide in the class of locally compact second countable spaces — and therefore each of these homology theories enjoys the desirable properties of the other. These results also point to how we might develop variants of these homology theories which enjoy their desirable properties, but which are less sensitive to set theory. This is joint work with Nathaniel Bannister, Jeff Bergfalk, and Stevo Todorcevic.

    • Seminars
      Seminars Colloquia & Seminar
      04-20-2016 General Relativity Seminar
      4:30 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: CMSA/MATH Fall Gathering
      4:30 pm-6:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      CMSA/MATH Fall Gathering

      Friday, Sep 23, 2022
      4:30–6:00 pm
      All CMSA and Math affiliates are invited.
    • Seminars
      Seminars Colloquia & Seminar
      3/20/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/13/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Joel D. Hamkins (Notre Dame and Oxford)

      Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers

      Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually, and in the talk I shall begin slowly with some easy elementary observations. By the end, however, we shall engage with sophisticated ideas in descriptive set theory, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses, for example, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.

    • Colloquium
      4:30 pm
      12/01/2024
    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Cenke Xu (UCSB)

      Title: Quantum field theory approach to quantum information

      Abstract: We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement and decoherence. The Euclidean space-time path integral allows us to map this problem to a quantum field theory with (temporal) boundary or defects. We therefore investigate two types of quantum many-body systems with nontrivial boundary physics: quantum critical points, and states with nontrivial topology, such as Chern insulator and symmetry protected topological states. For example, we demonstrate that a Wilson-Fisher quantum critical point can be driven into an “extraordinary-log” phase after weak-measurement. Another example is that, we argue that a system with higher form symmetry may be driven to a self-dual phase transition under weak measurement.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Seth Koren (Notre Dame)

      Title: Non-invertible symmetries, leptons, quarks, and why multiple generations

      Abstract: Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof.  After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this theory works by virtue of the SM having the same numbers of colors and generations.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      2/20/2019 Colloquium
      4:30 pm-5:00 pm
      12/01/2024
    • Topological Quantum Matter Seminar
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Kaifeng Bu (Harvard University)

      Title: Quantum information: the interplay of mathematics and physics

      Abstract: I will provide an introduction to quantum information, which points to a new connection with experiment on the one hand, and a potential new area of mathematical analysis on the other. I will introduce two recent results about the application of this new area in quantum information: (1) a novel Quantum Central Limit Theorem (QCLT), and (2) a physically realizable protocol for testing and measuring quantum advantage. This talk is based on a collaboration with Arthur Jaffe, and Weichen Gu (PNAS120(25)2023, arXiv: 2302.08423, arXiv:2306.09292).

       

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Yu-Shen Lin (Boston University)

      Title: Gravitational Instantons

      Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk, we will discuss the Torelli theorem of gravitational instantons, how the cohomological invariants of a gravitational instanton determine them. As a consequence, this leads to a description of the moduli space of gravitational instantons.

    • Colloquium
      4:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      02/21/2020 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/20/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      11/25/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      Colloquium 12/4/2019
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      4:30 pm-5:00 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4/17/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Dana Bartosova (University of Florida)

      Title: What do topological dynamics, combinatorics, and model theory have in common?

      Abstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory.  Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front, however, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts, which is an AIMSQuaRE project with Džamonja, Patel, and Scow.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Jeff W. Lichtman (Harvard University)

      Title: The analytical challenges of connectomics

      Abstract: Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      2/14/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      1/30/2019 Colloquium
      4:30 pm
      12/01/2024
    • Topological Quantum Matter Seminar
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar

      Speaker: Liujun Zou (Perimeter Institute)

      Title: Landscape of quantum phases in quantum materials

      Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.

    • CMSA EVENT: CMSA/MATH Bi-Annual Gathering
      4:30 pm-6:00 pm
      12/01/2024
      20 Garden Street, Cambridge, MA 02138 USA

      On Friday, March 24th, 4:30PM – 6PM, the CMSA will host the CMSA/MATH Bi-Annual Gathering for Harvard CMSA and Math affiliates in the Common Room at 20 Garden Street, Cambridge MA 02138.

    • Seminars
      Seminars Colloquia & Seminar
      4/24/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Topological Quantum Matter Seminar
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Topological Quantum Matter Seminar

      Speaker: Bruno Mera, Instituto Superior Tecnico

      Title: Uniqueness of Landau levels and their analogs with higher Chern numbers

      Abstract: Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged par- ticle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this talk, using the Stone-von Neumann the- orem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions.

      Ref: Bruno Mera and Tomoki Ozawa. Uniqueness of Landau levels and their analogs with higher Chern numbers. arXiv:2304.00866, 2023. arXiv:2304.00866.

       

    • Colloquium
      4:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Matthew Foreman (UC Irvine)

      Title: Impossibility results in classical dynamical systems

      Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.

       

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Manuel Cortés-Izurdiaga (University of Malaga)

      Title:  Homotopy categories of rings: some properties and consequences in module categories

      Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the first step in studying other (algebraic) homotopy categories, such as those associated to a scheme. To study these categories, one can use results from the category of modules or the category of complexes. In the first part of the talk, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes, for a natural number N greater than or equal to 2, using some techniques from module categories, such us the deconstruction of a class of modules.

      Another approximation is to use other methods for studying homotopy categories, like those coming from triangulated categories. In some cases, the results obtained in homotopy categories imply some consequences in the category of modules. In the second part of the talk, we will see how to prove the existence of Gorenstein-projective precovers for some specific rings using this approach.

    • Seminars
      Seminars Colloquia & Seminar
      9/18/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/28/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      9/25/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Cameron Krulewski (MIT) and Leon Liu (Harvard)

      Title: A Long Exact Sequence in Symmetry Breaking

      Abstract: We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES).

      The mathematical backbone of the SBLES is the Smith homomorphism, which gives a family of maps between twisted bordism groups. Though many examples have been studied, we give the first completely general account of the Smith homomorphism. We lift it to a map of Thom

      spectra and identify the cofiber, producing a long exact sequence of twisted bordism groups; the SBLES is the Anderson dual of that long exact sequence. Our work develops further the theory of higher Berry phase and its bulk-boundary correspondence and serves as a new computational tool for classifying symmetry protected topological phases.

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Boaz Barak (Harvard)

      Title: On Provable Copyright Protection for Generative Model

      Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set.

      Roughly speaking, a generative model p is k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content.

      Joint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870

    • Quantum Matter
      4:30 pm-6:00 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Quantum Matter Seminar

      Speaker: Clay Córdova (U Chicago)

      Title: Anomalies of Non-Invertible Symmetries

    • Seminars
      Seminars Colloquia & Seminar
      10/3/2019 RM & PT Seminar
      4:30 pm-5:00 pm
      12/01/2024
    • Seminars
      4:30 pm-5:30 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      4/4/2019 Random Matrix and Probability Theory Seminar
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/9/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      10/2/2019 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Brian Williams (Boston University)

      Title: Koszul duality in QFT

      Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello, Gaiotto, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory.

       

    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Sean Cox, Virginia Commonwealth University

      Title: Predicting non-continuous functions

      Abstract: One of the strangest consequences of the Axiom of Choice is the following Hardin-Taylor 2008 result: there is a “predictor” such that for every function $f$ from the reals to the reals—even nowhere continuous $f$—the predictor applied to $f \restriction (-\infty,t)$ correctly predicts $f(t)$ for *almost every* $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$-invariant predictors? Bajpai-Velleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular, do there exist analytic-invariant predictors? We have partially answered that question: assuming the Continuum Hypothesis (CH), the answer is “no”. Regarding other subgroups of Homeo^+(R), we have affirmative answers that rely solely on topological group-theoretic properties of the subgroup. But these properties are very restrictive; e.g., all known positive examples are metabelian. So there remain many open questions. This is joint work with Aldi, Buffkin, Cline, Cody, Elpers, and Lee.

    • Seminars
      Seminars Colloquia & Seminar
      3/11/2020 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Colloquium
      4:30 pm-5:30 pm
      12/01/2024
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA

      Speaker: Xuwen Zhu (Northeastern)

      Title: Analysis of ALH* gravitational instantons

      Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.

    • Seminars
      Seminars Colloquia & Seminar
      4/15/2020 Colloquium
      4:30 pm-5:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      04-18-2016 Social Science Application Forum
      4:31 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:33 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-19-2016 Geometric Analysis Seminar
      4:33 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:34 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-18-2016 Mathematical Physics Seminar
      4:34 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-21-2016 Evolution Equations Seminar
      4:35 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:36 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-20-2016 Random Matrix & Probability Theory Seminar
      4:37 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-26-2016 Geometric Analysis Seminar
      4:38 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:39 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-25-2016 Mathematical Physics Seminar
      4:39 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      4:41 pm
      12/01/2024
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      04-27-2016 Random Matrix & Probability Theory Seminar
      4:42 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-27-2016 General Relativity Seminar
      4:44 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-28-2016 CMSA Special Seminar
      4:45 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      3/4/2020 Colloquium
      4:45 pm-5:45 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      04-28-2016 Evolution Equations Seminar
      4:46 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-04-2016 General Relativity Seminar
      4:48 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      04-29-2016 CMSA Special Seminar
      4:49 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      05-02-2016 Mathematical Physics Seminar
      4:50 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-05-2016 Evolution Equations Seminar
      4:51 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      05-25-2016 General Relativity Seminar
      4:52 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      4:54 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      4:56 pm-5:56 pm
      12/01/2024

      Abstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learning-based approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, data-hungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.

    • General Relativity Seminar
      4:58 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      4:59 pm-6:59 pm
      12/01/2024

      Abstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible, and after considerable work by many authors, it is generally conjectured by computer scientists that as the size of matrices becomes large, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk, no knowledge of algebraic geometry or representation theory will be needed.

    • CMSA EVENT: 2017 Ding Shum Lecture
      5:00 pm-6:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      Leslie Valiant will be giving the inaugural talk of the Ding Shum Lectures on Tuesday, October 10 at 5:00 pm in Science Center Hall D, Cambridge, MA.

      Learning as a Theory of Everything

      Abstract: We start from the hypothesis that all the information that resides in living organisms was initially acquired either through learning by an individual or through evolution. Then any unified theory of evolution and learning should be able to characterize the capabilities that humans and other living organisms can possess or acquire. Characterizing these capabilities would tell us about the nature of humans, and would also inform us about feasible targets for automation. With this purpose we review some background in the mathematical theory of learning. We go on to explain how Darwinian evolution can be formulated as a form of learning. We observe that our current mathematical understanding of learning is incomplete in certain important directions, and conclude by indicating one direction in which further progress would likely enable broader phenomena of intelligence and cognition to be realized than is possible at present.

       

    • Seminars
      Seminars Colloquia & Seminar
      2018 HMS Focused Lecture Series
      5:00 pm
      12/01/2024

      As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building, 20 Garden Street, Room G10.

      The schedule will be updated below.

      DateSpeakerTitle/Abstract
      January 23, 25, 30 and February 1 

      3-5pm

      *Room G10*

      Ivan Losev 

      (Northeastern)

      Title: BGG category O: towards symplectic duality 

      Abstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting.

      Approximate (optimistic) plan of the lectures:

      1) Preliminaries and BGG category O.

      2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem.

      3) Localization theorem continued. Soergel modules.

      4) Koszul algebras and Koszul duality for categories O.

      Time permitting: other instances of Symplectic duality.

      Prerequisites:

      Semi-simple Lie algebras and their finite dimensional representation theory.

      Some  Algebraic geometry. No prior knowledge of category O/ Geometric

      Representation theory is assumed.

      Scanned from a Xerox Multifunction Device

      February 27, 

      and March 1

      3-5pm

      Colin Diemer 

      (IHES)

      Title: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS. 

      Abstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).

      March 6 and 8 

      4-5pm

      Adam Jacob 

      (UC Davis)

      Title: The deformed Hermitian-Yang-Mills equation 

      Abstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau.

      March 6, 8, 13, 15 

      3-4pm

      Dmytro Shklyarov 

      (TU Chemnitz)

      Title: On categories of matrix factorizations and their homological invariants 

      Abstract: The talks will cover the following topics:

      1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements.

      2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models.

      3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.

      April 10 & 12 

      3-4pm

      Mauricio Romo 

      (IAS)

      Title: Gauged Linear Sigma Models, Supersymmetric Localization and Applications 

      Abstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs).

      Lecture notes

      April 17, 19, 26 

      3-5pm

      Andrew  Harder 

      (University of Miami)

      Title: Perverse sheaves of categories on surfaces 

      Abstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc.

      I’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry, symplectic geometry, and category theory. Finally, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space.

       

      May 15, 17 

      1-3pm

      Charles Doran 

      (University of Alberta)

      Lecture One:
      Title: Picard-Fuchs uniformization and Calabi-Yau geometry
      Abstract:
      Part 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.
      Part 2:  We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, …), where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.

       

      Lecture Two:
      Title: Calabi-Yau fibrations: construction and classification
      Abstract:

      Part 1:  Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals.

      Part 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      05-11-2016 Random Matrix & Probability Theory Seminar
      5:00 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Jennifer Chayes Public Talk, 11-02-17
      5:00 pm-6:00 pm
      12/01/2024

      Jennifer Chayes (Microsoft Research) will be giving a public talk on November 02, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Network Science: From the Online World to Cancer Genomics

      Abstract: Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage many human diseases. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. I’ll discuss in some detail particular applications to cancer genomics, applying network algorithms to suggest possible drug targets for certain kinds of cancer.

       

    • Math Science Literature Lecture Series
      5:00 pm-6:30 pm
      12/01/2024
      Lecture_Sahai-pdf

      Amit Sahai  (UCLA)

      Title: Indistinguishability Obfuscation: How to Hide Secrets within Software

      Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way compiler” remained elusive for decades.

      In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running time) be indistinguishable to any efficient adversary. Leveraging the notion of punctured programming, introduced in our work with Waters in 2013, well over a hundred papers have explored the remarkable power of iO.

      We’ll then discuss the intense effort that recently culminated in our 2020 work with Jain and Lin, finally showing how to construct iO in such a way that, for the first time, we can prove the security of our iO scheme based on well-studied computational hardness conjectures in cryptography.

      Talk chair: Sergiy Verstyuk

      Video

    • Colloquium
      5:00 pm
      12/01/2024
    • CMSA EVENT: 2023 Ding Shum Lecture
      5:00 pm-6:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      Cynthia Dwork

      On March 21, 2023, the CMSA will host the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS and Microsoft Research).

      Time: 5:00-6:00 pm ET

      Location: Harvard University Science Center Hall D

      This event will be held in person and via Zoom webinar.

      Registration is required.

      In-person registration (link)

      Zoom Webinar registration (link)

      Title: Measuring Our Chances: Risk Prediction in This World and its Betters

      Abstract: Prediction algorithms score individuals, assigning a number between zero and one that is often interpreted as an individual probability: a 0.7 “chance” that this child is in danger in the home; an 80% “probability” that this woman will succeed if hired; a 1/3 “likelihood” that they will graduate within 4 years of admission. But what do words like “chance,” “probability,” and “likelihood” actually mean for a non-repeatable activity like going to college? This is a deep and unresolved problem in the philosophy of probability. Without a compelling mathematical definition we cannot specify what an (imagined) perfect risk prediction algorithm should produce, nor even how an existing algorithm should be evaluated. Undaunted, AI and machine learned algorithms churn these numbers out in droves, sometimes with life-altering consequences.

      An explosion of recent research deploys insights from the theory of pseudo-random numbers – sequences of 0’s and 1’s that “look random” but in fact have structure – to yield a tantalizing answer to the evaluation problem, together with a supporting algorithmic framework with roots in the theory of algorithmic fairness.

      We can aim even higher. Both (1) our qualifications, health, and skills, which form the inputs to a prediction algorithm, and (2) our chances of future success, which are the desired outputs from the ideal risk prediction algorithm, are products of our interactions with the real world. But the real world is systematically inequitable. How, and when, can we hope to approximate probabilities not in this world, but in a better world, one for which, unfortunately, we have no data at all? Surprisingly, this novel question is inextricably bound with the very existence of nondeterminism.

      Professor Cynthia Dwork is Gordon McKay Professor of Computer Science at the Harvard University John A. Paulson School of Engineering and Applied Sciences, Affiliated Faculty at Harvard Law School, and Distinguished Scientist at Microsoft. She uses theoretical computer science to place societal problems on a firm mathematical foundation.

      Her recent awards and honors include the 2020 ACM SIGACT and IEEE TCMF Knuth Prize, the 2020 IEEE Hamming Medal, and the 2017 Gödel Prize.

      Talk Chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)
      Moderator: Faidra Monachou (Harvard CMSA)

      The 2020-2022 Ding Shum lectures were postponed due to Covid-19.


      Watch the Lecture on Youtube:

      https://youtu.be/wGpZE8QrCKY

    • CMSA EVENT: Noga Alon Public Talk, 9-7-17
      5:00 pm-6:00 pm
      12/01/2024

      Noga Alon (Tel Aviv University) will be giving a public talk on September 7, 2017,as part of the program on combinatorics and complexity hosted by the CMSA during AY17-18.  The talk will be at 5:00pm in Askwith Hall, 13 Appian Way, Cambridge, MA.

      Title: Graph Coloring: Local and Global

      Abstract: Graph Coloring is arguably the most popular subject in Discrete Mathematics, and its combinatorial, algorithmic and computational aspects have been studied intensively. The most basic notion in the area, the chromatic number of a graph, is an inherently global property. This is demonstrated by the hardness of computation or approximation of this invariant as well as by the existence of graphs with arbitrarily high chromatic number and no short cycles. The investigation of these graphs had a profound impact on Graph Theory and Combinatorics. It combines combinatorial, probabilistic, algebraic and topological techniques with number theoretic tools. I will describe the rich history of the subject focusing on some recent results.

    • General Relativity Seminar
      5:02 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:02 pm-6:02 pm
      12/01/2024

      Abstract: Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the ““game” of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.

    • New Technologies in Mathematics Seminar
      5:03 pm-6:03 pm
      12/01/2024

      Abstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions, has allowed major progress on other related questions about M theory, and briefly discuss other applications in field theory and beyond.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-01-2016 Random Matrix & Probability Theory Seminar
      5:03 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      06-08-2016 Random Matrix & Probability Theory Seminar
      5:04 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:04 pm-6:04 pm
      12/01/2024

      Abstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size.

      We demonstrate the effectiveness of the SAT approach by presenting some recent successes, including the solution of the Boolean Pythagorean Triples problem, computing the fifth Schur number, and resolving the remaining case of Keller’s conjecture. Moreover, we constructed and validated a proof for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular, we discuss our progress on applying SAT solving techniques to the chromatic number of the plane (Hadwiger-Nelson problem), optimal schemes for matrix multiplication, an

    • Seminars
      Seminars Colloquia & Seminar
      07-12-2016 Chinese Economy Seminar
      5:06 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:07 pm-6:07 pm
      12/01/2024

      Speaker: Patrick Massot, Laboratoire de Mathématiques d’Orsay and CNRS

      Title: Why explain mathematics to computers?

      Abstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics, and I won’t assume any prior knowledge about formalization.

    • Seminars
      Seminars Colloquia & Seminar
      07-19-2016 Chinese Economy Seminar
      5:07 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      08-02-2016 China Gazetteer Seminar
      5:08 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-12-2016 Mathematical Physics Seminar
      5:10 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-19-2016 Mathematical Physics Seminar
      5:11 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:12 pm-6:12 pm
      12/01/2024
      CMSA-NTM-Seminar-11.03.21

      Abstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms.  This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers.  This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-21-2016 Random Matrix & Probability Theory Seminar
      5:13 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      5:15 pm-6:15 pm
      12/01/2024

      Abstract: Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

      In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

      Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      4-23-2018 Math Physics
      5:15 pm
      12/01/2024

      No additional detail for this event.

    • Colloquium
      Colloquium Colloquia & Seminar
      2/13/2019 Colloquium
      5:15 pm-6:15 pm
      12/01/2024
    • Colloquium
      Colloquium Colloquia & Seminar
      3/27/2019 Colloquium
      5:15 pm-6:15 pm
      12/01/2024
    • Colloquium
      5:15 pm-6:15 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      4-16-2018 Social Science Applications Forum
      5:16 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:17 pm-6:17 pm
      12/01/2024
      CMSA-NTM-Seminar-12.01.21

      Abstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data.

      In terms of their “microscopic” definition, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem, analogous to criticality, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting, we will explain how the interactions induce representation learning.

      This talk is based on a book, The Principles of Deep Learning Theory, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.

    • Seminars
      Seminars Colloquia & Seminar
      4-20-2018 Social Science Applications Forum
      5:18 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:32 pm-6:32 pm
      12/01/2024
      CMSA-NTM-Seminar-12.08.21

      Abstract: Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured images produced by DALL-E. These large language models are impressive but also very inefficient and costly, which limits their applications and accessibility. We postulate that having an explicit hierarchical architecture is the key to Transformers that efficiently handle long sequences. To verify this claim, we first study different ways to upsample and downsample activations in Transformers so as to make them hierarchical. We use the best performing upsampling and downsampling layers to create Hourglass – a hierarchical Transformer language model. Hourglass improves upon the Transformer baseline given the same amount of computation and can yield the same results as Transformers more efficiently. In particular, Hourglass sets new state-of-the-art for Transformer models on the ImageNet32 generation task and improves language modeling efficiency on the widely studied enwik8 benchmark.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      09-26-16 Mathematical Physics Seminar
      5:32 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      Fluid Dynamics Seminar
      5:33 pm
      12/01/2024

      Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. Links to connect can be found in the schedule below once they are created. 

      In the Spring 2019 Semester, the Center of Mathematical Sciences and Applications will be hosting a seminar on Fluid Dynamics. The seminar will take place on Wednesdays from 3:00-4:00pm in CMSA G10.

      Spring 2020:

      DateSpeakerTitle/Abstract
      2/25/2020Keaton Burns, MITTitle: Flexible spectral simulations of low-Mach-number astrophysical fluids

      Abstract: Fluid dynamical processes are key to understanding the formation and evolution of stars and planets. While the astrophysical community has made exceptional progress in simulating highly compressible flows, models of low-Mach-number stellar and planetary flows typically use simplified equations based on numerical techniques for incompressible fluids. In this talk, we will discuss improved numerical models of three low-Mach-number astrophysical phenomena: tidal instabilities in binary neutron stars, waves and convection in massive stars, and ice-ocean interactions in icy moons. We will cover the basic physics of these systems and how ongoing additions to the open-source Dedalus Project are enabling their efficient simulation in spherical domains with spectral accuracy, implicit timestepping, phase-field methods, and complex equations of state.

      3/4/2020

      G02

      3/11/2020
      3/18/2020
      3/25/2020
      4/1/2020
      4/8/2020 G02
      4/15/2020
      4/22/2020
      4/29/2020

      G02

      5/6/2020
      5/13/2020

      Fall 2019:

      DateSpeakerTitle/Abstract
      9/18/2019Jiawei Zhuang (Harvard)Title: Simulation of 2-D turbulent advection at extreme accuracy with machine learning and differentiable programming

       Abstract: The computational cost of fluid simulations grows rapidly with grid resolution. With the recent slow-down of Moore’s Law, it can take many decades for 10x higher resolution grids to become affordable. To break this major barrier in high-performance scientific computing, we used a data-driven approach to learn an optimal numerical solver that can retain high-accuracy at much coarser grids. We applied this method to 2-D turbulent advection and achieved 4x effective resolution than traditional high-order flux-limited advection solvers. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The model can achieve near-peak FLOPs on CPUs and accelerators via convolutional filters.

      9/25/2019Yantao Yang (Peking University)Title: Double diffusive convection and thermohaline staircases 

      Abstract: Double diffusive convection (DDC), i.e. the buoyancy-driven flow with fluid density depending on two scalar components, is omnipresent in many natural and engineering environments. In ocean this is especially true since the seawater density is mainly determined by temperature and salinity. In upper water of both (sub-) tropical and polar oceans, DDC causes the intriguing thermohaline staircases, which consist of alternatively stacked convection layers and sharp interfaces with high gradients of temperature and salinity. In this talk, we will focus on the fingering DDC usually found in (sub-)tropical ocean, where the mean temperature and salinity decrease with depth. We numerically investigate the formation and the transport properties of finger structures and thermohaline staircases. Moreover, we show that multiple states exit for the exactly same global condition, and individual finger layers and finger layers within staircases exhibit very different transport behaviors.

      10/2/2019No talk
      10/9/2019Samuel Rudy (MIT)Title: Data-driven methods for discovery of partial differential equations and forecasting

      Abstract: A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for partial differential equations with or without parametric dependencies and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will also be discussed.​

      10/16/2019No talk
      10/23/2019Kimee Moore (Harvard)Title: Using magnetic fields to investigate Jupiter’s fluid interior

      Abstract: The present-day interior structure of a planet is an important reflection of the formation and subsequent thermal evolution of that planet. However, despite decades of spacecraft missions to a variety of target bodies, the interiors of most planets in our Solar System remain poorly constrained. In this talk, I will discuss how actively generated planetary magnetic fields (dynamos) can provide important insights into the interior properties and evolution of fluid planets. Using Jupiter as a case study, I will present new results from the analysis of in situ spacecraft magnetometer data from the NASA Juno Mission (currently in orbit about Jupiter). The spatial morphology of Jupiter’s magnetic field shows surprising hemispheric asymmetry, which may be linked to the dissolution of Jupiter’s rocky core in liquid metallic hydrogen. I also report the first definitive detection of time-variation (secular variation) in a planetary dynamo beyond Earth. This time-variation can be explained by the advection of Jupiter’s magnetic field by the zonal winds, which places a lower bound on the velocity of Jupiter’s winds at depth. These results provide an important complement to other analysis techniques, as gravitational measurements are currently unable to uniquely distinguish between deep and shallow wind scenarios, and between solid and dilute core scenarios. Future analysis will continue to resolve Jupiter’s interior, providing broader insight into the physics of giant planets, with implications for the formation of our Solar System.

      10/30/2019No Talk
      11/6/2019Federico Toschi (Eindhoven University of Technology)Title: Deep learning and reinforcement learning for turbulence

      Abstract: This talk tells two stories.

      Chapter 1: We investigate the capability of a state-of-the-art deep neural model at learning features of turbulent velocity signals. Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected. We consider turbulent velocity signals, spanning decades in Reynolds numbers, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of the turbulent signals, we focus on the fundamental question of whether a deep neural network (DNN) is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. Can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning?

      Chapter 2: Thermally driven turbulent flows are common in nature and in industrial applications. The presence of a (turbulent) flow can greatly enhance the heat transfer with respect to its conductive value. It is therefore extremely important -in fundamental and applied perspective- to understand if and how it is possible to control the heat transfer in thermally driven flows. In this work, we aim at maintaining a Rayleigh–Bénard convection (RBC) cell in its conductive state beyond the critical Rayleigh number for the onset of convection. We specifically consider controls based on local modifications of the boundary temperature (fluctuations). We take advantage of recent developments in Artificial Intelligence and Reinforcement Learning (RL) to find -automatically- efficient non-linear control strategies. We train RL agents via parallel, GPU-based, 2D lattice Boltzmann simulations. Trained RL agents are capable of increasing the critical Rayleigh number of a factor 3 in comparison with state-of-the-art linear control approaches. Moreover, we observe that control agents are able to significantly reduce the convective flow also when the conductive state is unobtainable. This is achieved by finding and inducing complex flow fields.

      11/13/2019

       

      2:10pm

      G02

      Martin Lellep (Philipps University of Marburg, Germany)Title: Predictions of relaminarisation in turbulent shear flows using deep learning

       

      Abstract: Given the increasing performance of deep learning algorithms in tasks such as classification during the last years and the vast amount of data that can be generated in turbulence research, I present one application of deep learning to fluid dynamics in this talk. We train a deep learning machine learning model to classify if turbulent shear flow becomes laminar a certain amount of time steps ahead in the future. Prior to this, we use a 2D toy example to develop an understanding how the performance of the deep learning algorithm depends on hyper parameters and how to understand the errors. The performance of both algorithms is high and therefore opens up further steps towards the interpretation of the results in future work.

      11/19/2019

      Tuesday

      3-4 pm

      Pierce Hall 209, 29 Oxford Street 

      Detlef Lohse (University of Twente)Title: Rayleigh vs. Marangoni Abstract: In this talk I will show several examples of an interesting and surprising competition between buoyancy and Marangoni forces. First, I will introduce the audience to the jumping oil droplet – and its sudden death – in a density stratified liquid consisting of water in the bottom and ethanol in the top : After sinking for about a minute, before reaching the equilibrium the droplet suddenly jumps up thanks to the Marangoni forces. This phenomenon repeats about 30-50 times, before the droplet falls dead all the sudden. We explain this phenomenon and explore the phase space where it occurs.

      Next, I will focus on the evaporation of multicomponent droplets, for which the richness of phenomena keeps surprising us. I will show and explain several of such phenomena, namely evaporation-triggered segregation thanks to either weak solutal Marangoni flow or thanks to gravitational effects. The dominance of the latter implies that sessile droplets and pending droplets show very different evaporation behavior, even for Bond number << 1. I will also explain the full phase diagram in the Marangoni number vs Rayleigh number phase space, and show where Rayleigh convections rolls prevail, where Marangoni convection rolls prevail, and where they compete.

      The research work shown in this talks combines experiments, numerical simulations, and theory. It has been done by and in collaboration with Yanshen Li, Yaxing Li, and Christian Diddens, and many others.

      11/20/2019Time: 3:00-3:35 pm

      Speaker:  Haoran Liu

      Title: Applications of Phase Field method: drop impact and multiphase turbulence 

      Abstract: Will a mosquito survive raindrop collisions? How the bubbles under a ship reduce the drag force? In nature and industry, flows with drops and bubbles exist everywhere. To understand these flows, one of the powerful tools is the direct numerical simulation (DNS). Among all the DNS methods, we choose the Phase Field (PF) method and develop some models based on it to simulate the complicated flows, such as flows with moving contact lines, fluid-structure interaction, ternary fluids and turbulence. In this talk, I will firstly introduce the advantages and disadvantages of PF method. Then, I will show its applications: drop impact on an object, compound droplet dynamics, water entry of an object and multiphase turbulence.


      Time: 3:35-4:10 pm

      Speaker:  Steven Chong

      Title: Confined Rayleigh-Bénard, rotating Rayleigh-Bénard, double diffusive convection and quasi-static magnetoconvection: A unifying view on their scalar transport enhancement 

      Abstract: For Rayleigh-Bénard under geometrical confinement, under rotation or the double diffusive convection with the second scalar component stabilizing the convective flow, they seem to be the three different canonical models in turbulent flow. However, previous research coincidentally reported the scalar transport enhancement in these systems. The results are counter-intuitive because the higher efficiency of scalar transport is bought about by the slower flow. In this talk, I will show you a fundamental and unified perspective on such the global transport behavior observed in the seemingly different systems. We further show that the same view can be applied to the quasi-static magnetoconvection, and indeed the regime with heat transport enhancement has been found. The beauty of physics is to understand the seemingly unrelated phenomena by a simplified concept. Here we provide a simplified and generic view, and this concept could be potentially extended to other situations where the turbulent flow is subjected to an additional stabilization.

      11/27/2019
      12/4/2019
      12/11/2019

       

      See previous seminar information here.
    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      09-28-2016 Random Matrix & Probability Theory Seminar
      5:35 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      5:35 pm-6:35 pm
      12/01/2024
      CMSA-NTM-Seminar-12.15.21

      Abstract: A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular, we will consider the gapped ground states and Gibbs states on low dimensional lattices, which are believed to exhibit ‘low complexity’ due to the widely studied area law behaviour. Here, we will see the crucial role of complexity-theoretic methods in progress on the ‘area law conjecture’ and in the development of efficient algorithms to classically simulate quantum many-body systems.

    • Seminars
      5:36 pm
      12/01/2024

      As part of the Program on Topological Aspects of Condensed Mattera weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      DateSpeakerTitle/Abstract
      8/29/2018Zeng-Cheng GuTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory

      Abstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.

      9/10/2018Dominic Else, MIT

      Video

      Title: Phases and topology in periodically driven (Floquet) systems

      Abstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.

      9/17/2018Adrian Po, MIT

      Video

      Title: A modern solution to the old problem of symmetries in band theory

      Abstract: There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants.

      9/24/2018Maxim MetlitskiTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs

      Abstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.

      10/1/2018Cancelled
      10/9/2018

      Tuesday

      3:00-4:30pm

      Sagar VijayTitle: Fracton Phases of Matter

      Abstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations (“fractons”) that are strictly immobile at zero temperature, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions, and these states of matter are a gateway for exploring mechanisms for quantum information storage, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases, constructions of these states using well-studied two-dimensional topological phases, and a model in which the fracton excitations carry a protected internal degeneracy, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.

      10/15/2018Ethan LakeTitle: A primer on higher symmetries

      Abstract: The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.

      10/22/2018

      Room G02

      Yin-Chen He, PerimeterTitle: Emergent QED3 and QCD3 in condensed matter system

      Abstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.

      10/29/2018Dominic Williamson, Yale

      Video

      Title: Symmetry and topological order in tensor networks

      Abstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.

      11/13/2018

      Tuesday

      3:00-4:30pm

      Jason Alicea, CaltechTitle: Time-crystalline topological superconductors
      11/19/2018X. G. Wen, MIT

      Video

      Title: A classification of 3+1D topological orders

      Abstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.

      12/3/2018

      *Room G02*

      Claudio Chamon, Boston UniversityTitle: Many-body scar states with topological properties in 1D, 2D, and 3D.

      Abstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies.

      12/10/2018

      Room G02

      Anders Sandvik, Boston University and Institute of Physics, CAS, BeijingTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets

      Abstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.

      1/8/2019Lukasz Fidkowski, Univ. of Washington

      Video

      Title: Non-trivial quantum cellular automata in 3 dimensions

      Abstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.

      3/18/2019Ari Turner, Technion

      Video

      Title:  Trapping Excitations at Phantasmagoric Wave Vectors

      Abstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this, and also introduce “finite fields”, which are the number systems one needs to define exponentials mod. 2.

      4/1/2019Yi-Zhuang You (UCSD)Title: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points

      Abstract: Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP), which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.

      4/8/2019Adam Nahum (Oxford)Title: Emergent statistical mechanics of entanglement in random unitary circuits

      Abstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.

      4/16/2019

      Lyman 425

      1:30pm

      Xie Chen (Calthech)Title: Foliated Fracton Order

      Abstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk, I will present a new framework, which we call the “foliated fracton order”, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models, but also points to the direction of search for interesting new features.

      4/24/2019

      10:30am

      Michael Freedman (Microsoft Station Q)

      Video

      Title: Quantum cellular automata in higher dimensions

      Abstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.

      4/26/2019

      10:30am

      Maissam Barkeshli (University of Maryland)

      Video

      Title: Relative anomalies in (2+1)D symmetry enriched topological states

      Abstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.

      5/3/2019Yuan-Ming Lu (Ohio State)Title: Spontaneous symmetry breaking from anyon condensation

      Abstract: In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

      5/9/2019

      10:30am

      Michael Zaletel (UC Berkeley)Title: Three-partite entanglement in CFTs and chiral topological orders

      Abstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the “entanglement of purification,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience’s help in proving or disproving it.

      5/28/2019

      10:30am

      Masaki Oshikawa (U Tokyo)Title: Gauge invariance, polarization, and conductivity

       

      Abstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity.

      7/18/2019Eslam Khalaf (Harvard)

      Title: Dynamical correlations in anomalous disordered wires

      Abstract: In a (multichannel) disordered wire, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case, the classical dynamics are described by diffusion + drift, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.
      The problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.
      The mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
    • Seminars
      Seminars Colloquia & Seminar
      Spacetime and Quantum Mechanics Seminar
      5:38 pm
      12/01/2024

      As part of the program on Spacetime and Quantum Mechanics, the CMSA will be hosting a weekly seminar on Thursdays at 2:30pm in room G10.

      DateSpeakerTitle/Abstract
      9/12/2019Pasha Pylyavskyy (University of Minnesota)Title: Vector-relation configurations and plabic graphs
      19/18/2019

      2:00pm

      G02

      Francis Brown (University of Oxford)Title: Amplitudes, Polylogs and Moduli Spaces
      9/19/2019Chuck Doran (University of Alberta)Title: Calabi-Yau geometry of the N-loop sunset Feynman integrals

      Abstract: I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals.

      Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli.

      These include: (1) an iterated fibration structure which allows one to “bootstrap” both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (“jump loci”) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via “creative telescoping”; and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties.

      Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev.

      9/26/2019Tomasz Taylor (Northeastern)Title: Celestial Amplitudes
      10/3/2019Simon Caron-Huot (McGill)Title: Poincare Duals of Feynman Integrals
      10/10/2019

      3:30pm

      Yutin Huang (National Taiwan University)Title: Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian
      10/15/2019

      Tuesday

      3:30pm

       

      Sergey Fomin (Univ. of Michigan)

       

      Title: “Morsifications and mutations” (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston). 
      10/18/2019

      Friday 

      G02

      Sebastian Franco (The City College of New York)Title: Graded quivers, generalized dimer models, and topic geometry
      10/31/2019Junjie Rao (Albert Einstein Institute)Title: All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
      11/1/2019

      SC 232

      1:30pm

      George Lusztig (MIT)Title: Total positivity in Springer fibres
      11/12/2019

      Tuesday

      G02

      3:30pm

       

      Pierpaolo Mastrolia (University of Padova)

      Title: Feynman Integrals and Intersection Theory
      11/14/2019

      G02

      Pierpaolo Mastrolia (University of Padova)Title: Feynman Integrals and Intersection Theory Pt. II
      11/21/2019Cristian Vergu (Niels Bohr Institute)Title: The Octagonal Alphabet
      11/26/2019Stephan Stieberger (IAS)Title: Strings on the Celestial Sphere
      12/4/2019Hadleigh Frost (Oxford)Title: BCJ numerators, $\mathcal{M}_{0,n}$, and ABHY

      Abstract: We relate the BCJ numerator Jacobi property to the classical fact that the top homology group of $\mathcal{M}_{0,n}$ is isomorphic to a component of the free Lie algebra. We describe ways to get BCJ numerators, and caution that the BCJ Jacobi property doesn’t imply the existence of what has been called a ‘kinematic algebra.’

       12/5/2019David Kosower (IAS)Title: From scattering amplitudes to classical observables
      12/10/2019Ramis Movassagh (MIT)Title: Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law

      Abstract: In recent years, there has been a surge of activities in proposing “exactly solvable” quantum spin chains with surprising high amount of ground state entanglement–exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and ‘generic’ aspects of local spin chains.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/10/2018 Math-Physics Seminar
      5:41 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-05-2016 Random Matrix & Probability Theory Seminar
      5:41 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      5:42 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      3/14/2019 Random Matrix and Probability Theory Seminar
      5:45 pm
      12/01/2024
    • Seminars
      5:48 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      5:52 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      5:52 pm-6:52 pm
      12/01/2024

      Abstract:  Online marketplaces are the main engines of legal and illegal e-commerce, yet the aggregate properties of buyer-seller networks behind them are poorly understood. We analyse two datasets containing 245M transactions (16B USD)  between 2010 and 2021 involving online marketplaces: 28 dark web marketplaces (DWM), unregulated markets whose main currency is Bitcoin, and 144 product markets of one regulated e-commerce platform. We show how transactions in online marketplaces exhibit strikingly similar patterns of aggregate behavior despite significant differences in language, products, time, regulation, oversight, and technology. We find remarkable regularities in the distributions of (i) transaction amounts, (ii) number of transactions, (iii) inter-event times, (iv) time between first and last transactions. We then show how buyer behavior is affected by the memory of past interactions, and draw on these observations to propose a model of network formation able to reproduce the main stylised facts of the data. Our findings have important implications for understanding market power on online marketplaces as well as inter-marketplace competition.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/17/2018 Math-Physics Seminar
      5:53 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      9/24/2018 Math-Physics Seminar
      5:55 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      5:56 pm
      12/01/2024

      No additional detail for this event.

    • General Relativity Seminar
      5:59 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Additive Combinatorics, Oct. 2-6, 2017
      6:00 pm-6:01 pm
      12/01/2024-10/06/2017

      The workshop on additive combinatorics will take place October 2-6, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      Additive combinatorics is a mathematical area bordering on number theory, discrete mathematics, harmonic analysis and ergodic theory. It has achieved a number of successes in pure mathematics in the last two decades in quite diverse directions, such as:

      • The first sensible bounds for Szemerédi’s theorem on progressions (Gowers);
      • Linear patterns in the primes (Green, Tao, Ziegler);
      • Construction of expanding sets in groups and expander graphs (Bourgain, Gamburd);
      • The Kakeya Problem in Euclidean harmonic analysis (Bourgain, Katz, Tao).

      Ideas and techniques from additive combinatorics have also had an impact in theoretical computer science, for example

      • Constructions of pseudorandom objects (eg. extractors and expanders);
      • Constructions of extremal objects (eg. BCH codes);
      • Property testing (eg. testing linearity);
      • Algebraic algorithms (eg. matrix multiplication).

      The main focus of this workshop will be to bring together researchers involved in additive combinatorics, with a particular inclination towards the links with theoretical computer science. Thus it is expected that a major focus will be additive combinatorics on the boolean cube (Z/2Z)^n , which is the object where the exchange of ideas between pure additive combinatorics and theoretical computer science is most fruitful. Another major focus will be the study of pseudorandom phenomena in additive combinatorics, which has been an important contributor to modern methods of generating provably good randomness through deterministic methods. Other likely topics of discussion include the status of major open problems (the polynomial Freiman-Ruzsa conjecture, inverse theorems for the Gowers norms with bounds, explicit correlation bounds against low degree polynomials) as well as the impact of new methods such as the introduction of algebraic techniques by Croot–Pach–Lev and Ellenberg–Gijswijt.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Ben GreenSwastik KoppartyRyan O’DonnellTamar Ziegler.

      Monday, October 2

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amJacob FoxTower-type bounds for Roth’s theorem with popular differences

      Abstract: A famous theorem of Roth states that for any $\alpha > 0$ and $n$ sufficiently large in terms of $\alpha$, any subset of $\{1, \dots, n\}$ with density $\alpha$ contains a 3-term arithmetic progression. Green developed an arithmetic regularity lemma and used it to prove that not only is there one arithmetic progression, but in fact there is some integer $d > 0$ for which the density of 3-term arithmetic progressions with common difference $d$ is at least roughly what is expected in a random set with density $\alpha$. That is, for every $\epsilon > 0$, there is some $n(\epsilon)$ such that for all $n > n(\epsilon)$ and any subset $A$ of $\{1, \dots, n\}$ with density $\alpha$, there is some integer $d > 0$ for which the number of 3-term arithmetic progressions in $A$ with common difference $d$ is at least $(\alpha^3-\epsilon)n$. We prove that $n(\epsilon)$ grows as an exponential tower of 2’s of height on the order of $\log(1/\epsilon)$. We show that the same is true in any abelian group of odd order $n$. These results are the first applications of regularity lemmas for which the tower-type bounds are shown to be necessary.

      The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      10:20-11:00amCoffee Break 
      11:00-11:50amYufei ZhaoTower-type bounds for Roth’s theorem with popular differences

      Abstract:  Continuation of first talk by Jacob Fox. The first part of the talk by Jacob Fox includes an overview and discusses the upper bound. The second part of the talk by Yufei Zhao focuses on the lower bound construction and proof. These results are all joint work with Huy Tuan Pham.

      12:00-1:30pmLunch 
      1:30-2:20pmJop BriëtLocally decodable codes and arithmetic progressions in random settings

      Abstract: This talk is about a common feature of special types of error correcting codes, so-called locally decodable codes (LDCs), and two problems on arithmetic progressions in random settings, random differences in Szemerédi’s theorem and upper tails for arithmetic progressions in a random set in particular. It turns out that all three can be studied in terms of the Gaussian width of a set of vectors given by a collection of certain polynomials. Using a matrix version of the Khintchine inequality and a lemma that turns such polynomials into matrices, we give an alternative proof for the best-known lower bounds on LDCs and improved versions of prior results due to Frantzikinakis et al. and Bhattacharya et al. on arithmetic progressions in the aforementioned random settings.

      Joint work with Sivakanth Gopi

      2:20-3:00pmCoffee Break 
      3:00-3:50pmFernando Shao

      Large deviations for arithmetic progressions

      Abstract: We determine the asymptotics of the log-probability that the number of k-term arithmetic progressions in a random subset of integers exceeds its expectation by a constant factor. This is the arithmetic analog of subgraph counts in a random graph. I will highlight some open problems in additive combinatorics that we encountered in our work, namely concerning the “complexity” of the dual functions of AP-counts.

      4:00-6:00pmWelcome Reception

      Tuesday, October 3

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amEmanuele ViolaInterleaved group products

      Authors: Timothy Gowers and Emanuele Viola

      Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m, where s depends on m only. Similar statements can be made for other groups as well.

      These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).

      10:20-11:00amCoffee Break
      11:00-11:50amVsevolod LevOn Isoperimetric Stability

      Abstract: We show that a non-empty subset of an abelian group with a small edge boundary must be large; in particular, if $A$ and $S$ are finite, non-empty subsets of an abelian group such that $S$ is independent, and the edge boundary of $A$ with respect to $S$ does not exceed $(1-c)|S||A|$ with a real $c\in(0,1]$, then $|A|\ge4^{(1-1/d)c|S|}$, where $d$ is the smallest order of an element of $S$. Here the constant $4$ is best possible.

      As a corollary, we derive an upper bound for the size of the largest independent subset of the set of popular differences of a finite subset of an abelian group. For groups of exponent $2$ and $3$, our bound translates into a sharp estimate for the additive  dimension of the popular difference set.

      We also prove, as an auxiliary result, the following estimate of possible independent interest: if $A\subseteq{\mathbb Z}^n$ is a finite, non-empty downset, then, denoting by $w(z)$ the number of non-zero components of the vector $z\in\mathbb{Z}^n$, we have   $$ \frac1{|A|} \sum_{a\in A} w(a) \le \frac12\, \log_2 |A|. $$

      12:00-1:30pmLunch
      1:30-2:20pmElena GrigorescuNP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem

      Abstract: I will discuss the complexity of decoding Reed-Solomon codes, and some results establishing NP-hardness for asymptotically smaller decoding radii than the maximum likelihood decoding radius. These results follow from the study of a generalization of the classical Subset Sum problem to higher moments, which may be of independent interest. I will further discuss a connection with the Prouhet-Tarry-Escott problem studied in Number Theory, which turns out to capture a main barrier in extending our techniques to smaller radii.

      Joint work with Venkata Gandikota and Badih Ghazi.

      2:20-3:00pmCoffee Break
      3:00-3:50pmSean PrendivillePartition regularity of certain non-linear Diophantine equations.

      Abstract:  We survey some results in additive Ramsey theory which remain valid when variables are restricted to sparse sets of arithmetic interest, in particular the partition regularity of a class of non-linear Diophantine equations in many variables.

      Wednesday, October 4

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast 
      9:30-10:20amOlof SisaskBounds on capsets via properties of spectra

      Abstract: A capset in F_3^n is a subset A containing no three distinct elements x, y, z satisfying x+z=2y. Determining how large capsets can be has been a longstanding problem in additive combinatorics, particularly motivated by the corresponding question for subsets of {1,2,…,N}. While the problem in the former setting has seen spectacular progress recently through the polynomial method of Croot–Lev–Pach and Ellenberg–Gijswijt, such progress has not been forthcoming in the setting of the integers. Motivated by an attempt to make progress in this setting, we shall revisit the approach to bounding the sizes of capsets using Fourier analysis, and in particular the properties of large spectra. This will be a two part talk, in which many of the ideas will be outlined in the first talk, modulo the proof of a structural result for sets with large additive energy. This structural result will be discussed in the second talk, by Thomas Bloom, together with ideas on how one might hope to achieve Behrend-style bounds using this method.

      Joint work with Thomas Bloom.

      10:20-11:00amCoffee Break 
      11:00-11:50amThomas BloomBounds on capsets via properties of spectra

      This is a continuation of the previous talk by Olof Sisask.

      12:00-1:30pmLunch 
      1:30-2:20pmHamed HatamiPolynomial method and graph bootstrap percolation

      Abstract: We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results. This is based on a joint work with Lianna Hambardzumyan and Yingjie Qian.

      2:20-3:00pmCoffee Break
      3:00-3:50pmArnab BhattacharyyaAlgorithmic Polynomial Decomposition

      Abstract: Fix a prime p. Given a positive integer k, a vector of positive integers D = (D_1, …, D_k) and a function G: F_p^k → F_p, we say a function P: F_p^n → F_p admits a (k, D, G)-decomposition if there exist polynomials P_1, …, P_k: F_p^n -> F_p with each deg(P_i) <= D_i such that for all x in F_p^n, P(x) = G(P_1(x), …, P_k(x)). For instance, an n-variate polynomial of total degree d factors nontrivially exactly when it has a (2, (d-1, d-1), prod)-decomposition where prod(a,b) = ab.

      When show that for any fixed k, D, G, and fixed bound d, we can decide whether a given polynomial P(x_1, …, x_n) of degree d admits a (k,D,G)-decomposition and if so, find a witnessing decomposition, in poly(n) time. Our approach is based on higher-order Fourier analysis. We will also discuss improved analyses and algorithms for special classes of decompositions.

      Joint work with Pooya Hatami, Chetan Gupta and Madhur Tulsiani.

      Thursday, October 5

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amMadhur TulsianiHigher-order Fourier analysis and approximate decoding of Reed-Muller codes

       Abstract: Decomposition theorems proved by Gowers and Wolf provide an appropriate notion of “Fourier transform” for higher-order Fourier analysis. I will discuss some questions and techniques that arise from trying to develop polynomial time algorithms for computing these decompositions.

      I will discuss constructive proofs of these decompositions based on boosting, which reduce the problem of computing these decompositions to a certain kind of approximate decoding problem for codes. I will also discuss some earlier and recent works on this decoding problem.

      Based on joint works with Arnab Bhattacharyya, Eli Ben-Sasson, Pooya Hatami, Noga Ron-Zewi and Julia Wolf.

      10:20-11:00amCoffee Break
      11:00-11:50amJulia WolfStable arithmetic regularity

      The arithmetic regularity lemma in the finite-field model, proved by Green in 2005, states that given a subset A of a finite-dimensional vector space over a prime field, there exists a subspace H of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.

      Our main result is that, under a natural model-theoretic assumption of stability, the tower-type bound and non-uniform cosets in the arithmetic regularity lemma are not necessary.  Specifically, we prove an arithmetic regularity lemma for k-stable subsets in which the bound on the codimension of the subspace is a polynomial (depending on k) in the degree of uniformity, and in which there are no non-uniform cosets.

      This is joint work with Caroline Terry.

      12:00-1:30pmLunch 
      1:30-2:20pmWill Sawin

      Constructions of Additive Matchings

      Abstract: I will explain my work, with Robert Kleinberg and David Speyer, constructing large tri-colored sum-free sets in vector spaces over finite fields, and how it shows that some additive combinatorics problems over finite fields are harder than corresponding problems over the integers. 

      2:20-3:00pmCoffee Break
      3:00-3:50pmMei-Chu ChangArithmetic progressions in multiplicative groups of finite fields

      Abstract:   Let G be a multiplicative subgroup of the prime field F_p of size |G|> p^{1-\kappa} and r an arbitrarily fixed positive integer. Assuming \kappa=\kappa(r)>0 and p large enough, it is shown that any proportional subset A of G contains non-trivial arithmetic progressions of length r.

      Friday, October 6

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:20amAsaf FerberOn a resilience version of the Littlewood-Offord problem

      Abstract:  In this talk we consider a resilience version of the classical Littlewood-Offord problem. That is, consider the sum X=a_1x_1+…a_nx_n, where the a_i-s are non-zero reals and x_i-s are i.i.d. random variables with     (x_1=1)= P(x_1=-1)=1/2. Motivated by some problems from random matrices, we consider the question: how many of the x_i-s  can we typically allow an adversary to change without making X=0? We solve this problem up to a constant factor and present a few interesting open problems.

      Joint with: Afonso Bandeira (NYU) and Matthew Kwan (ETH, Zurich).

      10:20-11:00amCoffee Break
      11:00-11:50amKaave HosseiniProtocols for XOR functions and Entropy decrement

      Abstract: Let f:F_2^n –> {0,1} be a function and suppose the matrix M defined by M(x,y) = f(x+y) is partitioned into k monochromatic rectangles.  We show that F_2^n can be partitioned into affine subspaces of co-dimension polylog(k) such that f is constant on each subspace. In other words, up to polynomial factors, deterministic communication complexity and parity decision tree complexity are equivalent.

      This relies on a novel technique of entropy decrement combined with Sanders’ Bogolyubov-Ruzsa lemma.

      Joint work with Hamed Hatami and Shachar Lovett

      12:00-1:30pmLunch
      1:30-2:20pmGuy Kindler

      From the Grassmann graph to Two-to-Two games

      Abstract: In this work we show a relation between the structure of the so called Grassmann graph over Z_2 and the Two-to-Two conjecture in computational complexity. Specifically, we present a structural conjecture concerning the Grassmann graph (together with an observation by Barak et. al., one can view this as a conjecture about the structure of non-expanding sets in that graph) which turns out to imply the Two-to-Two conjecture.

      The latter conjecture its the lesser-known and weaker sibling of the Unique-Games conjecture [Khot02], which states that unique games (a.k.a. one-to-one games) are hard to approximate. Indeed, if the Grassmann-Graph conjecture its true, it would also rule out some attempts to refute the Unique-Games conjecture, as these attempts provide potentially efficient algorithms to solve unique games, that would actually also solve two-to-two games if they work at all.

      These new connections between the structural properties of the Grassmann graph and complexity theoretic conjectures highlight the Grassmann graph as an interesting and worthy object of study. We may indicate some initial results towards analyzing its structure.

      This is joint work with Irit Dinur, Subhash Khot, Dror Minzer, and Muli Safra.

    • CMSA EVENT: Current Developments In Mathematics 2018
      6:00 pm-5:00 pm
      12/01/2024-11/17/2018
      CDM2018

      Current Developments in Mathematics 2018 Conference.

      Friday, Nov. 16, 2018 2:15 pm – 6:00 pm

      Saturday, Nov. 17, 2018  9:00 am – 5:00 pm

      Harvard University Science Center, Hall B

      Visit the conference page here 

    • New Technologies in Mathematics Seminar
      6:00 pm-7:00 pm
      12/01/2024
      CMSA-New-Technologies-Seminar-01.26.2022-1553x2048-1

      Abstract: Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the four colour theorem are among the most notable. Up until now there hasn’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk we will discuss the results of our recent Nature paper, where we worked together with top mathematicians to use machine learning to achieve two new results – proving a new connection between the hyperbolic and geometric structure of knots, and conjecturing a resolution to a 50-year problem in representation theory, the combinatorial invariance conjecture. Through these examples we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/01/2018 Math-Physics Seminar
      6:01 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Fluid turbulence and Singularities of the Euler/ Navier Stokes equations
      6:02 pm
      12/01/2024-03/15/2018
      Fluid turbulence

      The Workshop on Fluid turbulence and Singularities of the Euler/ Navier Stokes equations will take place on March 13-15, 2019. This is the first of two workshop organized by Michael Brenner, Shmuel Rubinstein, and Tom Hou. The second, Machine Learning for Multiscale Model Reduction, will take place on March 27-29, 2019. Both workshops will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

      For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

      List of registrants

      Speakers: 

    • General Relativity Seminar
      6:03 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/08/2018 Math-Physics Seminar
      6:04 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:05 pm-7:05 pm
      12/01/2024
      CMSA-NTM-Seminar-02.02.2022-2-1583x2048

      Abstract: In this talk, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry, it is possible to provide a principled view on such GNN architectural choices as positional encoding and graph rewiring as well as explain and remedy the phenomena of oversquashing and bottlenecks.

    • CMSA EVENT: Blockchain Conference
      6:05 pm
      12/01/2024-01/25/2018
      Blockchain

      On January 24-25, 2019 the Center of Mathematical Sciences will be hosting a conference on distributed-ledger (blockchain) technology. The conference is intended to cover a broad range of topics, from abstract mathematical aspects (cryptography, game theory, graph theory, theoretical computer science) to concrete applications (in accounting, government, economics, finance, management, medicine). The talks will take place in Science Center, Hall D.

      https://youtu.be/FyKCCutxMYo

      List of registrants

      Photos

      Speakers: 

    • Seminars
      6:05 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      6:06 pm
      12/01/2024

      No additional detail for this event.

    • CMSA EVENT: Workshop on Algebraic Methods in Combinatorics
      6:07 pm
      12/01/2024-11/17/2017

      The workshop on Algebraic Methods in Combinatorics will take place November 13-17, 2017 at the Center of Mathematical Sciences and Applications, located at 20 Garden Street, Cambridge, MA.

      The main focus of the workshop is the application of algebraic method to study problems in combinatorics.  In recent years there has been a large number of results in which the use of algebraic technique has resulted in significant improvements to long standing open problems. Such problems include the finite field Kakeya problem, the distinct distance problem of Erdos and, more recently, the cap-set problem. The workshop will include talks on all of the above mentioned problem as well as on recent development in related areas combining combinatorics and algebra.

      Participation: The workshop is open to participation by all interested researchers, subject to capacity. Click here to register.

      A list of lodging options convenient to the Center can also be found on our recommended lodgings page.

      Confirmed participants include:

      Co-organizers of this workshop include Zeev DvirLarry Guth, and Shubhangi Saraf.

      Click here for a list of registrants.

      Monday, Nov. 13

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Jozsef Solymosi

       

      On the unit distance problem

      Abstract: Erdos’ Unit Distances conjecture states that the maximum number of unit distances determined by n points in the plane is almost linear, it is O(n^{1+c}) where c goes to zero as n goes to infinity. In this talk I will survey the relevant results and propose some questions which would imply that the maximum number of unit distances is o(n^{4/3}). 

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

       

      Orit RazIntersection of linear subspaces in R^d and instances of the PIT problem 

      Abstract: In the talk I will tell about a new deterministic, strongly polynomial time algorithm which can be viewed in two ways. The first is as solving a derandomization problem, providing a deterministic algorithm to a new special case of the PIT (Polynomial Identity Testing) problem. The second is as computing the dimension of the span of a collection of flats in high dimensional space. The talk is based on a joint work with Avi Wigderson.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Andrew Hoon Suk

      Ramsey numbers: combinatorial and geometric

      Abstract:  In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.  These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Josh Zahl

      Cutting curves into segments and incidence geometry

      4:00-6:00pmWelcome Reception

      Tuesday, Nov. 14

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Péter Pál Pach

      Polynomials, rank and cap sets

      AbstractIn this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like $\mathbb{Z}_4^n$ and $\mathbb{F}_q^n$ are exponentially small (compared to the size of the group). We will discuss lower and upper bounds for the size of the extremal subsets and mention further applications of the method.

      10:30-11:00amCoffee Break
      11:00-12:00pmJordan Ellenberg

      The Degeneration Method

      Abstract:  In algebraic geometry, a very popular way to study (nice, innocent, nonsingular) varieties is to degenerate them to (weird-looking, badly singular, nonreduced) varieties (which are actually not even varieties but schemes.)  I will talk about some results in combinatorics using this approach (joint with Daniel Erman) and some ideas for future applications of the method.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Larry GuthThe polynomial method in Fourier analysis

      Abstract: This will be a survey talk about how the polynomial method helps to understand problems in Fourier analysis.  We will review some applications of the polynomial method to problems in combinatorial geometry.  Then we’ll discuss some problems in Fourier analysis, explain the analogy with combinatorial problems, and discuss how to adapt the polynomial method to the Fourier analysis setting.

       

      2:30-3:00pm

      Coffee Break
      3:00-4:00pmOpen Problem

      Wednesday, Nov. 15

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

       

      Avi Wigderson

      The “rank method” in arithmetic complexity: Lower bounds and barriers to lower bounds

      Abstract: Why is it so hard to find a hard function? No one has a clue! In despair, we turn to excuses called barriers. A barrier is a collection of lower bound techniques, encompassing as much as possible from those in use, together with a  proof that these techniques cannot prove any lower bound better than the state-of-art (which is often pathetic, and always very far from what we expect for complexity of random functions).

      In the setting of  Boolean computation of Boolean functions (where P vs. NP is the central open problem),  there are several famous barriers which provide satisfactory excuses, and point to directions in which techniques may be strengthened.

      In the setting of Arithmetic computation of polynomials and tensors (where  VP vs. VNP is the central open problem) we have no satisfactory barriers, despite some recent interesting  attempts.

      This talk will describe a new barrier for the Rank Method in arithmetic complexity, which encompass most lower bounds in this field. It also encompass most lower bounds on tensor rank in algebraic geometry (where the the rank method is called Flattening).

      I will describe the rank method, explain how it is used to prove lower bounds, and then explain its limits via the new barrier result. As an example, it shows that while the best lower bound on the tensor rank of any explicit 3-dimensional tensor of side n (which is achieved by a rank method) is 2n, no rank method can prove a lower bound which exceeds 8n

      (despite the fact that a random such tensor has rank quadratic in n).

      No special background knowledge is assumed. The audience is expected to come up with new lower bounds, or else, with new excuses for their absence.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Venkat Guruswami

      Subspace evasion, list decoding, and dimension expanders

       Abstract: A subspace design is a collection of subspaces of F^n (F = finite field) most of which are disjoint from every low-dimensional subspace of F^n. This notion was put forth in the context of algebraic list decoding where it enabled the construction of optimal redundancy list-decodable codes over small alphabets as well as for error-correction in the rank-metric. Explicit subspace designs with near-optimal parameters have been constructed over large fields based on polynomials with structured roots. (Over small fields, a construction via cyclotomic function fields with slightly worse parameters is known.) Both the analysis of the list decoding algorithm as well as the subspace designs crucially rely on the *polynomial method*.

      Subspace designs have since enabled progress on linear-algebraic analogs of Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In particular, they yield an explicit construction of constant-degree dimension expanders over large fields. While constructions of such dimension expanders are known over any field, they are based on a reduction to a highly non-trivial form of vertex expanders called monotone expanders. In contrast, the subspace design approach is simpler and works entirely within the linear-algebraic realm. Further, in recent (ongoing) work, their combination with rank-metric codes yields dimension expanders with expansion proportional to the degree.

      This talk will survey these developments revolving around subspace designs, their motivation, construction, analysis, and connections.

      (Based on several joint works whose co-authors include Chaoping Xing, Swastik Kopparty, Michael Forbes, Nicolas Resch, and Chen Yuan.)

      12:00-1:30pmLunch
      1:30-2:30pm

       

      David Conlon

      Finite reflection groups and graph norms

      Abstract: For any given graph $H$, we may define a natural corresponding functional $\|.\|_H$. We then say that $H$ is norming if $\|.\|_H$ is a semi-norm. A similar notion $\|.\|_{r(H)}$ is defined by $\| f \|_{r(H)} := \| | f | \|_H$ and $H$ is said to be weakly norming if $\|.\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. Using results from the theory of finite reflection groups, we identify a much larger class of weakly norming graphs. This result includes all previous examples of weakly norming graphs and adds many more. We also discuss several applications of our results. In particular, we define and compare a number of generalisations of Gowers’ octahedral norms and we prove some new instances of Sidorenko’s conjecture. Joint work with Joonkyung Lee.

       

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Laszlo Miklós Lovasz

      Removal lemmas for triangles and k-cycles.

      Abstract: Let p be a fixed prime. A k-cycle in F_p^n is an ordered k-tuple of points that sum to zero; we also call a 3-cycle a triangle. Let N=p^n, (the size of F_p^n). Green proved an arithmetic removal lemma which says that for every k, epsilon>0 and prime p, there is a delta>0 such that if we have a collection of k sets in F_p^n, and the number of k-cycles in their cross product is at most a delta fraction of all possible k-cycles in F_p^n, then we can delete epsilon times N elements from the sets and remove all k-cycles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in particular, asked whether a polynomial bound holds. Despite considerable attention, prior to our work, the best known bound for any k, due to Fox, showed that 1/delta can be taken to be an exponential tower of twos of height logarithmic in 1/epsilon (for a fixed k).

      In this talk, we will discuss recent work on Green’s problem. For triangles, we prove an essentially tight bound for Green’s arithmetic triangle removal lemma in F_p^n, using the recent breakthroughs with the polynomial method. For k-cycles, we also prove a polynomial bound, however, the question of the optimal exponent is still open.

      The triangle case is joint work with Jacob Fox, and the k-cycle case with Jacob Fox and Lisa Sauermann.

      Thursday, Nov. 16

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Janos PachLet’s talk about multiple crossings

      Abstract: Let k>1 be a fixed integer. It is conjectured that any graph on n vertices that can be drawn in the plane without k pairwise crossing edges has O(n) edges. Two edges of a hypergraph cross each other if neither of them contains the other, they have a nonempty intersection, and their union is not the whole vertex set. It is conjectured that any hypergraph on n vertices that contains no k pairwise crossing edges has at most O(n) edges. We discuss the relationship between the above conjectures and explain some partial answers, including a recent result of Kupavskii, Tomon, and the speaker, improving a 40 years old bound of Lomonosov.

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Misha Rudnev

      Few products, many sums

      Abstract: This is what I like calling “weak Erd\H os-Szemer\’edi conjecture”, still wide open over the reals and in positive characteristic. The talk will focus on some recent progress, largely based on the ideas of I. D. Shkredov over the past 5-6 years of how to use linear algebra to get the best out of the Szemer\’edi-Trotter theorem for its sum-product applications. One of the new results is strengthening (modulo the log term hidden in the $\lesssim$ symbol) the textbook Elekes inequality

      $$

      |A|^{10} \ll |A-A|^4|AA|^4

      $$

      to

      $$|A|^{10}\lesssim |A-A|^3|AA|^5.$$

      The other is the bound 

      $$E(H) \lesssim |H|^{2+\frac{9}{20}}$$ for additive energy of sufficiently small multiplicative subgroups in $\mathbb F_p$.

      12:00-1:30pmLunch
      1:30-2:30pm

      Video

      Adam Sheffer

      Geometric Energies: Between Discrete Geometry and Additive Combinatorics

      Abstract: We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Discrete Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Discrete Geometry.  

      2:30-3:00pmCoffee Break
      3:00-4:00pm

      Video

      Boris Bukh

      Ranks of matrices with few distinct entries

      Abstract: Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

      Friday, Nov. 17

      TimeSpeakerTitle/Abstract
      9:00-9:30amBreakfast
      9:30-10:30am

      Video

      Benny Sudakov

      Submodular minimization and set-systems with restricted intersections

      AbstractSubmodular function minimization is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which it remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial algorithms are known are parity constraints, i.e., optimizing submodular function only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeter-minants are bounded by two in absolute value.

      We show that efficient submodular function minimization is possible even for a significantly larger class than parity constraints, i.e., over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. To obtain our results, we combine tools from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we establish an interesting connection between the correctness of a natural algorithm, and the non-existence of set systems with specific intersection properties.

      Joint work with M. Nagele and R. Zenklusen

      10:30-11:00amCoffee Break
      11:00-12:00pm

      Video

      Robert Kleinberg 

      Explicit sum-of-squares lower bounds via the polynomial method

      AbstractThe sum-of-squares (a.k.a. Positivstellensatz) proof system is a powerful method for refuting systems of multivariate polynomial inequalities, i.e. proving that they have no solutions. These refutations themselves involve sum-of-squares (sos) polynomials, and while any unsatisfiable system of inequalities has a sum-of-squares refutation, the sos polynomials involved might have arbitrarily high degree. However, if a system admits a refutation where all polynomials involved have degree at most d, then the refutation can be found by an algorithm with running time polynomial in N^d, where N is the combined number of variables and inequalities in the system.

      Low-degree sum-of-squares refutations appear throughout mathematics. For example, the above proof search algorithm captures as a special case many a priori unrelated algorithms from theoretical computer science; one example is Goemans and Williamson’s algorithm to approximate the maximum cut in a graph. Specialized to extremal graph theory, they become equivalent to flag algebras. They have also seen practical use in robotics and optimal control.

      Therefore, it is of interest to identify “hard” systems of low-degree polynomial inequalities that have no solutions but also have no low-degree sum-of-squares refutations. Until recently, the only known examples were either not explicit (i.e., known to exist by non-constructive means such as the probabilistic method) or not robust (i.e., a system is constructed which is not refutable by degree d sos polynomials, but becomes refutable when perturbed by an amount tending to zero with d). We present a new family of instances derived from the cap-set problem, and we show a super-constant lower bound on the degree of its sum-of-squares refutations. Our instances are both explicit and robust.

      This is joint work with Sam Hopkins.

      12:00-1:30pmLunch

       

    • New Technologies in Mathematics Seminar
      6:07 pm-7:07 pm
      12/01/2024
      CMSA-NTM-Seminar-02.09.2022-1553x2048

      Abstract: Over the past several years, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning, leading to advances in natural language processing, computer vision, code synthesis, protein structure prediction, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet, there is at present limited principled understanding of the reasons for its success. In this talk, I’ll explain how attention mechanisms and Transformers work, and then I’ll share the results of a preliminary investigation into why they work so well. In particular, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions, with statistical generalization guarantees akin to sparse regression.

    • New Technologies in Mathematics Seminar
      6:09 pm-7:09 pm
      12/01/2024
      CMSA-NTM-Seminar-02.16.2022-1553x2048

      Abstract: Hyperbolic manifolds are a class of Riemannian manifolds that are important in mathematics and physics, playing a prominent role in topology, number theory, and string theory. Associated with a given hyperbolic metric is a sequence of numbers corresponding to the discrete eigenvalues of the Laplace-Beltrami operator. While these eigenvalues usually cannot be calculated exactly, they can be found numerically and must also satisfy various bounds. In this talk, I will discuss a new approach for finding numerical bounds on the eigenvalues of closed hyperbolic manifolds using general consistency conditions and semidefinite programming, inspired by the approach of the conformal bootstrap from physics. Although these bootstrap bounds follow from seemingly trivial consistency conditions, they are surprisingly strong and are sometimes almost saturated by actual manifolds; for example, one such bound implies that the first nonzero eigenvalue of a closed hyperbolic surface must be less than 3.83890, and this is very close to being saturated by a particular genus-2 surface called the Bolza surface. I will show how to derive this and other bounds and will discuss some possible future directions for this approach.

    • Special Seminar
      6:10 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      6:11 pm-6:12 pm
      12/01/2024-10/25/2016

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/10/2018 RM & PT Seminar
      6:11 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:11 pm-7:11 pm
      12/01/2024
      03.2.2022-1553x2048-1

      Abstract:  Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes, and prospects for RL and other techniques.

    • General Relativity Seminar
      6:12 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:13 pm-7:13 pm
      12/01/2024
      CMSA-NTM-Seminar-03.09.2022

      Abstract: We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time.
      We curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics, Chemical Engineering, Chemistry, Computer Science, Economics, Electrical Engineering, Materials Science, Mathematics, Mechanical Engineering, Nuclear Science, Physics, and Statistics.
      We generate new questions and use them in a Columbia University course, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations, again for the first time.
      Our approach consists of five steps:
      (i) Given course questions, turn them into programming tasks;
      (ii) Automatically generate programs from the programming tasks using a Transformer model, OpenAI Codex, pre-trained on text and fine-tuned on code;
      (iii) Execute the programs to obtain and evaluate the answers;
      (iv) Automatically explain the correct solutions using Codex;
      (v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.
      This work is a significant step forward in applying machine learning for education, automating a considerable part of the work involved in teaching.
      Our approach allows personalization of questions based on difficulty level and student backgrounds, and scales up to a broad range of courses across the schools of engineering and science.

      This is joint work with students and colleagues at MIT, Harvard University, Columbia University, Worcester Polytechnic Institute, and the University of Waterloo.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-03-16 Mathematical Physics Seminar
      6:13 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:14 pm-7:14 pm
      12/01/2024
      CMSA-NTM-Seminar-03.23.2022-1553x2048-1

      Abstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems,  without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark,  automatically solving multiple challenging problems drawn from high school olympiads.

    • Seminars
      Seminars Colloquia & Seminar
      10/15/2018 Topology Seminar
      6:14 pm
      12/01/2024

      No additional detail for this event.

    • New Technologies in Mathematics Seminar
      6:15 pm-7:15 pm
      12/01/2024
      CMSA-NTM-Seminar-03.30.2022-1583x2048-1

      Abstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this talk, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.

      Video

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/15/2018 Math Physics Seminar
      6:15 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-12-2016 Random Matrix & Probability Theory Seminar
      6:16 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      6:17 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-24-2016 Random Matrix & Probability Theory Seminar
      6:18 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      6:19 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10/30/2018 RM & PT Seminar
      6:19 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      10/26/2018 Social Science Applications Forum
      6:20 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:22 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10/22/2018 Mathematical Physics Seminar
      6:24 pm
      12/01/2024
    • Member Seminar
      6:24 pm
      12/01/2024

      No additional detail for this event.

    • Member Seminar
      6:26 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:27 pm
      12/01/2024

      No additional detail for this event.

    • Member Seminar
      6:29 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:30 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:31 pm-7:31 pm
      12/01/2024

      Title: Naturalness and muon anomalous magnetic moment

      Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:32 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      6:34 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:34 pm-7:34 pm
      12/01/2024

      Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

      Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      6:36 pm
      12/01/2024

      No additional detail for this event.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-19-2016 Random Matrix & Probability Theory Seminar
      6:37 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:37 pm-7:37 pm
      12/01/2024

      Title: Cornering the universal shape of fluctuations and entanglement

      Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.

      Ref: arXiv:2102.06223

    • Quantum Matter
      6:38 pm-7:38 pm
      12/01/2024

      Title: Quantum gravity from quantum matter

      Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      9/23/2021 Interdisciplinary Science Seminar
      6:40 pm-8:40 pm
      12/01/2024

      Title: The number of n-queens configurations

      Abstract: The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.

      Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.

    • Member Seminar
      6:40 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-17-16 Mathematical Physics Seminar
      6:41 pm
      12/01/2024

      No additional detail for this event.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      10/7/2021 Interdisciplinary Science Seminar
      6:41 pm
      12/01/2024

      Title: SiRNA Targeting TCRb: A Proposed Therapy for the Treatment of Autoimmunity

      Abstract: As of 2018, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent, treatment options remain relatively poor, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness over time. Given this, new forms of therapy are needed. To this end, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted, novel means of therapy for the treatment of autoimmune disorders.

      This talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      10/14/2021 Interdisciplinary Science Seminar
      6:42 pm-8:42 pm
      12/01/2024

      Title: D3C: Reducing the Price of Anarchy in Multi-Agent Learning

      Abstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.

    • Quantum Matter
      6:44 pm-7:44 pm
      12/01/2024

      Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking

      Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.
      Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      10/21/2021 Interdisciplinary Science Seminar
      6:44 pm-8:44 pm
      12/01/2024

      Title: Mathematical resolution of the Liouville conformal field theory.

      Abstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David, Kupiainen, Rhodes, Vargas.

      Many works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable », the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras, representations of Virasoro algebras, the theory of conformal blocks). However, for Liouville Theory this was not done at the mathematical level by algebraic methods.

      I’ll explain how to combine probabilistic, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure, which is viewed as the space of fields, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space.

      This is joint work with A. Kupiainen, R. Rhodes and V. Vargas.

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      ARCH: Know What Your Machine Doesn’t Know
      6:45 pm-8:45 pm
      12/01/2024

      Speaker: Jie Yang, Delft University of Technology

      Title: ARCH: Know What Your Machine Doesn’t Know

      Abstract: Despite their impressive performance, machine learning systems remain prohibitively unreliable in safety-, trust-, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk, I will present our ongoing work on ARCH, a knowledge-driven, human-centered, and reasoning-based tool, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk, I will present several applications in which ARCH is currently being developed and tested, including health, finance, and smart buildings.

    • Quantum Matter
      6:46 pm-7:46 pm
      12/01/2024

      Title: Three-particle mechanism for pairing and superconductivity

      Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.

      [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)
      [2] V. Crepel and L. Fu, arXiv:2103.12060
      [3] K. Slagle and L. Fu,  Phys. Rev. B 102, 235423 (2020)

    • Interdisciplinary Science Seminar
      Interdisciplinary Science Seminar
      11/4/21 CMSA Interdisciplinary Science Seminar
      6:46 pm-8:46 pm
      12/01/2024
      CMSA-Interdisciplinary-Science-Seminar-11.04.21-1583x2048-1

      Title: Exploring Invertibility in Image Processing and Restoration

      Abstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., image-to-video conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      10-26-2016 Random Matrix & Probability Theory Seminar
      6:46 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:47 pm-7:47 pm
      12/01/2024

      Title: The Hilbert Space of large N Chern-Simons matter theories

      Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

    • Member Seminar
      6:52 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-24-16 Mathematical Physics Seminar
      6:53 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      6:54 pm-7:54 pm
      12/01/2024

      Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

      Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.

    • Random Matrix & Probability Theory Seminar
      Random Matrix & Probability Theory Seminar
      11-30-2016 Random Matrix & Probability Theory Seminar
      6:54 pm
      12/01/2024

      No additional detail for this event.

    • Special Seminar
      6:59 pm
      12/01/2024

      No additional detail for this event.

    • Yip Lecture Series
      Yip Lecture Series Event
      Third Annual Yip Lecture
      7:00 pm-8:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138

      Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

      Time: 7:00-8:00 pm ET

      Location: Harvard Science Center Hall A

      Registration is required.

      In-person Registration

      Zoom Webinar Registration

      Title: Black Holes: The Most Mysterious Objects in the Universe

      Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.

      Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.

      Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)

      Moderator: Daniel Kapec (Harvard CMSA)

      The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

       

      https://youtu.be/RpQhQ855WUY


      The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

    • Seminars
      Seminars Colloquia & Seminar
      11-01-2016 Social Sciences Applications Forum
      7:00 pm
      12/01/2024

      No additional detail for this event.

    • Yip Lecture Series
      7:00 pm-8:00 pm
      12/01/2024
      1 Oxford Street, Cambridge MA 02138
      Yip2022_poster_web

      Harvard CMSA hosted the second annual Yip Lecture on April 4, 2022.

      The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.
      This year’s speaker was Avi Loeb (Harvard).

       

      Extraterrestrial Life

      Abstract: Are we alone? It would be arrogant to think that we are, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System, such as `Oumuamua.

      Abraham (Avi) Loeb is the Frank B. Baird, Jr., Professor of Science at Harvard University and a bestselling author (in lists of the New York Times, Wall Street Journal, Publishers Weekly, Die Zeit, Der Spiegel, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986), led the first international project supported by the Strategic Defense Initiative (1983–1988), and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books, including most recently, Extraterrestrial (Houghton Mifflin Harcourt, 2021), and nearly a thousand papers (with an h-index of 118) on a wide range of topics, including black holes, the first stars, the search for extraterrestrial life, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences, the American Physical Society, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade.

      Click here for Loeb’s commentaries on innovation and diversity.

      Website: https://www.cfa.harvard.edu/~loeb/

      See the Harvard Gazette article featuring Avi Loeb: “Oh, if I could talk to the aliens” published March 8, 2022.

      Prof. Loeb’s books:
      Extraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)
      Life in the Cosmos: From Biosignatures to Technosignatures (2021)

      Avil Loeb is the head of the Galileo Project at Harvard.


      The previous Yip Lecture featured Peter Galison (Harvard), who spoke on the EHT’s hunt for an objective image of a black hole.

    • Seminars
      7:03 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      10-31-16 Mathematical Physics Seminar
      7:05 pm
      12/01/2024

      No additional detail for this event.

    • Quantum Matter
      7:30 pm-9:00 pm
      12/01/2024
    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
      CMSA-QMMP-02.09.2022-1544x2048-1

      Speaker: Yuji Tachikawa (Kavli IPMU, U Tokyo)

      Title: On the absence of global anomalies of heterotic string theories

      Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.

      In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.

      The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.

    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
      CMSA-QMMP-02.02.2022-1544x2048

      Title: Kramers-Wannier-like duality defects in higher dimensions

      Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.

    • Quantum Matter
      8:00 pm-9:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/15/2020 Quantum Matter Seminar
      8:30 pm-10:00 pm
      12/01/2024
    • Quantum Matter
      8:30 pm-10:00 pm
      12/01/2024
      CMSA-QMMP-Seminar-04.13.22-1583x2048-1

      Youtube Video

      Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.

      We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.

      We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.

      Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.

    • Quantum Matter
      8:30 pm-10:30 pm
      12/01/2024
      CMSA-QMMP-Seminar-05.18.22-1583x2048-1

      Speaker: Linhao Li (ISSP, U Tokyo)

      Title: Boundary conditions and LSM anomalies of conformal field theories in 1+1 dimensions

      Abstract: In this talk, we will study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state which is invariant under a symmetry, then the CFT can be gapped with a unique ground state by adding the corresponding gapping potential. This means that the symmetry of the CFT is anomaly free. Using this approach, we will systematically deduce the anomaly-free conditions for various types of CFTs with several different symmetries. When the symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis type ingappability of the system. Our results are consistent with, where available, known results in the literature. Moreover, we extend the discussion to other symmetries including spin groups and generalized time-reversal symmetries. As an application, we propose 1d LSM theorem involving magnetic space group symmetries on the lattice. The extended LSM theorems apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and chiral three-spin interactions.

    • Quantum Matter
      8:30 pm-10:00 pm
      12/01/2024

      Speaker: Nima Arkani-Hamed (IAS Princeton)

      Title: UV/IR and Effective Field Theory

    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Tropical disk counts
      8:30 pm-9:30 pm
      12/01/2024

      Abstract: (joint with S. Venugopalan)  I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan)  which is an open analog of the twenty-seven lines.  As an application, I will explain why the Floer cohomology of such tropical fibers is well-defined; this is a generalization fo a result of Fukaya-Oh-Ohta-Ono for toric varieties.

    • Quantum Matter
      8:30 pm-9:30 pm
      12/01/2024
      CMSA-QMMP-03.10.2022-1544x2048-1-1

      Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field.

      This work is based on arxiv: 2201.11681

    • Mathematical Physics Seminar
      Mathematical Physics Seminar
      12/10/2018 Mathematical Physics Seminar
      8:42 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/10/2018 Topology Seminar
      8:43 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      12/12/2018 Hodge Seminar
      8:43 pm
      12/01/2024

      No additional detail for this event.

    • Mathematical Physics Seminar
      8:45 pm
      12/01/2024

      No additional detail for this event.

    • Seminars
      Seminars Colloquia & Seminar
      1/16/2019 Hodge Seminar
      8:46 pm
      12/01/2024

      No additional detail for this event.

    • Fluid Dynamics Seminar
      Fluid Dynamics Seminar
      4/3/2019 Fluid Dynamics Seminar
      8:54 pm
      12/01/2024

      No additional detail for this event.

    • Program
      9:27 pm
      12/01/2024-12/31/2021

      The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications. This program is funded by the Simons Foundation.

      Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model).

      We envision that our goal of proving HMS in full generality can be accomplished by combining three main viewpoints:

      1. categorical algebraic geometry and non-commutative (nc) spaces: in this language, homological mirror symmetry is the statement that the same nc-spaces can arise either from algebraic geometry or from symplectic geometry.
      2. the Strominger-Yau-Zaslow (SYZ) approach, which provides a global geometric prescription for the construction of mirror pairs.
      3. Lagrangian Floer theory and family Floer cohomology, which provide a concrete path from symplectic geometry near a given Lagrangian submanifold to an open domain in a mirror analytic space.

      The Center of Mathematical Sciences and Applications is hosting the following short-term visitors for an HMS focused semester:

      • Jacob Bourjaily (Neils Bohr Institute)  4/1/2018 – 4/14/2018
      • Colin Diemer (IHES)  2/25/2018 – 3/10/2018
      • Charles Doran (University of Alberta) 5/13/2018 – 5/25/2018
      • Baohua Fu (Chinese Academy of Sciences)  4/15/2018 – 4/28/2018
      • Andrew Harder (University of Miami)  4/15/2018 – 4/28/2018
      • Shinobu Hosono (Gakushuin University) 2/25/2018 – 3/10/2018
      • Adam Jacob (UC Davis) 3/5/2018 – 3/16/2018
      • Tsung-Ju Lee (National Taiwan University) 4/18/2018 – 5/13/2018
      • Ivan Loseu (Northeastern University) 1/21/2018 – 2/3/2018
      • Cheuk-Yu Mak (Cambridge University) 4/1/2018 – 4/15/2018
      • Daniel Pomerleano (Imperial College) 3/19/2018 – 3/23/2018
      • Mauricio Romo (Tsinghua University) 4/1/2018 – 4/18/ 2018
      • Emanuel Scheidegger (Albert Ludwigs University of Freiburg) 2/22/2018 – 3/22/2018
      • Dmytro Shklyarov (Technische Universität Chemnitz) 3/4/2018 – 3/17/2018
      • Alan Thompson (University of Cambridge) 4/15/2018 – 4/21/2018
      • Weiwei Wu (University of Georgia) 4/27/2018 – 5/6/2018
      • Matt Young (Chinese University of Hong Kong) 1/15/2018 – 2/9/2018
      • Jeng-Daw Yu (National Taiwan University) 4/2/2018 – 4/6/2018
      • Minxian Zhu (Yau Mathematical Sciences Center, Tsinghua University) 1/ 22/2018 – 2/25/2018

      As part of their CMSA visitation, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester.  Click here for information.

      The Collaboration will include two workshops hosted by The Center. The workshops will take place January 10-13, 2018  and April 5-7, 2018 at CMSA. Click here for more information.

    • Seminars
      Seminars Colloquia & Seminar
      7/13/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      7/27/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/8/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/16/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Seminars
      Seminars Colloquia & Seminar
      6/22/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Joint Harvard-CUHK-YMSC Differential Geometry
      Joint Harvard-CUHK-YMSC Differential Geometry
      Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
      9:30 pm-10:30 pm
      12/01/2024

      Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

    • Seminars
      Seminars Colloquia & Seminar
      7/20/2020 Geometry and Physics Seminar
      9:30 pm-10:30 pm
      12/01/2024
    • Program
      9:32 pm
      12/01/2024-12/31/2021

      The methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example, the first topological states of matter discovered were the integer quantum Hall states. The two dimensional integer quantum Hall effect was characterized by an integral number which can be understood as a Chern number of the Berry phase. Chern numbers are topological invariants that play an important role in different areas of mathematics. More recently, new topological states of matter known as topological insulators and topological superconductors have been realized theoretically and experimentally. The characterization of new phases of matter using topological invariants has allowed for a better understanding and even predictions of new phases of matter. The use of topology could lead to the discovery of new electronic, photonic, and ultracold atomic states of matter previously unknown. The concrete problems in the physical phenomena could inspire new developments in the study of topological invariants in mathematics.

      Here is a list of the scholars participating in this program.

    • Program
      9:35 pm
      12/01/2024-12/31/2021

      A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as
      cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs, using tools such as random walk theory and harmonic analysis.

       

      Here is a list of the scholars participating in this program.

    • Program
      9:36 pm
      12/01/2024-12/31/2021

      In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory, general relativity, and quantum many-body theory.

      String theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as dramatic progress in old branches.

      Several examples from the recent past exemplifying this synergy include the prediction from string theory of mirror symmetry, a highly unexpected mathematical equivalence between distinct pairs of Calabi-Yau manifolds. This fueled exciting developments in algebraic, enumerative and symplectic geometry. At the same time the realization of string theory as a phenomenologically viable physical theory depends crucially on detailed mathematical properties of these manifolds. In Einstein’s theory of general relativity the proofs of the positive energy theorem and the stability of flat spacetime were accompanied by fundamental new results in functional analysis, differential geometry and minimal surface theory. In the coming decades we expect many more important discoveries to arise from the interface of mathematics and physics. The Cheng Fund will foster these efforts.

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

      NameTentative Visiting Dates
      Po-Ning Chen2/1/15-4/30/15
      Hong-Jian He3/5/15-5/5/15
      Monica Guica12/1/14-3/15/15
      Amer Iqbal1/8/15-4/8/15
      Suvrat Raju2/25/15-5/25/15
      Mithat Ünsal9/1/15-12/31/15
    • Program
      9:37 pm
      12/01/2024-12/31/2021

      Most physical phenomena, from the gravitating universe to fluid dynamics, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations.

      The subject underwent rapid developments in the last century and foundational results were established. Compared to linear equations, the difficulty of solving nonlinear equations is of a different order of magnitude and the methods employed in solving them are also much more diversified. To this date, it is an active field with recent exciting discoveries and renewed interests, and several long standing problems seem to be within reach. The special year aims to spur activity in this subject, to provide a natural setting for the most cutting edge results to be communicated, and to facilitate interaction among researchers of different backgrounds.

      During the year, there will be two weekly seminar programs.  Each program participants will be asked to give a talk on geometric analysis, or the evolution of equations, hyperbolic equations, and fluid dynamics.   

      Seminar on Geometric Analysis

      Seminar on Evolution Equations

      Seminar on General Relativity

      Concluding Conference on Nonlinear Equations Program

      Mini-School on Nonlinear Equations, Dec. 2016

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program

      NameHome InstitutionTentative Visiting Dates
      Stefano BianchiniSISSA04/01/2016 – 05/31/2016
      Lydia BieriUniversity of Michigan02/01/2016 – 04/30/2016
      Albert ChauUniversity of British Columbia02/26/2016 – 05/26/2016
      Binglong ChenSun Yat-sen University09/01/2015 – 11/30/2015
      Qingtao ChenETHZ (Swiss Federal Institute of Technology in Zurich)03/17/2016 – 04/04/2016
      Piotr ChruscielUniversity of Vienna03/01/2016 – 05/30/2016
      Fernando Coda MarquesPrinceton University04/25/2016 – 04/29/2016 05/23/2016 – 05/27/2016
      Mihalis DafermosPrinceton University04/01/2016 – 04/30/2016
      Camillo De LellisUniversity of Zurich02/01/2016 – 4/30/2016
      Michael EichmairUniversity of Vienna03/21/2016 – 04/01/2016
      Felix FinsterUniversitat Regensburg09/20/2015 – 10/20/2015 03/20/2016 – 04/20/2016
      Xianfeng David GuSUNY at Stony Brook04/01/2016 – 04/30/2016
      Zheng-Cheng GuPerimeter Institute for Theoretical Physics08/15/2015 – 09/15/2015
      Pengfei GuanMcGill University10/10/2015 – 10/17/2015
      Xiaoli HanTsinghua University01/20/2016 – 04/19/2016
      Thomas HouCalifornia Institute of Technology11/01/2016 – 11/30/2016
      Feimin HuangChinese Academy of Sciences02/15/2016 – 04/15/2016
      Xiangdi HuangChinese Academy of Sciences09/10/2015 – 12/10/2015
      Tom IlmanenETH Zurich10/19/2015 – 12/18/2015
      Niky KamranMcGill Univeristy04/04/2016 – 04/08/2016
      Nicolai KrylovUniversity of Minnesota11/01/2015 – 11/30/2015
      Junbin LiSun Yat-sen University02/01/2016 – 04/30/2016
      Yong LinRenmin University of China02/01/2016 – 03/31/2016
      Andre NevesImperial College London4/25/2016 – 4/29/2016; 5/23/2016 – 5/27/2016
      Duong H. PhongColumbia University04/08/2016 – 04/10/2016
      Ovidiu SavinColumbia University10/15/2015 – 12/14/2015
      Richard SchoenStanford University03/21/2016 – 03/25/2016
      Mao ShengUniversity of Science and Technology of China01/15/2016 – 01/28/2016
      Valentino TosattiNorthwestern University02/01/2016 – 04/15/2016
      John TothMcGill University04/04/2016 – 04/08/2016
      Chung-Jun TsaiNational Taiwan University05/01/2016 – 05/08/2016
      Tai-Peng TsaiUniversity of British Columbia03/20/2016 – 05/31/2016
      Li-Sheng TsengUC Irvine02/08/2016 – 02/19/2016; 04/27/2016 – 05/11/2016
      Chun Peng WangJilin University02/01/2016 – 04/30/2016
      Xu-Jia WangAustralian National University04/01/2016 – 05/31/2016
      Ben WeinkoveNorthwestern University02/28/2016 – 03/18/2016
      Sijue WuUniversity of Michigan04/01/2016 – 04/30/2016
      Chunjing XieShanghai Jiao Tong University09/08/2015 – 12/07/2015
      Zhou Ping XinThe Chinese University of Hong Kong10/01/2015 – 11/30/2015
      Hongwei XuZhejiang University09/01/2015 – 11/30/2015
      Peng YeUniversity of Illinois at Urbana-Champaign11/15/2015 – 11/22/2015
      Pin YuTshinghua University09/07/2015 – 12/10/2015
      Yi ZhangFudan University01/18/2016 – 05/31/2016
    • Program
      9:39 pm
      12/01/2024-12/18/2014

      arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal, Hermitian, or symplectic matrices with independent entries, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability, including combinatorics, partial differential equations, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models, or 2D matrix ensembles, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models, results in the direction of universality have already been obtained.

      Here is a partial list of the mathematicians who are participating in this program

    • Program
      9:44 pm
      12/01/2024-12/28/2013

      During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines.

      As part of the Program, the CMSA will be hosting two workshops:

      .

      Additionally, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10.

      Here is a partial list of the mathematicians who have indicated that they will attend part or all of this special program
      NameTentative Visiting Dates

      Jason Alicea

      11/12/2018-11/16/2018
      Maissam Barkeshli4/22/2019 – 4/26/2019
      Xie Chen4/15-17/2019 4/19-21/2019 4/24-30/2019

      Lukasz Fidkowski

      1/7/2019-1/11/2019

      Zhengcheng Gu

      8/15/2018-8/30/2018 & 5/9/2019-5/19/2019

      Yin Chen He

      10/14/2018-10/27/2018
      Anton Kapustin8/26/2018-8/30/2018 & 3/28/2019-4/5/2019

      Michael Levin

      3/11/2019-3/15/2019
      Yuan-Ming Lu4/29/2019-6/01/2019

      Adam Nahum

      4/2/2019- 4/19/2019

      Masaki Oshikawa

      4/22/2019-5/22/2019
      Chong Wang 10/22/2018-11/16/2018

      Juven Wang

      4/1/2019-4/16/2019
      Cenke Xu 8/26/2018-10/1/2018

      Yi-Zhuang You

      4/1/2019-4/19/2019

      Mike Zaletel

      5/1/2019-5/10/2019
    • Program
      9:45 pm-9:46 pm
      12/01/2024-12/31/2010

      During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology.

      Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape.

      In the century since its publication, we have seen a revolution in biology following the discovery of the genetic code, which has uncovered the molecular and cellular basis for life, combined with the ability to probe the chemical, structural, and dynamical nature of molecules, cells, tissues and organs across scales. In parallel, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems, and a gradual unveiling of the complexity of physical form. And in mathematics and computation, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry, statistics and inference.  So, how far are we from realizing a descriptive, predictive and controllable theory of biological shape?

      In Fall 2018, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems

      The CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics, Morphogenesis and Mathematics will take place on October 22-26. 

      A workshop on Morphogenesis: Geometry and Physics will take place on December 3-6, 2018.

      A workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.

    • Program
      9:48 pm
      12/01/2024-12/31/2010

      Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall 2019, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10.

      Organizers:

      .

      Workshops:

       

      Here is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor:

    • Program
      9:49 pm
      12/01/2024-12/23/2010

      The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years.

      A brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follow:


      Directors:


      Shing-Tung Yau (Harvard University)

      Born in Canton, China, in 1949, S.-T. Yau grew up in Hong Kong, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year, and was offered a professorship at UC Berkeley in 1977. He was there for a year, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science, and was elected a member of the US National Academy of Sciences. In 1982, he received a Fields Medal for “his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex MongeAmpre equations”. He was named Science Digest, America’s 100 Brightest Scientists under 40, in 1984. In 1991, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994, a US National Medal of Science in 1997, and a China International Scientific and Technological Cooperation Award, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers” in 2003. In 2010, he received a Wolf Prize in Mathematics, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships, which include a Sloan Fellowship in 1975-1976, a Guggenheim Fellowship in 1982, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry, topology, and mathematical physics. As a graduate student, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis, and applying the theory of nonlinear partial differential equations to solve problems in geometry, topology, and physics. His work in this direction include constructions of minimal submanifolds, harmonic maps, and canonical metrics on manifolds. The most notable, and probably the most influential of this, was his solution of the Calabi conjecture on Ricci flat metrics, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry, including Chern number inequalities, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years, through the creation of the theory of Calabi-Yau manifolds, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him, have developed many important tools and concepts in CY geometry and mirror symmetry, which have led to significant progress in deformation theory, and on outstanding problems in enumerative geometry. Lian, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry, Strominger, Yau, and Zaslow proposed a new geometric construction of mirror symmetry, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry, Yau has done influential work on nonlinear partial differential equations, generalized geometry, Kahler geometry, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers, Yau has trained more than 60 PhD students in a broad range of fields, and mentored dozens of postdoctoral fellows over the last 40 years.


      Professor Bong Lian (Brandeis University)

      BongBorn in Malaysia in 1962, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995, and has remained there since. Between 1995 and 2013, he had had visiting research positions at numerous places, including the National University of Taiwan, Harvard University, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013, for his “influential and fundamental contributions in mathematical physics, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director, since 2014, of the Tsinghua Mathcamp, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008, Lian has been the President of the International Science Foundation of Cambridge, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities, to promote basic research and education in mathematical sciences, especially in the Far East.” Over the last 20 years, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years, Lian’s mathematical work lies in the interface between representation theory, Calabi-Yau geometry, and string theory. Beginning in the late 80’s, Lian, jointly with Zuckerman, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin, as semi-infinite cohomology of braided vertex algebras, and led to a more recent discovery of new relationships between Courant algebroids, A-algebras, operads, and deformation theory of BV algebras. In 2010, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold, for infinitely many degrees. In 1996, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year, they announced their hyperplane conjecture, which gives a general formula for period integrals for a large class of CY manifolds, extending the formula of Candelas et al. Soon after, Lian, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003, inspired by mirror symmetry, Lian (jointly with Hosono, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014, Lian (jointly with Bloch, Chen, Huang, Song, Srinivas, Yau, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular, he answered an old question in physics on the completeness of Picard-Fuchs systems, and constructed new differential zeros of hypergeometric functions.


      Denis Auroux (Harvard University)

      AurouxDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties, open Riemann surfaces, etc.), and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France), Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004, and as Associate Professor from 2004 to 2009, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.
      Auroux has published over 30 peer-reviewed articles, including several in top journals, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005, was an invited speaker at the 2010 International Congress of Mathematicians, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations, won teaching awards at MIT and Berkeley, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.




      Senior Personnel:

      Artan Sheshmani (Harvard CMSA)

      unnamedArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry, such as, intersection theory, derived category theory, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants), local surface threefolds, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture, and his joint work has provided the proof to some cases of it, using degenerations, virtual localizations, as well as wallcrossing techniques. Recently, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour, Gukov, Liu, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover, in a recent joint work with Yau and Diaconescu, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3,4,5.

      Artan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology, Tehran, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM), since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT.

      An Huang (Brandeis University)

      unnamedThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry, the theory of special functions and mirror symmetry. With S. Bloch, B. Lian, V. Srinivas, S.-T. Yau, X. Zhu, he has developed the theory of tautological systems, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian, S.-T. Yau, and C.-L. Yu, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018, with B. Stoica and S.-T. Yau, he has initiated the study of p-adic strings in curved spacetime, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models.

      An Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.



      Siu Cheong Lau (Boston University)
      unnamed

      The research interest of Siu Cheong Lau lies in SYZ mirror symmetry, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung, H.H. Tseng and K. Chan, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong, he developed a noncommutative local mirror construction for immersed Lagrangians, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces.

      Siu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014.


      Affiliates:

      • Netanel Rubin-Blaier (Cambridge)
      • Kwokwai Chan (Chinese University of Hong Kong)
      • Mandy Cheung (Harvard University, BP)
      • Chuck Doran (University of Alberta)
      • Honsol Hong (Yonsei University)
      • Shinobu Hosono (Gakushuin University, Japan)
      • Conan Leung (Chinese University of Hong Kong)
      • Yu-shen Lin (Boston University)
      • Hossein Movassati (IMPA Brazil)
      • Arnav Tripathhy (Harvard University, BP)

       

      Postdocs:

      • Dennis Borisov
      • Tsung-Ju Lee
      • Dingxin Zhang
      • Jingyu Zhao
      • Yang Zhou

      Jobs:

      Postdoctoral Fellowship in Algebraic Geometry

      Postdoctoral Fellowship in Mathematical Sciences

       

      To learn about previous programming as part of the Simons Collaboration, click here.

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